
    UNITED STATES of America, Appellee, v. Gerald MILLER, Ronald Tucker, Roy Hale, Waverly Coleman, Harry Hunt, Shannon Jimenez, Raymond Robinson, aka “Ace”, Wilfredo Arroyo, aka “C-Justice”, aka “CJ.”, David Robinson, aka “Bing”, Defendants-Appellants.
    Nos. 343, 483, 344, 349, 383, 345-348, Dockets 95-1077(L), 95-1308, 95-1203, 95-1302, 95-1307, 95-1327, 95-1466, 95-1642 and 96-1031.
    United States Court of Appeals, Second Circuit.
    Argued Dec. 16, 1996.
    Decided June 20, 1997.
    
      Leslie R. Caldwell, Mark P. Ressler, Assistant United States Attorneys for the Eastern District of New York, Brooklyn, New York (Zachary W. Carter, United States Attorney, David C. James, Susan Corkery, Assistant United States Attorneys, Brooklyn, New York, on the brief), for Appellee.
    Joyce C. London, New York City, Jonathan Turley, Washington, DC, for Defendant-Appellant Gerald Miller; filed a supplemental brief pro se.
    Lloyd Epstein, New York City (Judith H. Weil, Epstein & Weil, New York City, on the brief), for Defendant-Appellant Ronald Tucker.
    
      Bennett M. Epstein, New York City, for Defendant-Appellant Roy Hale.
    Daniel Nobel, New York City, for Defendant-Appellant Waverly Coleman.
    Kenneth M. Tuceillo, New York City (Lawrence H. Schoenbach, New York City, on the brief), for Defendant-Appellant Harry Hunt.
    Donald A. Harwood, New York City, for Defendant-Appellant Shannon Jimenez.
    William Stampur, New York City (Jennifer L. Ritter, Hurwitz Stampur & Roth, New York City, on the brief), for Defendant-Appellant Raymond Robinson.
    Erica Horwitz, New York City (David Gordon, Gordon & Horwitz, New York City, on the brief), for Defendant-Appellant Wilfredo Arroyo.
    Joel M. Stein, New York City, for Defendant-Appellant David Robinson.
    Before: FEINBERG, KEARSE, and CARD AMONE, Circuit Judges.
   KEARSE, Circuit Judge:

Defendants Gerald Miller, Ronald Tucker, Roy Hale, Waverly Coleman, Harry Hunt, Shannon Jimenez, Raymond Robinson, Wilfredo Arroyo, and David Robinson, appeal from judgments entered in the United States District Court for the Eastern District of New York after jury trials before Raymond J. Dearie, Judge, convicting them of a host of crimes in connection with their participation in a criminal enterprise engaged in the distribution of narcotics. All nine defendants were convicted of conspiracy to distribute and to possess with intent to distribute cocaine base, in violation of 21 U.S.C. § 846 (1994); all except Jimenez were convicted of conducting the affairs of an enterprise through a pattern of racketeering activity, in violation of the Racketeer Influenced and Corrupt Organizations Act (“RICO”), 18 U.S.C. § 1962(e) (1994); most were convicted of distributing cocaine base, in violation of 21 U.S.C. §§ 841(a) and 841(b)(1)(A) (1994): Miller (four counts), Tucker (one count), Coleman (three counts), Raymond Robinson (two counts), Arroyo (four counts), and David Robinson (three counts); and three, Hale, Hunt, and Arroyo, were convicted on one count of possession with intent to distribute cocaine, in violation of 21 U.S.C. §§ 841(a)(1) and 841(b)(1)(C) (1994). In addition, Miller was convicted on one count of engaging in a continuing criminal enterprise, in violation of 21 U.S.C. §§ 848(a) and 848(b)(1)(A) (1994), and one count of conducting a financial transaction with proceeds from narcotics transactions, in violation of 18 U.S.C. § 1956(a)(1)(B) (1994); and Arroyo was convicted on one count of using a facility in interstate commerce to facilitate and promote unlawful activity, in violation of 18 U.S.C. § 1953(a)(3) (1994). Defendants were sentenced principally to the following terms of imprisonment: Miller to seven concurrent life terms, plus a 20-year term to be served concurrently with his life terms; Tucker to three concurrent 168-month terms; Hale to two concurrent life terms, plus a 20-year term to be served concurrently with his life terms; Coleman to five concurrent 156-month terms; Hunt to two concurrent life terms, plus a 20-year term to be served concurrently with his life terms; Jimenez to one 360-month term; Raymond Robinson to four concurrent 180-month terms; Arroyo to six concurrent life terms, plus one term of five years and one term of 20 years, both to be served concurrently with his life terms; and David Robinson to five 232-month terms, to be served concurrently with a sentence imposed in New York Supreme Court. Each period of imprisonment was to be followed by one or more periods of supervised release, generally five years in length.

On appeal, defendants make numerous challenges to their convictions, including challenges to the constitutional and statutory validity of the jury selection plan in effect in the Eastern District of New York at the time of their trial; the government’s use of evidence gathered through wiretaps and pen registers; the district court’s refusals to conduct a Massiah hearing concerning the testimony of a cooperating witness and a Mas-trangelo hearing concerning the admission of hearsay evidence as to statements by homicide victims; the court’s jury instructions and the sufficiency of the evidence with regard to certain aspects of the RICO count; and various other trial and procedural rulings and sentencing calculations. In addition, Miller contends, and the government concedes, that under the Double Jeopardy Clause, he could not properly be convicted of both narcotics conspiracy and engaging in a continuing criminal enterprise. Accordingly, we reverse Miller’s narcotics conspiracy conviction and remand to the district court for dismissal of that charge against him. For the reasons below, we find no basis for reversal in any of defendants’ other arguments, and we therefore affirm the judgments of conviction in all other respects.

I. BACKGROUND

The present appeals arise out of the prosecution of these defendants in connection with their participation in the activities of a gang known as the “Supreme Team,” whose business was the distribution of cocaine base (“crack”) by means of a RICO enterprise conducted through a campaign of violent enforcement and retribution. The seven defendants other than Coleman and Raymond Robinson were tried together (the “Miller Trial”). Coleman, who was arrested too late to be included in the main trial, and Raymond Robinson, to whose severance motion the government had consented, were tried together (the “Coleman Trial”).

At the Miller Trial, the government presented voluminous evidence, including tapes and transcripts of more than 100 wiretapped conversations among Supreme Team members, crime scene photographs, telephone records, fingerprint evidence, photographs of assembled Supreme Team members, firearms and ammunition, narcotics paraphernalia, and assorted documents. Among the government’s approximately 80 witnesses at that trial were former accomplices including Ernesto Piniella, the gang’s “chief of security”; Julio Hernandez, a member of the gang’s security force; Trent Morris, the gang’s primary drug courier; Toni McGee, a gang associate; and Ina McGriff, a corrupt former New York State Parole officer who had sold information to the gang. Scores of federal and state law enforcement officers testified about the discovery of homicide victims killed by the Supreme Team, crime scene analysis, searches, surveillances, and other investigative activities.

Much of the physical evidence, surveillance evidence, and testimony by law enforcement agents was also admitted at the Coleman Trial. With respect to that trial, however, the parties agreed that there would be no evidence as to the Supreme Team’s acts of violence, and the only accomplice witness was Trent Morris.

Taken in the light most favorable to the government, the government’s evidence revealed the following.

A. Gang Structure and Operations

The Supreme Team was a street gang organized in the early 1980s in the vicinity of the Baisley Park Houses in Jamaica, Queens, New York, by a group of teenagers who were members of a quasi-religious sect known as the “Five Percenters.” Under the leadership of Kenneth “Supreme” McGriff, with Miller, his nephew, as second-in-command, the gang concentrated its criminal efforts on the widespread distribution of crack cocaine. At its 1987 peak, the Supreme Team’s receipts exceeded $200,000 a day, and the gang regularly committed acts of violence and murder to maintain its stronghold on the area’s drug trade. After McGriff went to jail in 1987, leadership of the Supreme Team was assumed by Miller. Miller solidified his control by increasing the security force and employing it against rivals and against Team members suspected of disloyalty. During 1987 alone, Miller and the then-incarcerated McGriff ordered at least eight homicides.

The Supreme Team’s narcotics operations used dozens of employees, including layers of drug sellers to insulate the gang leaders from the street-level activity. Team members communicated in coded language and numerical systems. To thwart law enforcement efforts further, Miller used armed bodyguards and deployed sentinels with two-way radios on rooftops. The sophistication of the gang’s operation enabled it to survive the periodic targeting of various members for prosecution by the New York City Police Department (“NYPD”) and the Queens County District Attorney’s Office (collectively, the “State”).

In late 1987, however, while Miller was incarcerated on state charges, a task force of NYPD and Federal Bureau of Investigation (“FBI”) officers executed search warrants on a number of Supreme Team storage locations, drug outlets, and residences. Although the gang was tipped off about the raid shortly before it occurred and was able to remove 11 kilograms of cocaine and $200,-000 from targeted premises, authorities nonetheless seized an array of weapons, narcotics trade hardware, photographs, documents, and instructional manuals on criminal conduct, as well as a kilogram of cocaine and thousands of dollars. Following that raid and his own arrest by federal agents, McGriff ordered that the gang’s operations be shut down.

When Miller was released from prison in the spring of 1989, he began to rebuild the Supreme Team and regained control of two of its most lucrative retail locations known as “spots.” The reorganized gang under Miller included Arroyo as the second-in-command, Hunt as Miller’s bodyguard, Ernesto Piniella as head of security, and Hale, Jimenez, and Julio Hernandez as security workers. Tucker and Coleman managed retail spots and supervised crews of workers; long-time gang member David Robinson helped supervise the drug operations and kept records. Raymond Robinson assisted in arranging cocaine purchases, provided security during drug transactions, supervised the processing of cocaine into crack, and delivered crack to sales locations. The Supreme Team began to reclaim its hold on the area drug trade and built its gross receipts up to $10,000 a day.

The substantive narcotics distribution charges against the present defendants focused on the period from December 1989 to March 1990, during which the State was monitoring the gang’s activity with wiretaps. During that period, the Supreme Team conducted its business in the Baisley Park apartment of David Robinson’s mother. Tucker, Coleman, and David Robinson would deliver to the apartment the moneys received at the retail spots they supervised; Miller and the Team’s primary drug courier Trent Morris would negotiate cocaine deals by telephone with William Graham, a supplier who had Colombian connections; and Morris and Raymond Robinson would then drive to Graham’s apartment with money to purchase kilogram-quantities of cocaine. The cocaine would be brought back to the Robinson apartment, where it was processed as crack, packaged, and given to Arroyo, David Robinson, Tucker, or Coleman, who in turn arranged for its sale by street-level employees.

The gang also resumed its use of violence and homicide. The government presented evidence at trial, not all of which resulted in convictions, of homicides committed both pri- or to the Supreme Team’s 1987 shut-down and after its 1989 renascence.

1. The Bolden and Page Murders

In 1987, the Supreme Team was allied with another drug gang, led by Lorenzo (“Fat Cat”) Nichols, that supplied the Supreme Team with powder cocaine. Nichols suspected two men, Henry and Isaac Bolden, of robbing Nichols’s organization. While Nichols was incarcerated, he sought Miller’s assistance in locating the Boldens so that Nichols’s crew members could kill them.

To obtain that information, Miller sought the help of two corrupt New York State Parole Division employees, Parole Officer Ina McGriff (not related to Kenneth McGriff) and secretary Ronnie Younger. Ina McGriff was responsible for supervising the parole of Supreme Team security chief Ernesto Piniella but had become romantically involved with him; Younger had become romantically involved with Miller. The Team regularly paid both women for corrupt assistance. For example, McGriff falsely certified that Piniella was in compliance with parole requirements; she and Younger provided the gang leaders with information from their parole files, false identification documents, and information about the whereabouts of other parolees; and McGriff, who as a Parole Officer carried a gun, supplied Supreme Team members with ammunition.

Piniella and Ina McGriff testified that Miller paid the two women $3,000 for the addresses for the two Boldens and their families. Handwritten notes of such addresses were recovered in a raid of a Supreme Team apartment; the notes were written in part by Younger, according to a handwriting expert’s testimony, and in part by Ina McGriff, according to her own testimony. The notes provided Henry Bolden’s address in the Bronx, where, thereafter, he was shot; and they provided Isaac Bolden’s mother’s address, in the immediate vicinity of which he was thereafter shot and killed.

In 1987, Ina McGriff also gave Piniella copies of Parole Division documents indicating that Supreme Team member James Page was cooperating with authorities. Upon receiving that information, Kenneth McGriff, who had just been arrested on federal charges, ordered that Page be killed; Piniel-la subsequently arranged Page’s murder.

2. The Murders of Gus Rivera and Four Unidentified Suppliers

Gus Rivera was a Supreme Team member who had introduced the gang’s leaders to some of its Colombian suppliers. According to the trial testimony, four of these Colombian drug traffickers were robbed of their cocaine and brutally murdered in July 1989 by Miller, Arroyo, Hale, Hunt, and Jimenez. However, other than the testimony that two of these men were known as “Fernando” and “George,” the government was unable to present evidence as to their identities, and their bodies were never identified. The jury found that these murders, alleged as RICO predicate acts, were not proven beyond a reasonable doubt.

In the wake of these murders, the gang decided that Rivera was more of a liability than an asset. Accordingly, in August 1989, Arroyo arranged for him to be killed. Rivera was shot in the head in a Baisley Park courtyard, but he survived and hid from the gang, temporarily. Arroyo learned Rivera’s whereabouts from Rivera’s girlfriend by threatening to kill her. Arroyo and Hale proceeded to track Rivera to a Queens motel room, where they shot him to death.

3. The Suarez-Perlaza Murders

Fernando Suarez and Pablo Perlaza were also Columbian suppliers to the Supreme Team. In the summer of 1989, the Team decided to steal these suppliers’ cocaine rather than buy it. Accordingly, in August 1989, when Suarez and Perlaza arrived at Hale’s Baisley Park apartment, they were held at gunpoint by Julio Hernandez while Arroyo and Hale bound them with tape. Supreme Team members then tied the suppliers’ heads in plastic bags. While Suarez and Perlaza were suffocating, Hale beat their heads with a baseball bat. Thereafter, Hunt was called upon to help dispose of the bodies. After he arrived, the bodies were loaded into a car and dumped in separate locations in Queens. Later, knowing that her husband had gone to meet Arroyo before disappearing, Suarez’s wife telephoned Arroyo, who told her that Suarez was supposed to have met him but never arrived.

B. The Present Prosecution

In March 1990, after lengthy investigations, several members of the Supreme Team were arrested by State authorities and were charged with offenses similar to those at issue here. After certain pretrial motions were decided adversely to the State, see Part II.B.2. below, the State indictments were dismissed. In anticipation of those decisions, the State turned its evidence over to the United States, which brought the present prosecution.

In a 14r-count superseding indictment, the government charged all of the defendants with conducting the affairs of the Supreme Team through a pattern of racketeering, based in part on some of the acts of racketeering described above, in violation of RICO, 18 U.S.C. § 1962(c), and with conspiring to distribute and to possess with intent to distribute cocaine base, in violation of 21 U.S.C. § 846. All but Hunt were charged with one or more counts of distributing cocaine base at various times, in violation of 21 U.S.C. §§ 841(a) and 841(b)(1)(A); and Miller, Arroyo, Hale, Tucker, Hunt, and Jimenez were charged with one or more counts of possession with intent to distribute cocaine, in violation of 21 U.S.C. §§ 841(a)(1) and 841(b)(1)(C). In addition, Miller was charged with one count of engaging in a continuing criminal enterprise, in violation of 21 U.S.C. § 848, one count of threatening violence in connection with his position in a racketeering organization, in violation of 18 U.S.C. § 1959, and two counts of conducting financial transactions with proceeds of narcotics transactions, in violation of 18 U.S.C. § 1956(a)(1)(B); Miller and Coleman were charged with one count of distributing cocaine base within 1,000 feet of a public school, in violation of 21 U.S.C. § 841(a)(1); and Arroyo was charged with one count of using a telephone in interstate commerce to facilitate and promote the unlawful activities of the Supreme Team, in violation of 18 U.S.C. § 1953(a)(3) (1994).

