
    UNITED STATES of America, Appellee, v. Alan QUINONES, Diego B. Rodriguez, Defendants-Appellants, Hector Vega, Defendant.
    Docket Nos. 04-5554-cr(L), 04-5650-cr(CON).
    United States Court of Appeals, Second Circuit.
    Argued: May 10, 2006.
    Decided: Dec. 28, 2007.
    
      David L. Lewis, Lewis & Fiore, LLP, New York, New York, for Defendant-Appellant Alan Quinones.
    Jean D. Barrett, Ruhnke & Barrett, Montclair, New Jersey, for Defendanb-Ap-pellant Diego B. Rodriguez.
    David M. Rody, Assistant United States Attorney (David B. Anders, Karl Metzner, Assistant United States Attorneys, on the brief), for Michael J. Garcia, United States Attorney for the Southern District of New York, New York, New York, for Appellee.
    Before: WINTER, CABRANES, and RAGGI, Circuit Judges.
   REENA RAGGI, Circuit Judge:

Defendants Alan Quinones and Diego B. Rodriguez appeal from judgments of conviction entered on October 15, 2004, after a jury trial in the United States District Court for the Southern District of New York (Jed S. Rakoff, Judge) at which they were found guilty on substantive and conspiratorial counts of racketeering (“RICO”), see 18 U.S.C. § 1962(c), (d); substantive and conspiratorial counts of drug trafficking, see 21 U.S.C. §§ 841(a)(1), (b)(1)(C) & 846; and the murder of confidential informant Eddie Santiago in relation to a continuing drug enterprise, see id. at § 848(e)(1)(A). Although the guilty verdict on the § 848(e)(1)(A) count exposed the defendants to the death penalty, the jury ultimately decided against this punishment. Defendants are presently incarcerated serving terms of life imprisonment.

On this appeal, defendants seek reversal of their convictions or a remand for resen-tencing on the grounds that the district court erred in (1) empaneling an anonymous jury; (2) removing certain prospective jurors for cause based on their opposition to the death penalty as expressed in a written questionnaire, without any followup oral voir dire; (3) making various evi-dentiary rulings; (4) charging RICO by reference to only three elements; and (5) imposing life sentences. For the reasons discussed in this opinion, we reject these arguments and affirm the judgment of conviction.

I. Background

A. The Crimes of Conviction

In the course of a seven-week trial involving seventeen witnesses, including some of the defendants’ former accomplices, and more than 200 physical exhibits, the prosecution convincingly established defendants’ participation in a racketeering enterprise primarily focused on the distribution of cocaine and heroin. Quinones led the illicit enterprise while Rodriguez served as his chief lieutenant. After Qui-nones’s March 1999 arrest for selling heroin to an undercover police officer, defendants retaliated against Eddie Santiago, the confidential informant whom they blamed for Quinones’s arrest, by murdering Santiago and burning his body. We detail the trial evidence only as necessary to our discussion of the issues on appeal. Viewed in the light most favorable to the government, see Jackson v. Virginia, 443 U.S. 307, 318-19, 99 S.Ct. 2781, 61 L.Ed.2d 560 (1979), the evidence showed the following facts.

1. Narcotics Trafficking

a. Defendants’ Cocaine Operation

Through the testimony of drug confederates Glen Weissman and Johnnie Hedge-peth, the prosecution established that, in the late 1990s, defendants regularly procured wholesale quantities of cocaine from suppliers in Florida and New York for distribution primarily in Allentown, Pennsylvania. Hedgepeth reported meeting Quinones at various locations in New York where Quinones purchased kilogram quantities of cocaine from Hedgepeth’s partner, Joseph Sapia. Weissman testified that he accompanied Quinones to Florida to purchase cocaine from another source. Weissman further stated that, between January and March 1999, he transported cocaine on approximately five to seven occasions from Quinones’s Bronx residence to various locations in Allentown.

b. Defendants’ Heroin Operation

Defendants also distributed heroin, operating this side of their business, in part, out of the Bronx apartment of Quinones’s girlfriend, Janet Soto. Milton Rivera and Hector Vega, two Bronx drug dealers who procured heroin from the defendants, testified against them at trial.

Rivera stated that, by May 1999, defendants were steadily supplying him with multi-kilogram quantities of heroin. While Rivera originally bought heroin directly from Quinones, Quinones eventually introduced Rivera to Rodriguez who, thereafter, delivered the drugs and collected payment. Quinones maintained contact with Rivera to ensure that customers were satisfied with the quality of the heroin supplied.