Defendants made various unsuccessful pretrial motions, including challenges to the jury selection system, see Part II.A. below; motions to suppress pen register and wiretap evidence that had been gathered by the State, see Parts II.B.l. and 2. below; motions to exclude testimony by Julio Hernandez on the ground that his continued association with defendants after he had begun to cooperate with the government violated defendants’ Sixth Amendment rights to counsel, see Part II.C. below; and motions to exclude the testimony of the widow of homicide victim Fernando Suarez as to statements Suarez had made to her prior to his murder, see Part II.D. below. Following disposition of the pretrial motions, and the dismissal of two counts (ie., one of the financial transaction counts against Miller and the distribution-near-a-sehool count against Miller and Coleman), the two trials were held, and the evidence included that described above.

At the Miller Trial, Miller was acquitted on the possession count and the count of threatening violence; he was convicted on all of the other counts on which he was tried. Tucker was convicted on the RICO and narcotics conspiracy counts and on one distribution count; he was acquitted on all of the other counts against him. Hale was convicted on the RICO and narcotics conspiracy counts and on one possession count; he was acquitted on all of the other counts against him. Hunt and Arroyo were each acquitted on one count of possession, and they were convicted on all of the other counts against them. David Robinson was convicted on all of the counts against him. The jury found Jimenez not guilty on the possession count but guilty on all other counts against him; the district court subsequently granted Jimenez’s Rule 29 motion and entered judgments of acquittal for him on the RICO count and the distribution count, leaving him convicted only of narcotics conspiracy.

At their separate trial, Coleman and Raymond Robinson were each acquitted on one distribution count. They were convicted on all of the other counts on which they were tried.

Appellants were sentenced as indicated above, and these appeals followed.

II. DISCUSSION

On appeal, defendants make numerous challenges to their convictions, each joining in the contentions advanced by others, to the extent that those contentions are applicable to him. They contend principally (1) that the jury selection plan in effect in the Eastern District of New York at the time of their trial violated their statutory and constitutional rights; (2) that the district court erred in rejecting, without conducting evidentiary hearings, their contentions that (a) the State pen registers and wiretaps used to gather evidence were unlawful, (b) their Sixth Amendment rights would be violated by the receipt at trial of testimony from a cooperating witness, and (c) their Confrontation Clause rights would be violated by the introduction of hearsay evidence as to statements attributed to homicide victims; and (3) that the district court’s instructions to the jury with respect to the RICO count were erroneous. In addition, Hunt contends that the district court impermissibly allowed the government to amend the indictment to restore a count against him. Miller challenges his RICO conviction on the grounds that it was based on an improper legal predicate and that, in any event, the evidence was not sufficient to establish that predicate; and he contends that his conviction of both narcotics conspiracy and continuing criminal enterprise violated his rights under the Double Jeopardy Clause. Defendants also make a variety of other challenges to the district court’s pretrial decisions on suppression and procedural motions, to certain evidentiary rulings at trial, and to certain determinations affecting their sentences. Although we agree that there were flaws in some of the proceedings, we conclude, for the reasons that follow, that only Miller’s double jeopardy contention merits relief.

A. Contentions with Respect to Jury Selection

The Eastern District of New York comprises five counties. Three, Queens, Kings, and Richmond are part of New York City (collectively the “New York City counties”); the' other two counties are Nassau and Suffolk (collectively the “Long Island counties”). At the time defendants were tried, the jury selection plan for the Eastern District (the “Eastern District Plan” or “Plan”) provided for a master jury wheel that included residents of all five counties for trials held in the District’s courthouse in Brooklyn, and provided for a separate master jury wheel that included residents of only the Long Island counties for trials in the District’s courthouse in Uniondale, Long Island. See In re Jury Plan of the Eastern District of New York, 27 F.3d 9, 9-10 (2d Cir. Judicial Council 1994) (outlining history of the Eastern District’s jury selection plans).

Defendants’ trial was held in Brooklyn, and, in accordance with the Plan, the venire-persons summoned were selected at random from voter registration lists and licensed driver lists in the five counties. Defendants, pointing out that the Long Island counties have a relatively higher white population and the New York City counties have a relatively higher minority population, and arguing that jurors should have been summoned from census lists, contend that the Eastern District Plan (a) violated the requirements of the Jury Selection and Service Act, 28 U.S.C. § 1861 et seq. (1994) (“JSSA” or the “Act”), (b) resulted in a disproportionate underrep-resentation of minorities, in violation of their rights under the Equal Protection Clause of the Fifth Amendment, and (c) violated the fair-cross-section requirement of the Sixth Amendment. These contentions have no merit.

1. The Statutory Challenge

The JSSA requires each federal judicial district to have a plan for random selection of jurors that reflects the policy that jurors are to be “selected at random from a fair cross section of the community in the district or division wherein the court convenes,” 28 U.S.C. § 1861, and that no person is to be excluded from service as a juror for any invidious reason, see id. § 1862. See id. § 1863(a). The plan must provide procedures designed to “ensure that each county, parish, or similar political subdivision within the district or division is substantially proportionally represented in the master jury wheel.” Id. § 1863(b)(3). The JSSA’s “aim is to assure all litigants that potential jurors will be selected at random from a representative cross section of the community and that all qualified citizens will have the opportunity to be considered for jury service.” H.R.Rep. No. 90-1076 (1968) (“House Report”), reprinted in 1968 U.S.C.C.A.N. 1792, 1792. The Act provides that

[f]or the purposes of determining proportional representation in the master jury wheel, either the number of actual voters at the last general election in each county, parish, or similar political subdivision, or the number of registered voters if registration of voters is uniformly required throughout the district or division, may be used.

28 U.S.C. § 1863(b)(3). It also provides that the plan is to “prescribe some other source or sources of names in addition to voter lists where necessary to foster the policy and protect the rights secured by sections 1861 and 1862 of this title.” Id. § 1863(b)(2). The legislative history explains that the statute expresses a preference for the use of voter registration lists because “[tjhese lists provide the widest community cross section of any list readily available,” whereas “[c]en-sus data quickly become out of date and are not suitable.” House Report, reprinted in 1968 U.S.C.C.A.N. at 1794.

Once the master wheel is established in this manner, random selection “virtually eliminates the possibility of impermissible discrimination and arbitrariness at all stages of the jury selection process, and thereby tends to insure that the jury list will be drawn from a cross section of the community.” Id., reprinted in 1968 U.S.C.C.A.N. at 1794. The statute requires only that each county’s representation in the master jury wheel be “substantially” proportionate to the county’s portion of the population of the district as a whole. See 28 U.S.C. § 1863(b)(3). By imposing these requirements for the composition of a master jury wheel, Congress did “not [mean to] require that at any stage beyond the initial source list[,] the selection process shall produce groups that accurately mirror community makeup.” House Report, reprinted in 1968 U.S.C.C.A.N. at 1794.

In order to prevail on a JSSA challenge, a defendant must show a “substantial failure” in proportional representation. See 28 U.S.C. § 1867(a). “Mere technical violations of the procedures prescribed by the Act do not constitute substantial failure to comply with its provisions.” United States v. LaChance, 788 F.2d 856, 870 (2d Cir.) (internal quotation marks omitted), cert. denied, 479 U.S. 883, 107 S.Ct. 271, 93 L.Ed.2d 248 (1986). To establish a violation based on group underrepresentation, a defendant must show not only that the representation of a distinctive group in the community is not fair and reasonable in relation to the number of such persons in the community, but also that that underrepresentation is the result of systematic exclusion. See, e.g., United States v. Rioux, 97 F.3d 648, 654, 660 (2d Cir.1996). Although “it remains unclear whether statistics alone can prove systematic exclusion,” id. at 658, we have cautioned that “[e]ven if they can, however, they would have to be of an overwhelmingly convincing nature,” id. (citing Duren v. Missouri, 439 U.S. 357, 366, 99 S.Ct. 664, 669, 58 L.Ed.2d 579 (1979) (disapproving plan in which women, 54% of the population, constituted less than 15% of the jury venires)).

Defendants in the present case challenged the Eastern District Plan as violating the JSSA on the principal grounds that since jurors for the Long Island division were-summoned only from the Long Island counties, it was improper not to limit jurors for Brooklyn trials solely to residents of the New York City counties; and that, even if it were permissible to include Long Island residents in the master wheel for Brooklyn juries, the Plan produced a master wheel for trials in Brooklyn that did not contain a fair cross-section of the community because Long Island residents were overrepresented and minorities underrepresented. The district court properly rejected these contentions because defendants did not show either a systematic exclusion of minorities or a substantial failure to comply with the Act’s requirements.

The Eastern District Plan called for a source list for each of the five counties, compiled from both voter registration lists and motor vehicle records. The District’s jury administrator testified that the source lists were compiled every four years. The administrator culled a master jury wheel from those fists by starting at a random point on each fist and selecting every one-hundredth name thereafter. This procedure resulted in a wheel whose contents correlated with the number of potential jurors on the source fist for each county and thereby provided the appropriate balance of jurors of the several counties. The 1988 combined source fist, in use at the time of trial, contained 6,438,689 names. From that source list, 378,511 names were selected for a master jury wheel. Twice a year, questionnaires were sent out to between 10,000 and 15,000 persons drawn at random from the master jury wheel. Of that group, approximately one-quarter were found to be qualified for jury duty and, without regard to ethnicity or county residence, were placed on the qualified jury panel. From that group, prospective jurors were summoned at random for service.

Defendants did not show that members of any ethnic group had been hindered in their attempts to register to vote or to obtain driver licenses, and did not show any other kind of systematic exclusion of ethnic minorities. Nor did defendants undertake an adequate statistical examination in an effort to demonstrate underrepresentation; they rely on the juror questionnaires for the panels during only a two-month period. Although the questionnaires for those months did request ethnic data, the question was labeled “optional” and more than a quarter of the jurors refused to answer it. Defendants attempted to remedy this shortcoming by inferring from each questionnaire the citizen’s “probable ethnic background” based on address, religion, occupation, and other lifestyle data, including magazine subscriptions, and then comparing the resulting statistical profiles to the census data for residents of the district. The census, however, which counts, inter alios, resident aliens as well as citizens, and children as well as adults, does not accurately reflect the pool of qualified jurors. The district court properly declined to employ these speculative ethnic background figures in weighing the constitutionality of a jury selection plan, and it properly concluded that defendants did not make a sufficient showing of group underrepresentation.

Defendants also contend that they were hampered in making the necessary showing because they were improperly denied discovery. Though a defendant plainly has a right to discovery, see, e.g., Test v. United States, 420 U.S. 28, 30, 95 S.Ct. 749, 750, 42 L.Ed.2d 786 (1975) (per curiam), we see no improper curtailment of that right in the present case. The JSSA disclosure section provides, in pertinent part, that “[t]he contents of records or papers used by the jury commission or clerk in connection with the jury selection process shall not be disclosed, except ... as may be necessary in the preparation or presentation of a motion” challenging the district’s jury selection procedures. 28 U.S.C. § 1867(f). To the extent necessary with respect to such a motion, a defendant may “inspect, reproduce, and copy such records or papers.” Id. These provisions, revolving around records and papers that are or were “used” by the administrators in the jury selection process, plainly give a defendant access only to records and papers already in existence. We see nothing that entitles defendants to require the jury administrator to analyze data on their behalf. Cf. United States v. Rioux, 97 F.3d at 658 (defendant’s failure to show that undeliverable questionnaires went to blacks or Hispanics was decisive despite clerk’s lack of analysis of such data because the defendant “had unrestricted access to all the envelopes returned as undelivered” and “could have compiled his own list”).

Here, the district court permitted defendants to take testimony of the jury administrator and to receive geographic breakdowns. The court denied, however, defendants’ request to require the administrator to calculate the ethnic breakdown of jury panels in the Eastern District during a 14-month period, which would have required substantial work by the administrator’s office. The administrator explained:

[a]s far as the ethnicity, that would require several hours of work because we do have to check an index for where each person, qualification questionnaire is located and then within a particular batch of the questionnaires we have to shuffle through, find a given individual’s questionnaire.

(Transcript of Jury Selection at 428.) After hearing this testimony, the court concluded that defendants would be allowed to take testimony from the jury administrator and to examine the juror questionnaires themselves, but that it was inappropriate to require “court personnel to research manually thousands of responses.” (Id. at 434-35.) After further discussion, during which the district court considered permitting discovery beyond that required by the statute, the court adhered to its decision. The court’s considered denial of defense requests for disclosures that were not required by the statute and that the court deemed infeasible or irrelevant was not an abuse of discretion.

2. The Constitutional Challenges

Defendants contend that the Eastern District Plan, even if in compliance with the JSSA, produced an ethnic disparity in the jury wheel that violated their rights under the Fifth and Sixth Amendments. These contentions have no merit.

“To succeed on a Fifth Amendment equal protection challenge to a criminal jury selection system, the defendant must establish that (1) there is a cognizable group, (2) that is substantially underrepresented by reason of (3) a selection procedure that is not racially neutral, i.e., is the result of intentional discrimination by the District.” United States v. Rioux, 97 F.3d at 659. Absent intentional discrimination, a jury selection plan does not violate the Equal Protection Clause. See id. Defendants presented no evidence whatever of any intentional discrimination. “[AJbsent positive evidence that some groups have been hindered in attempting to register to vote, a jury venire drawn from voter registration lists violates neither the Sixth Amendment’s fair cross-section requirement nor the Fifth Amendment’s guarantee of Equal Protection.” Schanbarger v. Macy, 77 F.3d 1424, 1424 (2d Cir.1996) (per curiam); see also United States v. Biaggi, 909 F.2d 662, 676-78 (2d Cir.1990) (upholding jury plan using voter registration lists despite underrepresentation of minority groups in the master jury wheel of the Manhattan courthouse for the Southern District of New York, where there was no showing that registration by minorities had been hindered), cert. denied, 499 U.S. 904, 111 S.Ct. 1102, 113 L.Ed.2d 213 (1991).

The Sixth Amendment guarantees an accused “an impartial jury of the State and district wherein the crime shall have been committed.” U.S. Const., amend. VI. Defendants’ challenge to the inclusion of residents of the Long Island counties in the master wheel for Brooklyn trials carries no Sixth Amendment implications. That Amendment’s guarantees of an impartial jury “of the State and district” in which the crime was committed does not require a narrower geographical focus than the district itself. Cf. United States v. Bahna, 68 F.3d 19, 24 (2d Cir.1995) (rejecting challenges under JSSA and the Constitution to separate jury wheel for the Long Island counties), cert. denied, - U.S. -, 116 S.Ct. 1682, 134 L.Ed.2d 784 (1996).

Further, the Sixth Amendment’s fair-cross-section provision guarantees “the opportunity for a representative jury venire, not a representative venire itself.” United States v. Jackman, 46 F.3d 1240, 1244 (2d Cir.1995) (emphasis in original). In order to establish a violation of the Amendment based on group underrepresentation, a defendant need not prove intentional discrimination, but he must show

(1) that the group alleged to be excluded is a “distinctive” group in the community; (2) that the representation of this group in venires from which juries are selected is not fair and reasonable in relation to the number of such persons in the community; and (3) that this underrepresentation is due to systematic exclusion of the group in the jury-selection process.

Duren v. Missouri, 439 U.S. at 364, 99 S.Ct. at 668. These requirements mirror those for proof of a violation of the JSSA. See United States v. Rioux, 97 F.3d at 660. As discussed above, defendants did not show any systematic exclusion of minorities in the Eastern District jury-selection process.

B. Challenges to the Wiretap Evidence Gathered by the State

The evidence at the Miller and Coleman trials included more than 100 taped conversations among Supreme Team members. Defendants challenge the admission of these tapes on the principal grounds that warrants permitting the interception of these conversations (1) were issued partly on the basis of information obtained through the use of pen registers for which the State had not obtained court authorization, and (2) were otherwise improperly granted. Defendants also contend that the evidence should have been suppressed in the present case because it was suppressed in state-court prosecutions.

1. The Use of Pen Registers

During the investigation of the Supreme Team by State authorities, pen registers were used on telephones at the apartments of Supreme Team members or their relatives to identify the numbers dialed from those locations. Information thus gained was included in applications by the State for warrants permitting wiretaps. At a pretrial hearing during the State prosecution, an Assistant District Attorney (“ADA”) indicated that the registers used were likely of a new type that would have been capable, with minor alterations, of intercepting the contents of the telephone calls. The ADA stated, however, that the pen registers were not used to intercept contents.

Thereafter, while proceedings in the present prosecution were ongoing in the district court, the New York Court of Appeals decided People v. Bialostok, 80 N.Y.2d 738, 745, 594 N.Y.S.2d 701, 705, 610 N.E.2d 374 (1993), in which that court noted that although a traditional pen register recorded only the telephone numbers dialed and was incapable of intercepting the contents of the communications, the model at issue before it needed only the attachment of an audio cable, a tape recorder, and a wire to enable the interception of such contents. Although those modifications were not made until after a warrant was acquired, the court concluded that the ease of modification jeopardized the privacy of participants to wire communications and that a warrant should have been obtained prior to use of even the unmodified pen register.

In the present ease, relying chiefly on Bialostok, defendants contend that the district court should have held a hearing to determine whether the pen registers used in investigating the Supreme Team had the capability of intercepting the contents of the communications. They argue that if the pen registers employed had that capability, the State’s use of those devices did not conform to the requirements of State law; they contend that any resulting evidence should have been suppressed because under § 2516(2) of Title III of the Omnibus Crime Control and Safe Street Act, 18 U.S.C. § 2510-2521 (1994) (“Title III”), orders by a state court authorizing the interception of wire communications are required to be “in conformity with [18 U.S.C.] section 2518 ... and with the applicable State statute.” 18 U.S.C. § 2516(2) (emphasis added). In so arguing, defendants also rely on dicta in three cases in which we considered conflicting state and federal wiretap standards: United States v. Manfredi, 488 F.2d 588 (2d Cir.1973), cert. denied, 417 U.S. 936, 94 S.Ct. 2651, 41 L.Ed.2d 240 (1974); United States v. Rizzo, 491 F.2d 215 (2d Cir.), cert. denied, 416 U.S. 990, 94 S.Ct. 2399, 40 L.Ed.2d 769 (1974); and United States v. Marion, 535 F.2d 697 (2d Cir.1976). That trio of cases culminated in the following dictum: “If a state should set forth procedures more exacting than those of the federal statute ... the validity of the interceptions and the orders of authorization by which they were made would have to comply with that test as well.” Id. at 702 (emphasis in original). We have several difficulties with defendants’ arguments.

First, Title III does not apply to pen registers performing their routine functions of merely recording the numbers to and from which calls are dialed. Title III generally prohibits the intentional interception of wire communications, including telephone conversations, in the absence of authorization by court order. See 18 U.S.C. §§ 2511, 2516-2518. “[I]ntercept[ion]” is defined as “the aural or other acquisition of the contents of any wire, electronic, or oral communication through the use of any electronic, mechanical, or other device.” Id. § 2510(4) (emphasis added). A pen register used merely to record the numbers dialed does not intercept the contents of a communication. Accordingly, Title III does not require law enforcement authorities to obtain court authorization for the installation of a pen register. See Smith v. Maryland, 442 U.S. 735, 739-46, 99 S.Ct. 2577, 2579-83, 61 L.Ed.2d 220 (1979). Although the Smith Court dealt only with traditional models of pen register, we view its holding as applying also to models that have not been altered so as to enable interception of a wire communication’s contents. Title III guards against actual infringements of privacy, not purely hypothetical ones. Accord United States v. Veksler, 62 F.3d 544, 549 (3rd Cir.1995) (“mere suggestion that pen register equipment is now capable of misuse does not give us a basis to depart from the controlling precedent of the Smith case”), cert. denied, - U.S.-, 116 S.Ct. 780, 133 L.Ed.2d 731 (1996). We conclude that § 2516(2)’s reference to compliance with state law for wiretap authorizations was not applicable to the pen registers employed here and that that section provided no basis for requiring the district court to hold a hearing to determine whether those pen registers, though not capable in the form used of intercepting the contents of wire communications, were capable of being modified to enable such interception.

Second, even if Title III were applicable, defendants’ reliance on the Manfredi-Rizzo-Marion trilogy would be unavailing for several reasons. To begin "with, the dicta in those cases have never been applied to exclude evidence. This Court noted in United States v. Sotomayor, 592 F.2d 1219 (2d Cir.), cert. denied, 442 U.S. 919, 99 S.Ct. 2842, 61 L.Ed.2d 286 (1979), that even if given wiretap evidence would not be admissible in a New York State court, we did

not consider Manfredi and its progeny to obligate us automatically to apply in a federal proceeding all provisions of a state wiretap statute containing more stringent requirements than those prescribed by Title III. We believe that at most Manfredi requires us, in determining whether to admit a wiretap obtained by a state officer acting under a state court order issued pursuant to a state statute, to apply only those more stringent state statutory requirements or standards that are designed to protect an individual’s right of privacy, as distinguished from procedural rules that are essentially evidentiary in character.

Id. at 1225. Moreover, even the interpretive dicta of Sotomayor, suggesting that a state’s more stringent statutory requirements might be applied in a federal prosecution if those requirements were more substantive than procedural, have never been applied to bar the introduction of wiretap evidence. Cf. United States v. Rowell, 903 F.2d 899, 902-03 (2d Cir.1990) (criticizing the reasoning of So-tomayor, applying federal standards for probable cause to a state-issued wiretap warrant, and affirming denial of suppression motion); United States v. Workman, 80 F.3d 688, 695 n. 4 (2d Cir.) (noting that Sotomayor is “somewhat at odds with our holdings in more recent cases”), cert. denied, - U.S. -, 117 S.Ct. 319, 136 L.Ed.2d 233 (1996).

Further, we have refused to apply retroactively state decisions announcing a more restrictive interpretation of state wiretap law to evidence obtained by state officers acting in good faith based on existing interpretations of state law if doing so were contrary to the interests of justice. In United States v. Aiello, 771 F.2d 621 (2d Cir.1985), for example, we declined to suppress a state-authorized wiretap for failure to comply with timing requirements governing extension applications, even though two state decisions issued since the time of the wiretap had indicated that the relevant statute was designed to protect privacy interests. We held instead that “when the state officer ... relies in good faith on pre-existing less stringent state court interpretations, we will not apply new interpretations retroactively, at least when to do so would not serve the interests of justice.” Id. at 627. In United States v. Spadaccino, 800 F.2d 292 (2d Cir.1986), we again applied this “good faith” exception where there had been no prior “authoritative state court interpretation.” Id. at 297. Here, defendants rely on the New York Court of Appeals decision in Bialostok, which was handed down well after the state had completed its use of the pen registers in this case. There is no claim that the state officers who employed the pen registers violated then-existing state law, nor any basis on which to infer a need for a hearing into their good faith.

Finally, we note that even suppression of the fruits of the pen registers would not require suppression of the evidence obtained in the wiretaps. See generally United States v. Nanni, 59 F.3d 1425, 1433 (2d Cir.) (wiretap authorization will not be invalidated if flawed information in the application was so inconsequential that warrant would have been issued without that information), cert. denied, - U.S. -, 116 S.Ct. 576, 133 L.Ed.2d 499 (1995); People v. Bialostok, 594 N.Y.S.2d at 705, 610 N.E.2d 374 (erroneous use of pen register data in wiretap application was harmless where “other evidence supporting the application ... provided ... probable cause”). In the present case, the police relied on several other acceptable sources to show probable cause for authorization of the wiretaps, including the debriefings of multiple informants, surveillance of gang members, and permissibly intercepted telephone calls made from prisons. Thus, even if we were to conclude that the district court erred in not ruling that a warrant was required for the use of the pen registers in this case, we would conclude that that error was harmless.

2. Wiretap Evidence Gathered by the State

In August 1989, State agents installed a pen register on the home telephone of Polly Douglas, the mother of Jimenez. The register indicated that the telephone was used to place many calls to telephones where Supreme Team members lived or conducted illegal business, and that several calls were received from state prisons where gang members were incarcerated. Based on this and other information, the State subsequently obtained authorization to install a wiretap which became operational in December 1989 (the “Douglas wiretap”). The Douglas wiretap intercepted discussions of the Supreme Team’s narcotics trafficking between the Douglas home and the home of Miller. With this and other information, the State obtained authorization to tap the telephone in Miller’s home (the “Miller wiretap”); the Miller wiretap became operational in January 1990. The Miller wiretap intercepted the conversations of Miller, Arroyo, Hale, David Robinson, Raymond Robinson, Tucker, Coleman, and other Supreme Team members as they discussed narcotics trafficking. Miller was intercepted discussing drug transactions with William Graham on Graham’s home telephone, and the State soon thereafter obtained authorization to wiretap the latter telephone (the “Graham wiretap”); the Graham wiretap became operational in February 1990. The Graham wiretap also intercepted several incriminating conversations between Graham and other gang members, including Miller, Arroyo, Hale, David Robinson, and Raymond Robinson. All of the wiretaps were renewed at least once, and the Miller and Graham wiretaps remained in place until defendants, and William Graham, were arrested by State officers in March 1990.

In the State’s case against Graham, who was prosecuted separately from Miller and the other Supreme Team members, the state court suppressed the evidence gathered through the Graham and Miller wiretaps on the grounds that the State officers had not disclosed to the authorizing judge that Hale had been cooperating with the police, and that the officers had recklessly disregarded state-law requirements that the identities of all persons whose conversations are likely to be intercepted be disclosed in the warrant application. On the basis of that decision, Miller successfully moved to suppress the evidence collected through the Graham wiretap on the ground of collateral estoppel.

In the present case, defendants challenge the district court’s denial of their motion to suppress the evidence gathered through all three wiretaps. They contend principally that their convictions must be reversed and their indictments dismissed with prejudice because the indictments were obtained with the use of evidence suppressed in the state prosecutions of Miller and William Graham; Miller contends in his pro se brief that the state court’s suppression ruling was binding in the present case. Defendants also contend, inter alia, that their motion to suppress in the district court should have been granted on its merit because of the officers’ failures (a) to comply with the requirements that alternative investigative techniques be exhausted and that the availability of such techniques be disclosed to the issuing judge, and (b) to make proper disclosures in the warrant applications. We find none of defendants’ arguments persuasive.

a. The Effect of the State Court’s Suppression Orders

We reject first the contention that defendants are entitled to dismissal of the indictments by reason of the government’s presentation to the federal grand jury of evidence that was suppressed by the state court. A grand jury may make use of information obtained through a wiretap unless it is clear that the wiretap was illegal, such as when there is a government concession that the surveillance was unlawful, or there is “patent” illegality “such as, for example, when no prior court order was obtained, or when the unlawfulness of the Government’s surveillance has been established in a prior judicial proceeding.” In re Persico, 491 F.2d 1156, 1161 (2d Cir.) (ruling that grand jury witness, who was asked a question based on information gained through wiretaps, had no right under Title III to a suppression hearing as to whether the wiretap was lawful), cert, denied, 419 U.S. 924, 95 S.Ct. 199, 42 L.Ed.2d 158 (1974). Absent such clear or patent illegality, the grand jury is entitled to consider the wiretap evidence.

The Pérsico phrase “unlawfulness ... established in a prior judicial proceeding” does not refer to orders of suppression in state court prosecutions, for those orders do not “establish^ ]” unlawfulness for purposes of a proceeding in federal court. “[I]t has long been the rule in this Circuit that collateral estoppel never bars the United States from using evidence previously suppressed in a state proceeding in which the United States was not a party.” United States v. Davis, 906 F.2d 829, 832 (2d Cir.1990) (internal quotation marks omitted); see also United States v. Peterson, 100 F.3d 7,12 (2d Cir.1996) (discussing narrowness of exceptions). Indeed, when Graham (prosecuted separately in federal court) and Miller themselves appealed to this Court from the district court’s denial of their motions for a temporary restraining order to prevent the government from using the very wiretap evidence at issue here, we stated obiter that “state court rulings in a criminal trial are not binding on a federal court” because the “state and national sovereignty are separate and distinct from one another.” United States v. Miller, 14 F.3d 761, 763 (2d Cir.1994) (dismissing for mootness and lack of appellate jurisdiction). Thus, the state court’s suppression order did not foreclose consideration of the wiretap evidence by the grand jury, and it was not binding on the district court. The latter court properly held an evidentiary hearing on defendants’ suppression motion and considered the motion on its merits.

b. The Merits of the Suppression Motions

Both federal law and state law are designed to harmonize the needs of law enforcement officials with the privacy rights of the individual. Title III requires that wiretap applications include

a full and complete statement as to whether or not other investigative procedures have been tried and failed or why they reasonably appear to be unlikely to succeed if tried or to be too dangerous.

18 U.S.C. § 2518(l)(c); see also N.Y. Criminal Procedure Law § 700.20(2)(d) (McKinney 1995) (containing similar requirement). In United States v. Lilia, 699 F.2d 99 (2d Cir.1983), we disapproved of the use of wiretap evidence because the affidavit underlying the application for wiretap authorization “d[id] not reveal what, if any, investigative techniques were attempted prior to the wiretap request” and “d[id] not enlighten us as to why this narcotics case presented problems different from any other small-time narcotics case.” Id. at 104; see also id. at 102 (“discem[ing] no difference between the federal and state case law relating to this requirement”); People v. McGrath, 46 N.Y.2d 12, 412 N.Y.S.2d 801, 807, 385 N.E.2d 541 (1978) (New York statute was designed to harmonize “State standards for court authorized eavesdropping warrants with federal standards”), cert. denied, 440 U.S. 972, 99 S.Ct. 1535, 59 L.Ed.2d 788 (1979).

The requirement that there be disclosure as to the use, success, and potential success of other investigative techniques, however, does not mean “that any particular investigative procedures [must] be exhausted before a wiretap may be authorized.” United States v. Young, 822 F.2d 1234, 1237 (2d Cir.1987) (internal quotation marks omitted).

[T]he purpose of the statutory requirements is not to preclude resort to electronic surveillance until after all other possible means of investigation have been exhausted by investigative agents; rather they only require that the agents inform the authorizing judicial officer of the nature and progress of the investigation and of the difficulties inherent in the use of normal law enforcement methods.

United States v. Vazquez, 605 F.2d 1269, 1282 (2d Cir.) (internal quotation marks omitted), cert. denied, 444 U.S. 981, 100 S.Ct. 484, 62 L.Ed.2d 408 (1979). In reviewing a ruling on a motion to suppress wiretap evidence, we accord deference to the district court because “[t]he role of an appeals court in reviewing the issuance of a wiretap order ... is not to make a de novo determination of sufficiency as if it were a district judge, but to decide if the facts set forth in the application were minimally adequate to support the determination that was made.” United States v. Torres, 901 F.2d 205, 231 (2d Cir.) (internal quotation marks omitted), cert. denied, 498 U.S. 906, 111 S.Ct. 273, 112 L.Ed.2d 229 (1990).

As to the present case, when the State applied in state court for wiretap authorizations, it explained that it had been investigating the Supreme Team for some years and had nearly exhausted its battery of traditional investigative techniques with little significant success. Using normal techniques, the State had been unable to penetrate the Supreme Team or gain sufficient admissible evidence against any members other than those at the lowest echelons. The Team’s leaders had insulated themselves from police contact through extensive use of bodyguards and lookouts, and when the State applied for wiretap authorization it had yet to identify all of the upper and middle level members of the Supreme Team, or to determine where the narcotics and illegal proceeds were kept, or to identify the Team’s cocaine suppliers. The State had procured the cooperation of one accomplice, but it hesitated to attempt other undercover infiltration because of the extreme violence in which the Supreme Team engaged against persons it believed were threats to its security. Even by the time the State applied for the Graham wiretap, it was still unable to obtain the physical evidence whose existence could be gleaned from conversations intercepted by wiretap, given both the difficulty of infiltration by undercover officers and the unreliability of cooperating defendants. For example, Hale at one time agreed to cooperate and then at various points refused to cooperate; his history of homicide and drug abuse further decreased his reliability. Thus, the State sought wiretaps in order to identify the Team’s leaders and suppliers and to locate their drug storage facilities. We conclude that the district court did not err in ruling that the State met its burden of showing its need for a wiretap.

Defendants fare no better in their challenge to the Miller wiretap on the ground that affidavits supporting the application for that tap omitted material information that had been provided by informants who were cooperating with the State. A challenge to the veracity of such an affidavit will succeed only when it establishes intentional or reckless omissions or false statements that are “necessary to the finding of probable cause” supporting the wiretap authorization. Franks v. Delaware, 438 U.S. 154, 156, 98 S.Ct. 2674, 2676, 57 L.Ed.2d 667 (1978); see Rivera v. United States, 928 F.2d 592, 604 (2d Cir.1991).

In the present case, the district court held an evidentiary hearing to determine whether State officers had sought to mislead the state-court judges to induce them to authorize wiretaps. The court found that

[t]he credible testimony of assistant district attorneys Quinn and Ruiz and Detective Ryan at that supplemental hearing establishe[d] beyond any doubt that these state officials did not seek to deceive the state court, nor did they act in a suspiciously careless manner in the preparation of the wire tap application.

District Court Memorandum dated March 10, 1993, at 1-2. Although the Miller and Graham wiretaps had been suppressed by the state court, the district court “found no reason to grant the relief, applying either state or federal law to the resolution of the issues.” Id. at 1. Giving due deference to the district court’s assessment of witness credibility, we can see no basis for overturning its refusal to suppress evidence on this ground.

Finally, the district court properly rejected defendants’ contention that they were entitled to suppression because the State, knowing that Graham was engaged in criminal activity with Miller and that Graham’s conversations would likely be intercepted, omitted Graham’s name from the application for the Miller wiretap. Although the state court, relying in part on state-court decisions, ruled that the State was “obligated to identify ... Graham when the Miller warrant was obtained,” People v. Graham, Ind. No. QN13137/90, Memorandum Decision at 21 (N.Y.Sup.Ct. Nov. 15, 1991), there is no such requirement under federal law. See United States v. Donovan, 429 U.S. 413, 435, 97 S.Ct. 658, 671, 50 L.Ed.2d 652 (1977) (where wiretap meets Title III standards, “the failure to identify additional persons who are likely to be overheard engaging in incriminating conversations could hardly invalidate an otherwise lawful judicial authorization”).

We have considered all of defendants’ challenges to the wiretap evidence and have found them to be without merit. The district court properly denied the motion to suppress.

C. The Massiah Challenge to the Testimony of Julio Hernandez

The present prosecution was commenced in January 1992, and Supreme Team member Julio Hernandez was arraigned on the federal charges in February. Federal agents immediately made the usual efforts to persuade him to cooperate, and although Hernandez showed some interest, he gave little information, and no further cooperation session was scheduled. More than a month later, Hernandez’s court-appointed counsel contacted the government to request a proffer session. Such a session was held in April 1992, and Hernandez recounted the details of several of the crimes charged in the indictment; in May he signed a formal cooperation agreement. From the time of his federal arraignment until July 2, 1992, Hernandez was held in the Metropolitan Correctional Center (“MCC”), where the other Supreme Team members too were being detained. Several times prior to, during, or after trial, one or more defendants moved to dismiss the indictment or to preclude Hernandez’s testimony, contending that their Sixth Amendment rights had been violated because the government had permitted Hernandez to remain housed with them and to attend defense strategy sessions with the attorneys after he had begun cooperating with the government. The district court denied the motion, finding that the government neither intended to violate defendants’ rights nor benefited from these events. Defendants challenge these rulings on appeal, contending that the court at least erred in failing to hold a hearing. For the reasons that follow, we see no error.

It is well settled that the Sixth Amendment right to counsel is violated when a private individual, acting as a government agent, “deliberately elicit[s]” incriminating statements from an accused in the absence of his counsel. Massiah v. United States, 377 U.S. 201, 206, 84 S.Ct. 1199, 1203, 12 L.Ed.2d 246 (1964). With respect to the detention of a cooperating witness in proximity to other defendants, the Massiah rule applies only to situations that “ ‘look’ like government interrogations,” United States v. Stevens, 83 F.3d 60, 64 (2d Cir.), cert. denied, - U.S.-, 117 S.Ct. 255, 136 L.Ed.2d 181 (1996); we have declined to “treat every inmate who hopes to cut some future deal as a ‘government informant,’ ” id.

The right to counsel may also be violated when a cooperating defendant participates with noncooperating defendants and their attorneys in joint strategy sessions. See, e.g., Maine v. Moulton, 474 U.S. 159, 176-77, 106 S.Ct. 477, 487-88, 88 L.Ed.2d 481 (1985). Although it is obviously preferable that cooperating witnesses be separated from noncooperating codefendants and not attend joint defense strategy meetings, such isolation is not always possible. For example, a cooperating witness’s continued association with his codefendants may be necessary in order to conceal the cooperation and thereby protect the cooperating defendant’s family. In such an instance, a Massiah claim will fail unless it is shown that the government benefited from the cooperating defendant’s attendance. See, e.g., United States v. Ginsberg, 758 F.2d 823, 833 (2d Cir.1985) (“Where the presence of the government’s agent or informant at the defense conference is either unintentional or justified by the necessity of protecting the informant’s identity, there can be no violation of the sixth amendment without some communication of valuable information derived from the intrusion to the government....”).

A defendant’s claim of a Massiah violation does not automatically require an evidentiary hearing. “In order to require a hearing on such a claim, assuming that the government has not interfered with the attorney-client relationship deliberately, the defendant bears the burden of alleging specific facts that indicate communication of privileged information to the prosecutor and prejudice resulting therefrom.” United States v. Aulicino, 44 F.3d 1102, 1117 (2d Cir.1995); see United States v. Ginsberg, 758 F.2d at 833 (e.g., a showing “that a prosecution witness testified concerning privileged communications, that prosecution evidence originated in such communications, or that such communications have been used in any other way to the substantial detriment of the defendant”).

Defendants made no showing here sufficient to warrant a hearing. When Hernandez was first placed in federal custody in February, he gave the government no reason to believe he would become a government witness. He provided little information when the agents urged him to cooperate, and, therefore, no further meetings with him were scheduled. There was no basis for an assumption that he would become a government witness until April, when he met again with the government and made disclosures about several of the crimes charged in the indictment. Until that proffer session, there was no impetus for the government to separate Hernandez from his codefendants.

In the wake of Hernandez’s eventual decision to cooperate, his attorney and the Assistant United States Attorney (“AUSA”) discussed the possibility of separating Hernandez from the defendants, but that option was rejected because of concern that it would signal to the Supreme Team that Hernandez was cooperating and would thus endanger his family. His family’s whereabouts were known to the gang, and one family member had undergone surgery and could not be relocated until after a period of recuperation. Thus, it was decided to delay Hernandez’s removal from MCC until his family could be moved; Hernandez was returned to MCC with instructions to minimize his contact with his codefendants to the extent possible. At a later meeting with the government, Hernandez’s guilty plea was scheduled for June 19, 1992, a date by which it was expected that the relocation of his family could be accomplished, and Hernandez was again instructed to avoid his eode-fendants and refrain from attending their meetings to the extent possible. As it turned out, Hernandez pleaded guilty as scheduled, but the recuperating family member was still too ill to be moved at that time, so Hernandez was returned to MCC, again with the instruction to avoid his codefend-ants. By July 2, 1992, Hernandez’s family had been relocated, and Hernandez was promptly removed from MCC.

The soundness of the concern for the safety of Hernandez’s family is well documented. When Supreme Team member Trent Morris was scheduled to testify for the prosecution at Miller’s state trial in 1991, Trent’s brother William received communications and threats to himself and the Morris family if Trent were to testify. In anticipation of Trent Morris’s testimony, his wife and child had been relocated. In a taped conversation with William Moms before that trial and after the relocation, Miller noted that Trent had “ ‘send [sic ] them away,’ ” but pointed out to William, “ ‘[h]e ain’t send [sic ] you away, he ain’t send [sic] away his moms [sic] and them, you know what I’m saying?’ ” (Affidavit of AUSA Leslie R. Caldwell dated September 9, 1992, in support of motion for anonymous jury, ¶ 18, at 16 (quoting transcript).) Miller then asked whether William Morris still lived at a certain address; after receiving a negative response, Miller said, “ ‘If you notice, Robin’s still staying in, in Baisley Projects.’ ” (Id. ¶ 18, at 17-18 (quoting transcript).) Robin Carrington was Trent Morris’s sister-in-law who lived in the Baisley Park Houses with her father. (Id. ¶ 18, at' 18 n. 2.) Miller said, “ ‘if I really wanted to do anything to anybody, it would be a snap of a finger.’ ” (Id. ¶ 18, at 18 (quoting transcript).) Notwithstanding this and other efforts to persuade Trent Morris not to testify, he began his testimony against Miller in the state-court trial. On that night, Trent Morris’s sister-in-law Robin Carring-ton and her father were killed; the first letter of Miller’s nickname was carved in their torsos. Against this background, prudent concern for human life plainly required that Hernandez’s decision to cooperate not be revealed prematurely. The failure to separate him from his codefendants until his family could be relocated thus did not constitute a Massiah violation unless defendants could show that the government thereby gained valuable information.

Although defendants argue that “it would be naive simply to conclude ... that Hernandez made no efforts to obtain incriminating statements” from defendants (Arroyo brief on appeal at 42), the record indicates that no such efforts were made. Rather, it appears that after Hernandez agreed to cooperate, he carefully adhered to the government’s instruction to minimize contact with his code-fendants. For example, he risked angering Miller by refusing to attend a defense meeting that Miller ordered him to attend. Further, defendants’ suggestions as to what benefits the government may have gained do not withstand scrutiny. For example, defendants claim that Hernandez had learned that certain witnesses would be called by the defense, and that the defense was considering calling Tucker as a witness because of his relatively short criminal history and the purported weakness of the evidence against him; they point to Hernandez’s trial testimony that it was during conversations with defendants while in detention that Hernandez learned Tucker’s first name, and to the fact that during their detention a superseding indictment was filed, alleging a new RICO predicate act against Tucker. But it is difficult to perceive any benefit to the government from Hernandez’s learning Tucker’s name while Hernandez was in custody; Tucker’s first name was in the indictment. Nor would the government have needed the information that Tucker might be called as a defense witness in order to file a superseding indictment charging him with the additional RICO predicate act; that act was reflected in a prior state-court conviction. Defendants also argue that Hernandez may have learned of the plan to call one Ivan Bonner as a witness, and they point to trial testimony by Bonner that government agents visited him in jail to warn him not to testify on Miller’s behalf. But the government hardly needed a tip that Bonner might be a defense witness; he, like many of the witnesses called by the defense, had been a defense witness at Miller’s state trial. Defendants’ assertion that Hernandez’s trial testimony was fabricated from defendants’ incriminating jailhouse statements was rejected by the district judge, who presided over the trial and heard all of the evidence, including the testimony of Hernandez. The court stated, “there’s absolutely no reasonable indication in the record that the evidence or the testimony of Mr. Hernandez was the product of any infiltration, if you will, much less government sponsored infiltration.” (Arroyo Sentencing Transcript at 18.)

We see nothing in the record to indicate that the government was benefited or that defendants were prejudiced by Hernandez’s remaining in MCC until he and his family could be safely relocated and nothing to suggest that the district court erred in rejecting defendants’ Massiah claims without conducting an evidentiary hearing.

D. Hearsay Testimony as to Statements of Murdered Declarants

At trial, Meisner Suarez, the widow of homicide victim Fernando Suarez, testified, inter alia, that her husband, prior to being murdered, told her that on one occasion he had gone to Jamaica, Queens, to meet a group of black men, one of whom was big with a scar on his face, a description that fit Hale. In addition, Toni McGee, Rivera’s girlfriend, testified that before his death, Rivera told her that “[h]e had killed some Colombians” and had taken from them “two keys of coke.” (Transcript of Miller Trial (“Miller Trial Tr.”) at 2512.) The district court admitted these hearsay statements against Hale and Arroyo notwithstanding defendants’ inability to confront the declarants, on the basis that the declarants had been murdered by defendants and thus defendants had caused their unavailability. See, e.g., United States v. Mastrangelo, 693 F.2d 269 (2d Cir.1982) (“Mastrangelo ”). Defendants challenge the admission of this testimony, contending (a) that the Mastrangelo rationale is applicable only to eases in which a witness is murdered to prevent his testimony at a proceeding that is underway, and that no proceeding was pending at the time of these two murders, and (b) that the court could not properly admit this testimony without having a hearing to determine whether or not the declarant’s absence had been procured by defendants. Although we agree that the district court should have had a hearing before admitting the testimony, we conclude that the error in failing to do so was harmless.

The right to confront hostile witnesses may be constructively waived by a defendant’s conduct. In Mastrangelo, we held that

if a witness’ silence is procured by the defendant himself, whether by chicanery ... or by actual violence or murder ..., the defendant cannot then assert his confrontation clause rights in order to prevent prior grand jury testimony of that witness from being admitted against him. Any other result would mock the very system of justice the confrontation clause was designed to protect.

Id. at 272-73; see United States v. Aguiar, 975 F.2d 45, 47 (2d Cir.1992). In such circumstances, “the defendant will be deemed to have “waived his sixth amendment rights and, a fortiori, his hearsay objection’ to the admission of the declarant’s statements.” United States v. Thai, 29 F.3d 785, 814 (2d Cir.) (quoting Mastrangelo, 693 F.2d at 273), cert. denied, 513 U.S. 977, 115 S.Ct. 456, 130 L.Ed.2d 364 (1994); see United States v. Potamitis, 739 F.2d 784, 788-89 (2d Cir.), cert. denied, 469 U.S. 918, 105 S.Ct. 297, 83 L.Ed.2d 232 (1984). Although we first articulated this rule in admitting a murdered witness’s prior grand jury testimony, see Mastrangelo, 693 F.2d at 273, we have since extended it to allow evidence of unsworn statements made to a detective prior to the declarant’s murder by the defendant, see United States v. Thai, 29 F.3d at 814-15, and of unsworn statements of a witness who was not murdered but whose planned testimony was withheld in response to the defendant’s intimidation, see United States v. Aguiar, 975 F.2d at 47.

We have never indicated that Mastrangeb did not apply to a defendant’s procurement of the unavailability of the declarant unless there was an ongoing proceeding in which the declarant was scheduled to testify, and we see no reason to do so now. Although a “finding that [defendants’] purpose was to prevent [a declarant from] testifying,” United States v. Thai, 29 F.3d at 815, is relevant, such a finding is not required. The relevant issue is

the [defendant’s participation in [the deceased witnesses murder. If the District Court finds that [the defendant] was in fact involved in the death of [the witness] through knowledge, complicity, planning or in any other way, it must hold his objections to the use of [the witnesses testimony waived. Bare knowledge of a plot to kill [the witness] and a failure to give warning to appropriate authorities is sufficient to constitute a waiver.

Mastrangelo, 693 F.2d at 273-74.

However, before the court admits evidence of statements by absent declarants on the ground of such a waiver, it must hold a hearing: “an evidentiary hearing in the absence of the jury is necessary before a finding of [Confrontation Clause rights] waiver may be made.” Mastrangelo, 693 F.2d at 273 (remanding for hearing); see also United States v. Thai, 29 F.3d at 814-15 (hearing held); United States v. Aguiar, 975 F.2d at 47 (same). Further, “in order to avoid the admission of facially unreliable hearsay, the district court should undertake a balancing of probative value against prejudicial effect in accordance with Fed.R.Evid. 403.” United States v. Thai, 29 F.3d at 814 (internal quotation marks omitted). At a Mastrangeb hearing, the government’s burden is (1) to show that the declarant’s unavailability was caused by the defendant’s misconduct, and (2) to establish that fact by a preponderance of the evidence. See Mastrangelo, 693 F.2d at 273.

In the present case, when the defense moved at the outset of the trial to exclude hearsay statements attributed to deceased declarants, the district court declined to hold a hearing. Rather, the court stated that “[t]he indictment establishes probable cause” ' (Miller Trial Tr. at 109), and that “in light of the finding inherent in the charging instrument, there is no need at this point to stop what we’re doing, bring the witnesses out, have a little mini-trial as to the culpability of Mr. Hale and Mr. Arroyo relative to these homicides” (id. at 114). The court stated that the Suarez and Rivera statements would be admitted “subject to connection” (id. at 112), indicated that it would review the matter using a clear-and-convincing-evidence standard (id. at 114), and warned that the government would be “proceed[ing] at its peril” (id. at 115).

This procedure did not comport with the requirements set forth in Mastrangeb. The district court’s reliance on the fact that the indictment charged defendants with the murders of Suarez and Rivera was misplaced. A grand jury’s indictment is based on probable cause, not on a preponderance of the evidence, and that body makes its judgment after an ex parte proceeding at which the target of its inquiry is normally not permitted to call or cross-examine witnesses. The grand jury’s conclusion, after such a proceeding, that there is probable cause to indict a defendant for murder is not an acceptable surrogate for a court’s finding, after a hearing at which both sides have the opportunity to be heard, that the defendant’s responsibility for that murder is established by a preponderance of the evidence. If the government cannot persuade the court that it is more likely than not true that the defendant to whom the declarant’s statement related was responsible for the declarant’s unavailability, the basis for a finding of waiver of confrontation rights will not have been established. In that event, further inquiry will be required into other possible bases for admissibility, which may or may not be found. Admitting the statements as the district court did here, “subject to connection,” is not an adequate substitute for a hearing, for if the connection is not forthcoming, valuable constitutional and trial rights may be lost.

Nonetheless, we conclude that, in the circumstances of the present case, the district court’s admission of the hearsay evidence without holding a Mastrangeb hearing was harmless error. At trial, there was ample evidence from Supreme Team members and associates as to the defendants’ procurement of the deaths of Suarez and Rivera. Further, there was an abundance of evidence that the Supreme Team made it a practice to murder members whose cooperation with authorities was suspected or who posed a threat to the gang’s operations. If presented with even a fraction of this evidence at a hearing, the district court could not fail to find it established by a preponderance of the evidence that defendants were responsible for the deaths of Suarez and Rivera. (See Parts I.A.2. and 3. above.) Further, any suggestion that defendants were prejudiced by the admission of the Rivera statement that “[h]e had killed some Colombians” and took “two keys of coke” from them is belied by the fact that each of the defendants charged with possession of the cocaine allegedly taken from the four unnamed Colombians slain in July 1989 was acquitted on that count. We conclude that the failure to hold a Mastrangeb hearing was harmless error.

E. Hunt’s Challenge to the Correction of the Indictment

Hunt contends that he is entitled to dismissal of count six of the superseding indictment (“indictment”), charging certain defendants with possession of the cocaine taken from Fernando Suarez and Pablo Perlaza when the latter were murdered. Hunt contends that although he was originally one of those named in count six, the district court dismissed that count against him and that it was therefore impermissible for the court to reinstate the count against him. The record does not support either Hunt’s factual premise or his legal conclusion.

At the outset of the Miller Trial, the government voluntarily moved to dismiss count 11, which charged Miller with distributing cocaine base within 1,000 feet of a public school, along with two racketeering acts, neither of which contained allegations against Hunt. The district court granted that motion. Count six was not mentioned and was not dismissed. The court instructed the government to prepare a redacted indictment for trial. In complying with that instruction, the government inadvertently omitted Hunt’s name from count six of the redacted document. The government apparently did not discover the omission until late in the trial. It moved to have the indictment corrected to restore Hunt’s name as an accused in count six, and the court granted that motion.

It is well established that “[u]nder the Fifth Amendment, a criminal defendant has the right to be tried only on the charges contained in the indictment returned by a grand jury.” United States v. Helmsley, 941 F.2d 71, 89 (2d Cir.1991), cert. denied, 502 U.S. 1091, 112 S.Ct. 1162, 117 L.Ed.2d 409 (1992). “An unconstitutional amendment of the indictment occurs when the charging terms are altered.... ” Id. However, the correction of merely technical errors, such as typographical or clerical mistakes, is permissible where it does not alter the essential substance of the charging terms. See, e.g., United States v. Willoughby, 27 F.3d 263, 266 (7th Cir.1994); United States v. Lake, 985 F.2d 265, 271 (6th Cir.1993)

The insertion of a defendant’s name into an indictment count, either by the government in providing a modified document, or by the court in instructing the jury, would plainly violate the Fifth Amendment if the grand jury had not included the defendant in that count. However, where the grand jury in fact indicted the defendant on the count in question, and there was neither a motion to dismiss him from that count nor an order dismissing him from that count, the inadvertent omission of his name from that count of the indictment is merely a clerical error. Where the error was discovered prior to the submission of the ease to the jury, the court’s decision to allow restoration of the defendant’s name to that count is not ground for reversal unless restoration caused the defendant unfair prejudice. In the present case, it is plain that there was no such prejudice.

First, it is undisputed that the grand jury did in fact indict Hunt on count six. It is also undisputed that in moving to dismiss part of the indictment the government specified the allegations it wished to dismiss, and count six was not mentioned. It cannot reasonably be argued that the government’s omission of Hunt’s name was anything but inadvertent. Nor could Hunt reasonably have believed that the government meant to refer to count six in its motion since none of the allegations the government sought to dismiss had been directed at Hunt.

Although Hunt claims that he was prejudiced by the omission and late correction of the indictment because he was lulled into not defending against count six at trial, the record belies that contention as well. When the matter was raised at Hunt’s sentencing, the district court asked Hunt’s attorney whether, knowing that his client had been named in count six, he had believed the government had abandoned that charge. Counsel’s response was as follows:

MR. SCHOENBACH [Attorney for Hunt]: I don’t know what I thought then, Judge. It’s been quite a long time. I noticed it immediately.
THE COURT: One would expect you noticed it, and I bet your client noticed it.
MR. SCHOENBACH: That’s right. It was something that I didn’t reveal to anyone, especially the government, to the close of the case, for obvious reasons.
Certainly, I can’t say to you that I didn’t prepare for confronting Count 6 immediately prior to the trial. I did, because Mr. Hunt was named in Count 6.

(Hunt Sentencing Transcript at 6.) The court thus summarized as follows:

THE COURT: Let me see if I understand.
You were a party to the conversation, and certainly present when the government announced that it was abandoning certain predicate acts, and that — and that for use at trial, a redacted indictment would be prepared.
Upon inspecting that redacted indictment, you noticed that Mr. Hunt’s name no longer appeared as a defendant, or no longer appeared at all in Count 6 as alleged. His name had been, in effect — had appeared to have been dropped or omitted.
You chose not to bring that — as you said, for obvious reasons you chose not to bring that to the attention of the court or the United States Attorney. At the same time, you chose to modify your theory of the defense, based upon what you perceive to be a decision by the United States Attorney, unannounced in court, to abandon this charge against your client.
MR. SCHOENBACH: I think that accurately states my position, Judge.

(Id. at 8-9.) Thus, contrary to any suggestion that Hunt believed that count six had been dismissed against him, it is plain that he did not bring the omission to the government’s attention precisely because he knew the omission of his name was inadvertent. In Hunt’s counsel’s own words, counsel “noticed [the omission] immediately” and did not “reveal [it] to anyone, especially the government, to the close of the case, for obvious reasons”; but he was prepared on count six immediately prior to trial “because Mr. Hunt was named in Count 6.” Having made a strategic decision to hope the government would not discover its error until too late for correction, any prejudice Hunt suffered by not defending against count six would be attributable only to his own tactical choice.

Further, the suggestion that Hunt did not defend against the allegations made in count six is hardly credible, for the substance of that count was expressly incorporated in another count against him. In both the unre-dacted and the redacted versions of the indictment, Hunt was charged with a RICO violation in count one, predicate act four of which was the very narcotics trafficking offense that was alleged in count six; the indictment’s description of that predicate act stated that the conduct in question was “as alleged in” count “6.” (Indictment count one, racketeering act four.) Thus, the need to defend against the conduct alleged in count six remained intact by reason of racketeering act four’s express incorporation of count six.

In an effort to distinguish count six from racketeering act four “as alleged in” count “6,” Hunt argues that racketeering act four’s statutory reference was solely to 21 U.S.C. § 841, and that he was thus accused of violating RICO only as a principal, whereas count six cited in addition 18 U.S.C. § 2, which imposes liability on a defendant as an aider and abetter. In fact, however, count one cited 18 U.S.C. § 2 with respect to the entire RICO count. Accordingly, Hunt’s attempted distinction is fallacious.

We conclude that the district court properly ruled that the government’s omission of Hunt’s name from count six of the redacted indictment was inadvertent and that the restoration of his name to that count caused Hunt no prejudice.

F. The Instructions on the RICO Count

RICO makes it “unlawful for any person employed by or associated with any enterprise engaged in, or the activities of which affect, interstate or foreign commerce, to conduct or participate, directly or indirectly, in the conduct of such enterprise’s affairs through a pattern of racketeering activity.” 18 U.S.C. § 1962(c). Defendants contend that, in light of two recent Supreme Court cases, the trial court’s instructions to the jury on the RICO count were erroneous with respect to both the participation and the interstate commerce elements. We agree as to the participation element, but we find no basis for reversal.

1. Level of Participation

At both trials, the district court instructed the jury, in part, in the following language:

The third element, which the government must prove beyond a reasonable doubt, is that the defendant conducted or participated in the affairs of the enterprise.
The terms “conduct” and “participate in the conduct” of an enterprise, include the performance of the acts, functions or duties that are necessary or helpful to the operation of the enterprise.
A person may participate in the conduct of an enterprise even though he had no part in the management or control of the enterprise and no share in any profits. But the participation must be wilful and knowing.

(Transcript of Coleman Trial (“Coleman Trial Tr.”) at 751-52; see Miller Trial Tr. at 6053-54.) Coleman and Raymond Robinson objected to this instruction at their trial, contending that it did not properly reflect the standard set by the Supreme Court in Reves v. Ernst & Young, 507 U.S. 170, 113 S.Ct. 1163, 122 L.Ed.2d 525 (1993) (“Reves ”). It does not appear that there was such an objection at the Miller Trial.

In Reves, in assessing the RICO liability of an outside accounting firm for racketeering activity carried on by its client, the Supreme Court addressed the question of “whether one must participate in the operation or management of the enterprise itself to be subject to liability under this provision.” Id. at 172, 113 S.Ct. at 1166. The Court answered the question in the affirmative, though noting that one may be liable for participating in the enterprise’s “operation” without being a member of its “upper management.” Id. at 184, 113 S.Ct. at 1172. As we observed in United States v. Thai,

the Reves Court concluded that “[i]n order to ‘participate, directly or indirectly, in the conduct of such enterprise's affairs,’ one must have some part in directing those affairs.”_ Nonetheless, while thus adopting what it called an “ ‘operation or management’ test,” ... and stating that one is liable under RICO only if he “participated in the operation or management of the enterprise itself,” ... the Court also said that “the word ‘participate’ makes clear that RICO liability is not limited to those with primary responsibility” ... and that “liability under § 1962(c) is not limited to upper management,”.... The Court observed that, in addition, within the meaning of § 1962(c), “[a]n enterprise is ‘operated’ ... also by lower-rung participants in the enterprise who are under the direction of upper management.”_ The Court declined to “decide in [Reves} how far § 1962(c) extends down the ladder of operation.”

United States v. Thai, 29 F.3d at 816 (quoting Reves, 507 U.S. at 179, 183, 184 & n. 9, 113 S.Ct. at 1170, 1172, 1173 & n. 9). In light of Reves, we have held that an instruction virtually identical to the one given in the present case was erroneous. See United States v. Viola, 35 F.3d 37, 41 (2d Cir.1994), cert. denied, 513 U.S. 1198, 115 S.Ct. 1270, 131 L.Ed.2d 148 (1995).

The failure of the district court to give an instruction that comports with the Reves standard, however, is not a basis for automatic reversal. If the defendants timely objected to the erroneous instruction, the error will not warrant reversal if, in light of the evidence introduced as to their roles, the error was harmless. See, e.g., United States v. Masotto, 73 F.3d 1233, 1238-39 (2d Cir.), cert. denied, - U.S.-, 117 S.Ct. 54, 136 L.Ed.2d 18 (1996); Napoli v. United States, 45 F.3d 680, 683-84 (2d Cir.) (convictions of defendants, who were “high up on the ‘ladder of operation,’ ” were unaffected by Reves error), cert. denied, 514 U.S. 1084, 115 S.Ct. 1796, 131 L.Ed.2d 724 (1995); see also Metromedia Co. v. Fugazy, 983 F.2d 350, 369 (2d Cir.1992) (error in RICO pattern instruction subject to harmless-error analysis), cert, denied, 508 U.S. 952, 113 S.Ct. 2445, 124 L.Ed.2d 662 (1993); United States v. Tillem, 906 F.2d 814, 824-25 (2d Cir.1990) (same). If there was no objection to the erroneous instruction, the instruction is reviewable on appeal only for “plain error,” that is, error that affected the defendant’s substantial rights. See Fed.R.Crim.P. 52(b); United States v. Thai, 29 F.3d at 816.

In United States v. Viola, in which the trial court instructed the jury, without objection, that “[a] person may participate in the conduct of an enterprise even though he had no part in the management or control of the enterprise and no share in any profits,” 35 F.3d at 41 (emphasis in original), we found the error plain as to defendant Michael Formisano. Viola and several others, including Formisano, had been charged with participating in a drug and stolen property importation and distribution ring. Formisano was a janitor who performed menial tasks for Viola, a coffee company proprietor, and the only evidence against Formisano was that on two occasions, at the direction of Viola, he had sold stolen beer and lamps and brought the proceeds to Viola. Although the government asserted that Formisano knew of the broader enterprise, we noted that he was “hardly even mentioned” in the trial evidence concerning the enterprise. Id. at 44. For example, the government’s year-long electronic surveillance did not reveal a single conversation between Formisano and other members of the conspiracy; and in their trial testimony, witnesses who had been “participants in the conspiracy ... never mentioned Formisano, much less indicated their familiarity with him.” Id. We noted that while Reves holds that liability may attach to “lower rung participants in the enterprise,” Reves, 507 U.S. at 184, 113 S.Ct. at 1172, Formisano “was not on the ladder at all, but rather, as Viola’s janitor and handyman, was sweeping up the floor underneath it.” United States v. Viola, 35 F.3d at 43. Given the dearth of evidence against Formisano, we reversed his RICO conviction outright, rather than remanding for a new trial before a properly instructed jury.

In the present ease, there was no such dearth of evidence; indeed, the evidence with respect to the defendants’ management or operating roles shows that the error here was entirely harmless. For example, the Supreme Team had scores of workers who were lower on its organizational ladder than Coleman and Raymond Robinson. Coleman had responsibility for groups of workers and sales operations at three Supreme Team drug locations; he was described by former Supreme Team member Trent Morris as one of the organization’s “lieutenant[s].” Raymond Robinson, whose tenure with the organization was limited and whose rank was somewhat lower than that of Coleman, nonetheless also participated in the Supreme Team’s operations at an important level: on wiretaps he was overheard arranging the gang’s purchase of cocaine; he acted as security during drug transactions and served as Miller’s personal bodyguard; he supervised the processing of cocaine into crack and delivered it to sales locations; and he participated in the gang’s move into rival territory. In light of this evidence, Coleman and Raymond Robinson plainly met the standard of participation required by Reves, and we conclude that the jury was not affected by the error in the court’s instructions. The erroneous instruction was harmless.

We reach the same result with respect to the defendants tried in the Miller Trial, whether or not they objected to the instruction, for the evidence was that each of the six defendants eventually convicted on the RICO count after that trial (Jimenez prevailed on his motion for acquittal on this count) had substantial responsibility for the management of, or discretion in the operation of, the Supreme Team’s operations. Miller was the leader; Arroyo was second-in-command. David Robinson helped supervise the drug operations; Tucker managed a retail spot and supervised a crew of workers. Hunt was Miller’s bodyguard, and Hale was a security guard; by the nature of their duties as providers of security, Hunt and Hale had discretion to take action without direction from those higher on the chain of command; and both had considerable responsibility for dealing with the Supreme Team’s perceived enemies. For example, when Rivera was targeted to be killed, Hunt shot him; when Rivera survived and was tracked down, Hale was one of the men who killed Rivera. It is plain that all six of these defendants had roles that met the standard of participation required by Reves. We conclude that the erroneous instruction was harmless and, a fortiori, was not plain error.

2. Nexus with Interstate Commerce

With respect to so much of RICO as reaches persons “employed by or associated with any enterprise engaged in, or the activities of which affect, interstate or foreign commerce,” 18 U.S.C. § 1962(c), the trial court initially instructed the jury, to the extent pertinent here, that “the government must prove beyond a reasonable doubt ... that the conduct of the enterprise affected interstate ... commerce,” that “[t]he defendants need not know that their acts would affect such commerce,” and that that effect “need not be substantial. Indeed, a minimal effect is sufficient.” (Coleman Trial Tr. at 755.) In response to a later inquiry from the jury, the court gave a similar supplemental instruction, and added that the government was required to show that “the activities of the enterprise, involved some at least minimum effect on interstate commerce. Those affairs, such as the purchasing of supplies from time to time, should you so find — gasoline, anything of the sort that you find satisfies the element of interstate commerce.” (Coleman Trial Tr. at 844.) Defendants contend that these instructions did not meet the standard set by the Supreme Court in United States v. Lopez, 514 U.S. 549, 115 S.Ct. 1624, 131 L.Ed.2d 626 (1995) (“Lopez ”). We disagree.

In Lopez, the Supreme Court considered Congress’s power to regulate the carrying of guns near schools. The Court concluded that the statute extended the federal government’s reach beyond the permissible boundaries of the Commerce Clause of the Constitution because the activity in question “ha[d] nothing to do with ‘commerce’ or any sort of economic enterprise” and therefore could not “be sustained under [the Court’s] cases upholding regulations of activities that arise out of or are connected with a commercial transaction, which mewed in the aggregate, substantially affects interstate commerce,” Lopez, 514 U.S. at 561, 115 S.Ct. at 1630-31 (emphasis added). The Court reiterated its longstanding view, however, that “ “where a general regulatory statute bears a substantial relation to commerce, the de minimis character of individual instances arising under that statute is of no consequence.’ ” Id. at 558, 115 S.Ct. at 1629 (quoting Maryland v. Wirtz, 392 U.S. 183, 197 n. 27, 88 S.Ct. 2017, 2024, 20 L.Ed.2d 1020 (1968) (emphasis in Lopez), overruled on other grounds, National League of Cities v. Usery, 426 U.S. 833, 96 S.Ct. 2465, 49 L.Ed.2d 245 (1976), in turn overruled by Garcia v. San Antonio Metropolitan Transit Authority, 469 U.S. 528, 105 S.Ct. 1005, 83 L.Ed.2d 1016 (1985)).

As the Lopez Court itself indicated, Lopez did not alter the principle that where the type of activity at issue has been found by Congress to have a substantial connection with interstate commerce, the government need only prove that the individual subject transaction has a de minimis effect on interstate commerce. See United States v. Genoa, 79 F.3d 1333, 1386-37 (2d Cir.1996) (Lopez “did not purport to overrule those cases that have upheld application of the Commerce Clause power to wholly intrastate activities”); see also United States v. Robertson, 514 U.S. 669, 670-72, 115 S.Ct. 1732, 1733, 131 L.Ed.2d 714 (1995) (per curiam) (reinstating RICO conviction where government had shown that the enterprise itself engaged in interstate commerce); Prayect v. United States, 101 F.3d 11, 14 (2d Cir.1996) (per curiam) (“The fact that certain intrastate activities within this class [of regulated activities concerning controlled substances], such as growing marijuana solely for personal consumption, may not actually have a significant effect on interstate commerce is therefore irrelevant.”); United States v. Leslie, 103 F.3d 1093, 1100 (2d Cir.) (same re money laundering), cert. denied, - U.S. -, 117 S.Ct. 1713, 137 L.Ed.2d 837 (1997).

Of especial importance to the present case, we have held that “[b]eeause narcotics trafficking represents a type of activity that Congress reasonably found substantially affected interstate commerce, the actual effect that each drug conspiracy has on interstate commerce is constitutionally irrelevant.” United States v. Genao, 79 F.3d at 1336. It follows that where, as here, the RICO enterprise’s business is narcotics trafficking, that enterprise must be viewed as substantially affecting interstate commerce, even if individual predicate acts occur solely within a state. We conclude that there was no error in the court’s instructions on the interstate commerce element.

G. Miller’s RICO, Conspiracy, and CCE Convictions

Miller, who was convicted of, inter alia, racketeering, narcotics conspiracy, and continuing criminal enterprise (“CCE”), challenges his RICO conviction by contending principally that (1) criminal facilitation of murder is not a proper RICO predicate; (2) the evidence was insufficient to establish either that he facilitated the murder in question or that there was a nexus between the murder facilitation and the Supreme Team enterprise; and (3) the court’s calculation of his sentence under the federal Sentencing Guidelines (“Guidelines”) with respect to that aspect of his RICO conviction was erroneous. He also contends that, under the Double Jeopardy Clause, he could not properly be convicted of both narcotics conspiracy and CCE. We find merit only in the last contention.

1. Facilitation of Murder as Racketeering Activity

RICO defines “racketeering activity” to include “any act ... involving murder ... which is chargeable under State law and punishable by imprisonment for more than one year.” 18 U.S.C. § 1961(1)(A). The RICO count of the indictment alleged that Miller had engaged in a number of predicate acts, including the following:

In or about the summer of 1987, within the Eastern District of New York, the defendant GERALD MILLER, a/k/a/ “Prince”, believing it probable that he was rendering aid to a person who intended to commit murder, knowingly and intentionally engaged in conduct which provided such person with means and opportunity for the commission of that crime, and which in fact aided in the commission of that crime, namely, the August 6, 1987 murder of Isaac Bolden, a/k/a “Just Me”, in violation of New York Penal Law Sections 115.05 and 20.00.

(Indictment count one, racketeering act 10.) Miller argues that criminal facilitation cannot be viewed as an act involving murder because murder is an intentional and violent crime, and the New York Penal Law neither requires that the facilitator have intended that the underlying crime be committed nor classifies facilitation itself as a violent felony. This sophistic argument is far from the mark.

RICO provides that “racketeering activity” refers to any of a number of federal or state crimes. See 18 U.S.C. § 1961(1). Its references to federal law, see id. § 1961(1)(B)-(F), are specific, citing various statutes by name or by United States Code title and section; its references to state law, see id. § 1961(1)(A), are not to chapter and verse but are instead “generic,” “serving] ... to identify generally the kind of activity made illegal by the federal statute,” United States v. Bagaric, 706 F.2d 42, 62-63 (2d Cir.) (internal quotation marks omitted), cert. denied, 464 U.S. 840, 104 S.Ct. 134, 78 L.Ed.2d 128 (1983). RICO was not intended to incorporate “the elements of the penal codes of the various states where acts of racketeering occurred,” id. at 62, but only to provide general substantive frames of reference.

By defining racketeering activity to include “any act ... involving murder,” 18 U.S.C. § 1961(1)(A) (emphasis added), Congress made it clear that the RICO defendant’s act need not be murder, so long as it directly concerns murder. See generally Webster’s Third New International Dictionary 1191 (1976) (defining “involve” to mean, inter alia, “concern directly”). Thus, in United States v. Ruggiero, 726 F.2d 913 (2d Cir.), cert. denied, 469 U.S. 831, 105 S.Ct. 118, 83 L.Ed.2d 60 (1984), noting that Congress intended that RICO be liberally construed to effectuate its remedial purposes, we ruled that “conspiracy to murder in violation of New York’s Penal Law ... is an ‘act involving ’ murder and therefore may constitute ‘racketeering activity’ within the meaning of the RICO statute.” Id. at 919 (emphasis added).

The New York Penal Law provisions cited in the racketeering act 10 allegation against Miller are §§ 115.05 and 20.00. Section 115.05 provides that a defendant is guilty of criminal facilitation, a Class C felony, “when, believing it probable that he is rendering aid to a person who intends to commit a class A felony [e.g., murder, see N.Y. Pen. L. § 125.25 (McKinney 1987)], he engages in conduct which provides such person with means or opportunity for the commission thereof and which in fact aids such person to commit such class A felony.” N.Y. Pen. L. § 115.05 (McKinney 1987). A Class C felony such as facilitation is punishable by imprisonment for 1-15 years. See N.Y. Pen. L. §§ 70.00 (McKinney 1987). Section 20.00 imposes liability on one who, “with the mental culpability required for the commission thereof, ... intentionally aid[ed]” the perpetrator to commit the substantive offense. Id. § 20.00 (McKinney 1987). Such a person is punishable as a principal. See id. Practice Commentary.

Insofar as the underlying substantive state offense is murder, we have no difficulty in concluding that the accessorial offenses described in these state-law provisions “involve” murder within the meaning of RICO. Nor have we any difficulty in concluding that the conduct at issue here involved murder. Where a defendant is asked for and provides information that he reasonably knows is meant to enable the inquirer to commit a murder, he has plainly performed an act that directly concerns murder. We conclude that the criminal facilitation charge against Miller was a proper RICO predicate.

2. The Sufficiency of the Evidence of Facilitation and Nexus

To establish criminal facilitation of murder as a RICO predicate act, the government is required to prove not only that the defendant committed the acts described in the facilitation statute, discussed above, but also that there was a nexus between the predicate act and the criminal enterprise. See 18 U.S.C. § 1961(5) (1994); United, States v. Thai, 29 F.3d at 815; United States v. Simmons, 923 F.2d 934, 951 (2d Cir.), cert. denied, 500 U.S. 919, 111 S.Ct. 2018, 114 L.Ed.2d 104 (1991). “That relationship is satisfied if the offense was related to the enterprise’s activities, whether or not it was in furtherance of those activities, or if the defendant was enabled to commit the offense solely by virtue of his position in the enterprise.” United States v. Thai, 29 F.3d at 815; see, e.g., United States v. Locascio, 6 F.3d 924, 943 (2d Cir.1993), cert. denied, 511 U.S. 1070, 114 S.Ct. 1646, 128 L.Ed.2d 365 (1994); United States v. Simmons, 923 F.2d at 951; United States v. Robilotto, 828 F.2d 940, 947-48 (2d Cir.1987), cert. denied, 484 U.S. 1011, 108 S.Ct. 711, 98 L.Ed.2d 662 (1988); United States v. LeRoy, 687 F.2d 610, 617 (2d Cir.1982), cert. denied, 459 U.S. 1174, 103 S.Ct. 823, 74 L.Ed.2d 1019 (1983).

Miller, arguing that he did not know Nichols meant to kill Isaac Bolden and that Nichols already knew where Bolden’s mother lived, contends that the government failed to prove that Miller’s furnishing the mother’s address actually facilitated Isaac Bolden’s murder. He also argues that even if the government proved facilitation, it failed to prove that Miller’s conduct was related to the business of the Supreme Team, rather than merely a personal favor to Nichols. In challenging the sufficiency of the evidence to support his conviction, a defendant “bears a heavy burden.” United States v. Matthews, 20 F.3d 538, 548 (2d Cir.1994). In reviewing such a challenge, we must view the evidence in the light most favorable to the government, see, e.g., Glasser v. United States, 315 U.S. 60, 80, 62 S.Ct. 457, 469, 86 L.Ed. 680 (1942); United States v. Gordon, 987 F.2d 902, 906 (2d Cir.1993); United States v. Sumnicht, 823 F.2d 13, 15 (2d Cir.1987), crediting all inferences that could have been drawn in the government’s favor, see, e.g., United States v. Gordon 987 F.2d at 906; United States v. Bagaric, 706 F.2d at 64. Pieces of evidence must be viewed not in isolation but in conjunction, see, e.g., United States v. Matthews, 20 F.3d at 548; United States v. Brown, 776 F.2d 397, 403 (2d Cir.1985), cert. denied, 475 U.S. 1141, 106 S.Ct. 1793, 90 L.Ed.2d 339 (1986); and where there are conflicts in the testimony, we must defer to the jury’s resolution of the weight of the evidence and the credibility of the witnesses, see, e.g., United States v. Stratton, 779 F.2d 820, 828 (2d Cir.1985), cert. denied, 476 U.S. 1162, 106 S.Ct. 2285, 90 L.Ed.2d 726 (1986); United States v. LeRoy, 687 F.2d at 616. We must affirm the conviction so long as, from the inferences reasonably drawn from the record as a whole, the jury might fairly have concluded that the defendant was guilty beyond a reasonable doubt, see, e.g., United States v. Skowronsky 968 F.2d 242, 247 (2d Cir.1992); United States v. Sumnicht, 823 F.2d at 15. The weight of the evidence is a matter for argument to the jury, not a ground for reversal on appeal. See, e.g., United States v. Roman, 870 F.2d 65, 71 (2d Cir.), cert. denied, 490 U.S. 1109, 109 S.Ct. 3164, 104 L.Ed.2d 1026 (1989). Miller has failed to carry his burden.

The evidence at trial included proof that the Nichols organization had been robbed of a substantial sum by the Bolden brothers and that Nichols asked Miller for assistance in locating them. Supreme Team security chief Ernesto Piniella testified that Miller asked him to get addresses for the Boldens and their families; Piniella contacted Ina McGriff and Ronnie Younger, the gang’s accomplices in the Parole Division, who obtained the information. Notes in the two women’s handwriting were found in an apartment used by the Supreme Team, showing the addresses of, inter alios, Isaac Bolden and his mother. Though there may have been some question at trial as to which of the two women provided which items of information, there was no doubt that all of the information was provided at the behest of Miller. Piniella testified that Miller then passed the information on to Nichols. Thereafter, Isaac Bolden was shot near his mother’s house. The matter of whether the information provided by Miller actually.assisted the murder if Nichols already knew the mother’s address was merely a matter for argument to the jury. Nichols himself was in jail at the time of the murder, and the jury could easily infer that his organization needed and made use of the assistance that was requested and obtained from Miller.

Miller’s professed lack of belief that Nichols intended to murder Bolden was also a matter for argument to the jury. The evidence at trial included proof that Miller knew of Nichols’s view that the Boldens had stolen from Nichols’s organization; that the Supreme Team itself had carried out numerous murders for similar transgressions; and that Miller knew from his extensive dealings with Nichols that the Nichols organization was as violent as the Supreme Team. Ina McGriff testified that when, having furnished the Bol-den addresses, she saw a newspaper article reporting Isaac Bolden’s murder, she asked Miller whether “this was the same Bolden that I had given him the information about,” and Miller “just smirked.” (Miller Trial Tr. at 1816.) The jury could easily conclude that Miller had considered it likely that Nichols would order the murder of Isaac Bolden once Miller provided the information as to where Bolden might be located.

Finally, Miller’s contention that even if he did facilitate the murder, he did so as a personal favor to Nichols, rather than in connection with the Supreme Team enterprise, could also easily be rejected by the jury. There was a business relationship between the Supreme Team and Nichols’s organization, which supplied the Supreme Team with cocaine. Clearly the jury was entitled to infer that Miller aided Nichols at least in part to preserve and enhance good will with one of the Supreme Team’s suppliers. Moreover, even had there been no business relationship with Nichols to preserve or cultivate on behalf of the Supreme Team, the jury could have inferred that Miller had access to the public employees who could obtain the needed addresses by reason of the facts that those corrupt employees were on the payroll of the Supreme Team and he was the organization’s leader.

In sum, the evidence was more than sufficient to support the jury’s conclusion that Miller criminally facilitated the murder of Isaac Bolden and did so in connection with the Supreme Team criminal enterprise.

3. RICO Sentencing

In determining Miller’s sentence for his RICO conviction, the district court looked to the Guidelines offense level for aiding and abetting first-degree murder, see Guidelines §§ 2X2.1, 2Al.l(a), which prescribed a sentence of life imprisonment. Miller challenges the court’s use of the aiding-and-abetting guideline, arguing that since the state offense of murder facilitation does not require an intent that a murder occur, see N.Y. Pen. L. § 115.10 (McKinney 1987) (“It is no defense to a prosecution for criminal facilitation that ... [t]he defendant himself ... did not act with the intent” required for the commission of the underlying offense), aiding and abetting murder has a higher scienter requirement than facilitation of murder and hence was an inappropriate frame of reference. We disagree.

For a defendant convicted of a RICO offense in violation of 18 ' U.S.C. § 1962, the Guidelines base offense level is the higher of 19 or the offense level that would be applicable to the defendant’s underlying racketeering activities. See Guidelines § 2E1.1. The commentary to § 2E1.1. states that “[i]f the underlying conduct violates state law, the offense level corresponding to the most analogous federal offense is to be used.” Id. Application Note 2; see also Guidelines § 2X5.1 (for an offense “for which no guideline expressly has been promulgated,” sentencing court must “apply the most analogous offense guideline”; if there is no analogous guideline, the court is to proceed with “due regard for the relationship of the sentence imposed to sentences prescribed by guidelines applicable to similar offenses and offenders, and to the applicable policy statements of the Sentencing Commission,” 18 U.S.C. § 3553(b)). Since the determination of an analogous guideline “involves the application of a guideline to the facts of a case, ... 18 U.S.C. § 3742(e) mandates that we give ‘due deference’ to such applications by the district court, rather than review them de novo.” United States v. Cefalu, 85 F.3d 964, 968 n. 6 (2d Cir.1996). “A sentence imposed for an offense for which there is no applicable sentencing guideline will only be reversed if it is plainly unreasonable.” Id. at 966 (citing 18 U.S.C. § 3742(e)(4)).

In the present case, the district court noted the substantive difference between criminal facilitation, described in New York’s § 115.05, and the federal offense of aiding and abetting; but it found that aiding and abetting was the closest offense dealt with by the Guidelines and was especially close to the offense described in New York’s § 20.00:

[0]n the surface of it intending to murder someone is a different crime than facilitating the murder without any intention yourself of killing the victim. However, if you’re talking about which guideline most closely resembles the offense of conviction, given the fact that there was charged not only the facilitation but also violation of Section 20 of the New York Penal Law, which is virtually [the same as our] aiding and abetting, I think .... [t]he guideline that most closely resembles the offense of conviction in this case, given the facts of this case and the level of Mr. Miller’s knowledge relative to Bolden, is the aiding and abetting of a murder.

(Miller Sentencing Transcript at 15.)

We can see no basis on which to disturb the district court’s conclusion that, on the facts of this case, aiding and abetting provided the most appropriate analogy.

4. The Overlapping Convictions for CCE and Conspiracy

Finally, Miller contends that the district court erred in entering a judgment of conviction for conspiracy to distribute narcotics in violation of 21 U.S.C. § 846, as that conspiracy was a lesser included offense of conducting a continuing criminal enterprise in violation of 21 U.S.C. § 848, of which he was also convicted. He contends that convicting him on both counts constitutes multiple punishment for the same offense, which violates the Double Jeopardy Clause of the Fifth Amendment. Given the Supreme Court’s recent decision in Rutledge v. United States, - U.S. -, 116 S.Ct. 1241, 184 L.Ed.2d 419 (1996), ruling that “[a] guilty verdict on a § 848 charge necessarily includes a finding that the defendant also participated in a conspiracy violative of § 846; conspiracy is therefore a lesser included offense of CCE,” id. at-, 116 S.Ct. at 1250, the government concedes, and we agree, that Miller’s conviction for narcotics conspiracy should be reversed, and that count of the indictment against him should be dismissed.

Although the former practice of this Court, when a defendant had been convicted of both offenses, was to instruct the district courts to “combine” the “conviction[ ] on the lesser offense[ ] ... with the conviction on the greater offense,” United States v. Osorio Estrada, 751 F.2d 128, 135 (2d Cir.1984), modified on reh’g on other grounds, 757 F.2d 27 (2d Cir.), cert, denied, 474 U.S. 830, 106 S.Ct. 97, 88 L.Ed.2d 79 (1985), leaving the defendant convicted of two offenses but punished for only one, the Supreme Court in Rutledge instructed that instead, one of the convictions must be dismissed, see - U.S. at- -, 116 S.Ct. at 1250-51 (remanding for dismissal of one of the counts). Accordingly, we remand for the district court to dismiss the narcotics conspiracy count against Miller.

Miller also argues that his CCE conviction too must be set aside because the narcotics conspiracy was an impermissible predicate for CCE. We reject that contention. A lesser included § 846 conspiracy may serve as a predicate offense for a § 848 CCE conviction. See United States v. Young, 745 F.2d 733, 748-52 (2d Cir.1984), cert. denied, 470 U.S. 1084, 105 S.Ct. 1842, 85 L.Ed.2d 142 (1985). The decision in Rutledge did not purport to alter this principle. In Rutledge itself, the § 846 conspiracy was a predicate for the CCE count, see - U.S. at-n. 2, 116 S.Ct. at 1244 n. 2, and that Court remanded for dismissal of only one of the two convictions, id. at-, 116 S.Ct. at 1250-51. Accordingly, the CCE conviction is affirmed.

H. Other Contentions

Defendants’ other contentions include challenges to a variety of procedural decisions, evidentiary rulings, and sentencing calculations. None of these contentions has merit; only the following warrant discussion.

1. Severance

Tucker, Hale, Jimenez, and David Robinson contend that the district court erred in denying their motions for severance of their trials from the trial of Miller, Arroyo, and Hunt, and they contend that they were denied a fair trial because of prejudicial spillover from the evidence of their codefendants’ acts of violence. These contentions are meritless.

There is a preference, in the federal system, that defendants who have been indicted together be tried jointly. See Zafiro v. United States, 506 U.S. 534, 537, 113 S.Ct. 933, 936, 122 L.Ed.2d 317 (1993). The district court should grant a motion for severance “only if there is a serious risk that a joint trial would compromise a specific trial right of the moving defendant or prevent the jury from making a reliable judgment about guilt or innocence.” United States v. Rosa, 11 F.3d 315, 341 (2d Cir.1993), cert. denied, 511 U.S. 1042, 114 S.Ct. 1565, 128 L.Ed.2d 211 (1994). “Evidence at the joint trial of alleged coconspirators that, because of the alleged conspiratorial nature of the illegal activity, would have been admissible at a separate trial of the moving defendant is neither spillover nor prejudicial....” Id.) see United States v. Villegas, 899 F.2d 1824, 1347-48 (2d Cir.), cert. denied, 498 U.S. 991, 111 S.Ct. 535, 112 L.Ed.2d 545 (1990); United States v. Bari, 750 F.2d 1169, 1178 (2d Cir.1984), cert. denied, 472 U.S. 1019, 105 S.Ct. 3482, 87 L.Ed.2d 617 (1985). A defendant challenging the denial of his severance motion thus bears a heavy burden. “In order to secure a reversal, he must show prejudice so severe that his conviction constituted a miscarriage of justice ... and that the denial of his motion constituted an abuse of discretion....” United States v. Rosa, 11 F.3d at 341. Indeed, we have described the denial of a severance motion as “virtually unreviewable.” United States v. Friedman, 854 F.2d 535, 563 (2d Cir.1988) (internal quotation marks omitted), cert. denied, 490 U.S. 1004, 109 S.Ct. 1637, 104 L.Ed.2d 153 (1989).

In the present case there was no abuse of discretion in the court’s refusal to allow Tucker, Hale, Jimenez, and David Robinson to be tried separately from Miller, Arroyo, and Hunt. All seven were indicted on the conspiracy and racketeering counts, and thus, the evidence of the workings of the Supreme Team and its violent acts would have been admissible against all of these defendants even if each had been tried separately.

Moreover, the district court gave limiting instructions in order to deter any potential spillover. At the outset, the court instructed the jury that “[t]here’s no group culpability here” (Miller Trial Tr. at 22); in its final charge, the court told the jury, “you must consider the case against each defendant on each charge separately. In effect, we have ... seven separate trials that have taken place before you” (id. at 6037). The verdicts indicate that the jury heeded these instructions and painstakingly assessed the evidence against each defendant individually. For example, all defendants except David Robinson were acquitted on at least one count, some were acquitted on several counts, and the jury returned a different verdict with respect to each of the defendants who challenges the severance denial. We see no miscarriage of justice here.

2. David Robinson’s Postr-Arrest Statement

At trial, the government introduced a postarrest statement by David Robinson “that [Robinson] wasn’t a big guy like Fat Cat [Lorenzo Nichols], he hadn’t hurt anybody, he had just sold some drugs to take care of his children.” (David Robinson Suppression Transcript at 14.) Robinson contends that the district court should have granted his pretrial motion to suppress that statement on the ground that it was the product of an impermissible interrogation. In light of the record at the hearing on Robinson’s suppression motion, this contention is meritless.

A person in custody is entitled to Miranda warnings prior to official interrogation. See, e.g., Miranda v. Arizona, 384 U.S. 436, 444, 86 S.Ct. 1602, 1612, 16 L.Ed.2d 694 (1966). Once an accused has unequivocally invoked his right to counsel, interrogation, see generally Rhode Island v. Innis, 446 U.S. 291, 300-01, 100 S.Ct. 1682, 1689-90, 64 L.Ed.2d 297 (1980), is to cease. See, e.g., Davis v. United States, 512 U.S. 452, 458, 114 S.Ct. 2350, 2354, 129 L.Ed.2d 362 (1994); Edwards v. Arizona, 451 U.S. 477, 484-85, 101 S.Ct. 1880, 1884-85, 68 L.Ed.2d 378 (1981). An agent’s statement informing an arrestee “that any cooperation would be brought to the attention of the Assistant United States Attorney constitute^] ‘interrogation’” if the statement was “unsolicited” by the arrestee. United States v. Montana, 958 F.2d 516, 518 (2d Cir.1992); see United States v. Johnson, 812 F.2d 1329, 1331 (11th Cir.1986). If there is questioning after the arrestee inyokes his right to counsel, his responses may be admitted in evidence “only on finding that [the arrestee] (a) initiated further discussions with the police, and (b) knowingly and intelligently waived the right he had invoked.” Smith v. Illinois, 469 U.S. 91, 95, 105 S.Ct. 490, 492, 83 L.Ed.2d 488 (1984) (per curiam). If, after receiving Miranda warnings and invoking the right to counsel, “the accused himself initiates further communication, exchanges, or conversations with the police,” Edwards v. Arizona, 451 U.S. at 484-85, 101 S.Ct. at 1884-85 those unsolicited statements are admissible. “Any statement given freely and voluntarily without any compelling influences is, of course, admissible in evidence.” Miranda, 384 U.S. at 478, 86 S.Ct. at 1629.

In the present case, David Robinson contends that his statement admitting his involvement in selling drugs was the product of interrogation by FBI Special Agent David Recame, urging him to cooperate with the government. In light of Recame’s testimony at the suppression hearing, Robinson’s contention is doubly flawed because (a) the agent’s reference to cooperation, which occurred prior to the giving of Miranda warnings, was not unsolicited, and (b) the statement of whose admission Robinson complains was made only after he had received Miranda warnings and was not made in response to any post-Miranda warning questions or statements. Recame testified to the following pertinent sequence. David Robinson was arrested; Recame asked him pedigree questions, including the names of his employer, wife, and children. In answering the pedigree questions, Robinson “bemoaned the fact that he was under arrest and that he had five children to take care of, that it would be difficult for the children and his wife without him [sic] being present,” and asked what the charge against him was and what the possible penalties were. (David Robinson Suppression Transcript at 11.) The agents told him his punishment could be 10 years to life imprisonment if the judge so sentenced him, but that he might obtain a lesser sentence by cooperating with the government. Robinson made no statement in response, and the agents did not pursue the matter. Thereafter, Robinson was given his Miranda warnings; Robinson stated that he understood, and he invoked his rights by shaking his head to indicate that he did not wish to answer questions. There was no further questioning or comment on the case by the agents. After several minutes, Robinson blurted out “that he wasn’t a big guy like Fat Cat, he hadn’t hurt anybody, he had just sold some drugs to take care of his children.” (Id. at 14.)

The district court was entitled to credit the testimony of Recame, in preference to the testimony offered by David Robinson who denied having made any statement whatever about being involved in drugs. Given the sequence described by Recame, the agents’ pre-Miranda warning statement that Robinson could help himself by cooperating did not constitute interrogation since it was not unsolicited but was made in response to Robinson’s own question as to what penalties he faced. In any event, Robinson’s admission to selling drugs was made only after Miranda warnings had been administered and was made without any p os t-Miratida-warning interrogation. As a statement initiated solely by Robinson, it was admissible.

3. The Government’s Failure To Produce a Document

At trial, the government introduced a document, seized by NYPD officers during a search of David Robinson’s residence, which contained detailed records of drugs and money. The government concedes that it failed to provide the document to Robinson prior to trial as required by Fed.R.Crim.P. 16. David Robinson contends that the trial court should have excluded the document and that its failure to do so entitles him to a new trial. We disagree.

When the government has failed to comply with Rule 16, the district court has broad discretion to determine what remedial action, if any, is appropriate. See Fed. R.Crim.P. 16(d)(2) (court “may order [the government] to permit the discovery or inspection, grant a continuance, or prohibit the [government] from introducing evidence not disclosed, or it may enter such other order as it deems just under the circumstances”). The court’s determination will not be set aside absent abuse of discretion. United States v. Giraldo, 822 F.2d 205, 212 (2d Cir.), cert. denied, 484 U.S. 969, 108 S.Ct. 466, 98 L.Ed.2d 405 (1987). A “reversal will only be warranted if the nondisclosure results in substantial prejudice to the defendant.” United States v. Sanchez, 912 F.2d 18, 21 (2d Cir.1990). We have described “substantial prejudice” in the Rule 16 context as “mean[ing] more than that the statement was damaging to the defendant: the defendant must demonstrate that the untimely disclosure of the statement adversely affected some aspect of his trial strategy.” United States v. Adeniji, 31 F.3d 58, 64 (2d Cir.1994).

In the present case, the government disclosed the document in question to David Robinson shortly before calling its final direct-case witnesses in the two-month-long Miller Trial. When Robinson moved to exclude the document, the government explained to the court that the government had only belatedly realized that it did not have the document in its possession and that the government had then obtained the document pursuant to a subpoena to the NYPD property clerk and disclosed it to Robinson. There seems to have been no dispute that the government’s nondisclosure to Robinson was the inadvertent consequence of the belatedness of the subpoena. (See Miller Trial Tr. at 3609 (“MR. STEIN [Attorney for David Robinson]: Of course, they didn’t get it themselves until the other day.”)) When Stein was asked what prejudice Robinson claimed from the late disclosure, he stated that he was deprived of the opportunity to consult handwriting and fingerprint experts with respect to the document. The court indicated that this was not an adequate demonstration of prejudice since Robinson could present such expert testimony during the defense case, that the court would entertain a request for a continuance if needed, and that in the absence of prejudice the court would admit the document. We see no abuse of discretion in this ruling.

In this Court, David Robinson states that the belated disclosure of the document adversely affected his trial strategy of arguing that he could not have been a member of a drug gang because he was so poor; he contends that the document’s references to money refuted his claim of penury. We are unpersuaded. Robinson plainly was not prevented from pursuing his strategy of claiming destitution. He introduced a photograph of the poorly furnished basement apartment he shared with his girlfriend and their five children, showing graphically that he lived in relative squalor, and he called an FBI agent in his defense ease to testify to that effect. Moreover, the government in no way suggested that Robinson had kept the money listed in the document seized from his apartment. Rather, the government’s evidence showed that the Supreme Team lieutenants turned their sales revenue over to Miller, who then paid them as he saw fit. We conclude that David Robinson was not substantially prejudiced by the delay in his receipt of the document.

4. Evidence Concerning Hale’s Prior Narcotics Arrest

In 1990, Hale was arrested by NYPD officers and made statements that the government proposed to introduce at the Miller Trial. The district court initially ruled that the evidence would be admitted against Hale but must be redacted to exclude references to his codefendants. Eventually, the court ruled that the statements would not be admitted at all. Defendants contend, however, that they were prejudiced by the timing of the court’s decision and trial events prior to the ultimate exclusion of the statements.

Hale claims that he suffered prejudice because, inter alia, his attorney, in anticipation of the government’s introduction of the statements, had elicited testimony from NYPD Lieutenant Robert Crowe that Hale was a narcotics addict, planning to argue that Hale was therefore incapable of making such statements. Even if we credited the possibility that Hale could be prejudiced by evidence of his drug use, given the far more serious charges against him, Crowe’s testimony as to such use was immaterial because Julio Hernandez and Ernesto Piniella testified about Hale’s drug addiction. Hale also claims that he was prejudiced because his attorney elicited testimony concerning the existence of outstanding warrants for his arrest. However, that evidence could hardly have had an impact since Piniella and Trent Morris testified that they had been in jail with Hale.

Nor is there merit in the contention of the other defendants that their rights under the Confrontation Clause, see Bruton v. United States, 391 U.S. 123, 137, 88 S.Ct. 1620, 1628, 20 L.Ed.2d 476 (1968), were violated by NYPD Detective William Ryan’s testimony that he had been advised, after Hale’s arrest, that an arrestee wanted to provide information concerning the Supreme Team. After Ryan’s mention of the Supreme Team, the district court promptly instructed the jury to ignore testimony from Ryan concerning any statement from Hale about the Supreme Team. And eventually, as indicated above, the court excluded Hale’s statements. Ryan’s mere testimony that an arrestee had made statements about the Supreme Team, in the absence of any testimony as to the substance of the statements, did not violate defendants’ rights under the Confrontation Clause.

5. Admissibility of Evidence of Violent Acts

At the Miller Trial, the government introduced evidence of numerous killings by the Supreme Team security force, including evidence that Hale had killed a person named “Dre” and that various others had killed several other persons who were considered to be threats to the Team’s operations. Defendants contend that since these murders were not alleged in the indictment, evidence concerning them should have been excluded pursuant to Fed.R.Evid. 404(b). We disagree because the government did not offer this as evidence of “other” acts within the meaning of Rule 404(b) but rather offered it as proof of the existence of the RICO enterprise alleged in the indictment which used such acts of violence in furtherance of its narcotics conspiracy. Where, as here, the indictment contains a conspiracy charge, “uncharged acts may be admissible as direct evidence of the conspiracy itself.” United States v. Thai, 29 F.3d at 812. “An act that is alleged to have been done in furtherance of the alleged conspiracy ... is not an ‘other’ act within the meaning of Rule 404(b); rather, it is part of the very act charged.” United States v. Concepcion, 983 F.2d 369, 392 (2d Cir.1992), cert. denied, 510 U.S. 856, 114 S.Ct. 163, 126 L.Ed.2d 124 (1993).

The district court concluded that the proof of these murders was relevant to show the existence and nature of the enterprise and the conspiracy and that the probative value of the evidence was not substantially outweighed by its potential for unfair prejudice, see Fed.R.Evid. 403. Such an assessment is reviewable only for abuse of discretion, see, e.g., United States v. Thai, 29 F.3d at 813, and we see no abuse of discretion here. Nor could it be inferred that the jury made improper use of the evidence of the uncharged killings to convict defendants randomly of all of the violent acts alleged in the indictment, for the jury refused to find that defendants had killed the four unidentified Colombian suppliers as alleged in the indictment. The evidence of the uncharged acts of murder was properly admitted.

6. The Claims of Improper Summation

Defendants claim that they are entitled to a new trial because of improper statements by the government in summation. Defendants tried in the Miller Trial contend that the government improperly bolstered the testimony of cooperating witnesses by implying that the trial judge would have intervened if those witnesses were not telling the truth. Coleman and Raymond Robinson contend that the AUSA in their trial improperly expressed belief in their guilt when he concluded his rebuttal summation with the statement, “And those two fish right there got. caught and they’re guilty on all counts” (Coleman Trial Tr. at 713). We find no basis for reversal.

It is a given that a prosecutor may not personally vouch for the truth of the government’s evidence. See, e.g., United States v. Modica, 663 F.2d 1173, 1178-79 (2d Cir.1981) (collecting cases), cert. denied, 456 U.S. 989, 102 S.Ct. 2269, 73 L.Ed.2d 1284 (1982). We have also held it “clearly improper” for the government to state that “ ‘[the trial judge] knows [the cooperating witness] is telling the truth,’ ” United States v. Melendez, 57 F.3d 238, 240 (2d Cir.1995) (quoting prosecutor), although we have indicated that it is hot impermissible for the government to state “that some time in the future the Judge will have to consider the witness’s credibility” because “sentencing [of the witness] would depend on [the trial judge]’s view of his credibility,” id. at 241. In analyzing a claim of prosecutorial misconduct, we assess “the severity of the misconduct, the curative measures taken by the court, and the certainty of conviction absent the misconduct.” United States v. Rivera, 22 F.3d 430, 437 (2d Cir.1994). “Only prosecutorial conduct so severe and significant as to result in the denial of ... a fair trial will lead to reversal.” United States v. Orena, 32 F.3d 704, 717 (2d Cir.1994) (internal quotation marks omitted). Furthermore, we are “reluctant to reverse where the transgression was isolated.” United States v. Parker, 903 F.2d 91, 98 (2d Cir.), cert. denied, 498 U.S. 872, 111 S.Ct. 196, 112 L.Ed.2d 158 (1990). An acquittal by the jury on some counts may be evidence that the trial was not unfair. See United States v. Myerson, 18 F.3d 153, 163 (2d Cir.), cert. denied, 513 U.S. 855, 115 S.Ct. 159, 130 L.Ed.2d 97 (1994).

At the Miller Trial in the present case, the AUSA, unlike the prosecutor in Melendez, did not tell the jury that the trial judge knew the cooperating witnesses were telling the truth; rather she stated that the witnesses would be sentenced by the judge, who might be lenient if the judge believed their testimony. For example, the AUSA stated that Julio Hernandez’s “sentence is up to Judge Dearie, who sat here just as you did and watched him testify for days on end. If Julio Hernandez gets one day less than 20 years, it will be because Judge Dearie has determined at the appropriate time that is an appropriate sentence.” (Miller Trial Tr. at 5270-71; see also id. at 5275 (similar statement with respect to Ina McGriff).) There apparently was no objection to these statements in the district court, and we do not see that there was error, much less plain error.

The AUSA’s statement at the Coleman Trial that the two defendants tried there were “guilty on all counts” came after extensive discussion of the evidence against Coleman and Raymond Robinson and of the defense theory of the case. That discussion included the AUSA’s urging the jury “to decide this case based on the evidence in this case, based upon these tapes, based upon the testimony, based upon the video, based upon the photographs” (Coleman Trial Tr. at 695). We doubt that the statement that Coleman and Raymond Robinson were “guilty on all counts” would have been viewed by the jury as more than an exhortation to find them guilty based on the evidence.

In any event, given the overwhelming evidence of guilt, and given the jury’s acquittal of all defendants except David Robinson on one or more counts, we are convinced that the challenged summation statements had no impact whatever on the jury.

7. Sentencing

Several defendants also make a variety of sentencing challenges, none of which has merit. Defendants’ contention that the district court should have “invalidate[d] the 100:1 crack cocaine/powder ratio guideline” (Jimenez brief on appeal at 43) is foreclosed by our prior decisions. See, e.g., United States v. Canales, 91 F.3d 363, 370 (2d Cir.1996) (“The 1995 [Sentencing Commission] Report [recommending modifying the crack-cocaine ratio] and Congress’s rejection of its recommendations .... leav[e] us just where we were before the 1995 Report was published. A district court has no power to depart based on the sentencing disparity between offenses involving crack and non-crack cocaine. ... [T]he 1995 Report has no effect on this Circuit’s precedent....”); United States v. Jimenez, 68 F.3d 49, 51 (2d Cir.1995) (rejecting equal protection challenge); United States v. Jackson, 59 F.3d 1421, 1424 (2d Cir.1995) (per curiam) (rejecting equal protection and Eighth Amendment challenges), cert. denied, - U.S.-, 116 S.Ct. 1428, 134 L.Ed.2d 551 (1996); United States v. Haynes, 985 F.2d 65, 70 (2d Cir.1993) (crack-cocaine ratio is not a basis for downward departure).

Their other contentions challenge various factual findings by the sentencing court with regard to, e.g., the quantity of crack attributable to them under the Guidelines, the perjurious nature of testimony they presented at trial, and Jimenez’s use of a firearm. Facts, for purposes of sentencing, need be established only by a preponderance of the evidence, see, e.g., United States v. Cousineau, 929 F.2d 64, 67 (2d Cir.1991) (conduct related to quantity of narcotics); United States v. Mafanya, 24 F.3d 412, 414 (2d Cir.1994) (facts re obstruction); United States v. Gigante, 94 F.3d 53, 56 (2d Cir.1996) (facts re use of firearm), and the court’s factual findings are reviewed only for clear error, see 18 U.S.C. § 3742(e); Unite6d States v. Mafanya, 24 F.3d at 414. Further, the quantity of narcotics attributable to a given defendant may be approximated, see Guidelines § 2D1.1 Application Note 12 (“[w]here there is no drug seizure or the amount seized does not reflect the scale of the offense, the court shall approximate the quantity of the controlled substance”), and where a defendant was a member of a narcotics distribution conspiracy, all transactions entered into by him or by his eoconspirators, if they were either known to him or reasonably foreseeable by him, may be attributed to him for purposes of calculating his sentence under the Guidelines, see, e.g., id. § 1B1.3 Application Note 1; United States v. Cardenas, 917 F.2d 683, 687 (2d Cir.1990) (defendant should be sentenced on basis of amount of narcotics he “could reasonably have foreseen ... if he had cared to inquire”); United States v. Candito, 892 F.2d 182, 185-86 (2d Cir.1989). Under these standards, we see no merit in defendants’ challenges.

Hale and Hunt claim that the district court erred in calculating their sentences by holding them accountable for 15 kilograms of crack. That quantity was justifiable, given the evidence that during the period in which Hale and Hunt were members of the Supreme Team, the gang regularly acquired kilogram quantities of cocaine that it converted into crack and that its receipts from crack sales were approximately $10,000 a day. Moreover, even a ruling that a far smaller quantity was attributable to Hale and Hunt would not have affected their sentences, since the district court ruled that their base offense level was 38, for which the threshold amount of crack is 1.5 kilograms. See Guidelines § 2Dl.l(c)(l). A single Team purchase could have sufficed to meet that threshold, and there was ample evidence of the knowing involvement of Hale and Hunt. For example, Hale was heard in wiretapped conversations discussing Supreme Team drug business. Further, the jury found Hale and Hunt guilty of possession of cocaine with intent to distribute in August 1989 in connection with the Supreme Team’s decision to kill the suppliers Fernando Suarez and Pablo Perlaza and take their cocaine. Hale helped to carry out this mission, participating in suffocating and bludgeoning them to death in his own apartment; Julio Hernandez, who also participated, testified that Hunt, upon arriving to help dispose of the bodies, asked “ ‘How much did they get?’ ” and showed “frustration]” when the answer was “only ... two keys.” (Miller Trial Tr. at 2012.) The district court could not fail to find that both defendants knew or reasonably should have known their organization distributed at least 1.5 kilograms of crack.

Jimenez received an increase in his offense level for attempting to obstruct justice by testifying at trial on behalf of Miller and denying all familiarity with the Supreme Team. In light of the other evidence at trial, there was no clear error in the district court’s finding that his testimony was false, material, and intentionally perjurious. Hunt received a similar increase on the ground that he called two alibi witnesses who gave what the district court found to be false testimony as to his lengthy absence from New York during a period for which a parole officer testified that the records showed Hunt had regularly reported to the Queens parole office. Although Hunt disputed the accuracy of the records based on certain discrepancies, there was no clear error in the district court’s crediting of the documents, especially in light of testimony by Piniella that also placed Hunt in New York during the period in question.

Finally, Jimenez challenges the court’s enhancement of his offense level pursuant to Guidelines § 2Dl.l(b)(l) for use of a firearm in connection with the conspiracy. He notes that, in support of the enhancement, the court referred to the murders of the four unnamed Colombians, and he argues that this was impermissible (a) because there was no recommendation for such an enhancement in the presentenee report (“PSR”), and the government did not timely object to the PSR, and (b) because the jury acquitted him with respect to the alleged July 1989 murders of the four unnamed Colombians. These contentions are meritless. First, the sentencing judge is not bound by the recommendations of the PSR, and we see no procedural unfairness. Jimenez does not suggest that he was denied an opportunity to oppose the government’s somewhat tardy objection. Second, the sentencing court is entitled to rely on any type of information known to it, see, e.g., United States v. Carmona, 873 F.2d 569, 574 (2d Cir.1989), including evidence at trial that the jury viewed as insufficient to establish the government’s case beyond a reasonable doubt. Thus, the district court here was free to consider, inter alia, evidence concerning the July 1989 murders of the four Colombians despite Jimenez’s acquittal. The court noted that although the jury had not found those murders proven beyond a reasonable doubt, the court itself found it established by more than a preponderance (see Jimenez Sentencing Transcript at 15 (“well-beyond the standard of preponderance of the evidence”)) that Jimenez possessed firearms in connection with the Supreme Team drug trafficking conspiracy “on a regular basis” (id.). We see no error in that ruling.

CONCLUSION

We have considered all of defendants’ contentions on these appeals and, with the exception of Miller’s double jeopardy challenge to his conviction on the 21 U.S.C. § 846 count, we have found in them no basis for reversal. We remand to the district court for entry of a new judgment of conviction as to Miller, dismissing the § 846 count against him. In all other respects, the judgments of conviction are affirmed.  