Vega, who distributed heroin from three different Bronx locations, testified that Quinones first offered to supply him with heroin in late 1998 or early 1999 and identified Janet Soto as a point of contact. In April 1999, after Vega had a falling out with his established supplier, he contacted Soto who promptly supplied him with ten to twenty bundles of heroin. That same day, Quinones visited Vega to check that the drugs were satisfactory. From May through August 1999, Quinones — acting through Rodriguez and Soto — regularly supplied Vega with approximately seventy-five bundles of heroin a week.

2. The Murder of Eddie Santiago

a. Santiago’s Cooperation Leads to Quinones’s Arrest

In March 1999, Eddie Santiago, a paid informant of the New York City Police Department, introduced Quinones to an undercover officer who, on March 18, 1999, and again on March 26, 1999, purchased small quantities of heroin directly from the defendant. At the conclusion of the latter transaction, police placed Quinones under arrest. Santiago, who was present at the time of the arrest, promptly voiced concern about his safety to the undercover officer because Quinones would now know Santiago was an informant.

b. Quinones’s Search for Santiago

Santiago’s fears were not unwarranted. Immediately after Quinones secured release on bail, he began hunting for Santiago. Hector Vega testified to a conversation in March 1999 during which Quinones stated that he was looking for a man named “Eddie,” who Quinones believed had set him up for arrest. Over the next several months, Quinones regularly asked Vega whether he had encountered anyone named “Eddie” in his neighborhood. In April 1999, Quinones also tried to locate Santiago through Milton Rivera. Qui-nones told Rivera, “I am going to put his [i.e., Santiago’s] head in a box.” Trial Tr. at 529.

By June 1999, Quinones had obtained a photograph of Santiago. When Quinones showed the picture to Vega, the latter identified Santiago as someone who had tried to sell him heroin in another undercover transaction. Vega reported that his cousin Louis Malave knew Santiago, prompting Quinones to ask if Malave could arrange a meeting with Santiago because Quinones “wanted to get him.” Id. at 1411. Quinones further asked whether Malave could be trusted to “keep his mouth shut.” Id. Vega assured Quinones that Malave, who had done “time in the state,” would not “open his mouth.” Id.

On Friday, June 25, 1999, Quinones offered Malave $1,000 to “set up” Santiago. Id. at 870. Malave agreed and attempted to arrange a meeting for that night on Tremont Avenue in the Bronx. When Santiago failed to keep the appointment, Quinones and Malave proceeded to formulate an alternative plan.

c. The Abduction and Murder of Santiago

(1) Santiago Is Lured to Gutierrez’s Apartment

Pursuant to that plan, on Saturday, June 26, Malave solicited Santiago’s assistance in helping some drug dealers cook crack cocaine. Meanwhile, Quinones arranged with Nilsa Gutierrez, a friend of Janet Soto’s, to use her Bronx apartment on Sunday, June 27. On Sunday afternoon, Quinones directed Malave and Rodriguez to pick up Santiago and bring him to the apartment. Quinones instructed the men to use a small two-door car registered to his wife, Carmen Quinones, and to make sure Santiago sat in the rear “because he didn’t want [Santiago] to get away.” Id. at 899.

In executing these instructions, Malave introduced Rodriguez to Santiago as “the guy that had the crack” that needed to be cooked. Id. at 900. When the three men arrived at Gutierrez’s apartment for this purported purpose, Rodriguez led Santiago inside, while Malave lingered in the hallway. Almost immediately, Malave heard “a tussle,” as if people were “wrestling” inside the apartment. Id. at 908. He soon left the scene to report to Vega what was happening.

About thirty minutes later, Malave and Vega returned to Gutierrez’s apartment. Vega testified that, as soon as he entered the apartment, Quinones hugged him, whereupon Vega saw a groggy Santiago lying on the living room floor, handcuffed and hogtied, with blood running from his mouth. Vega also saw Rodriguez in the room and a gun lying on a sofa. Vega soon left the apartment but, on a return trip later that afternoon, he saw Janet Soto screaming at Santiago that he was getting what he deserved for being a “rat.” Id. at 1443. Rodriguez also taunted Santiago by spitting in his face. Meanwhile, Quinones threatened Santiago, yelling, “I beat one body before and I’ll beat your body.” Id.

While her apartment was thus being used, Nilsa Gutierrez spent the day at Soto’s residence. When, in the afternoon, Gutierrez indicated that she wished to return to her home, Soto told her she could not do so because “the guy that snitched on Alan” was in Gutierrez’s apartment. Id. at 1910.

(2) The Removal of Santiago’s Body and Quinones’s Admissions to Murder

Later on Sunday night, Vega saw Rodriguez and Soto carrying what appeared to be a weed trimmer and a can of gasoline into Gutierrez’s apartment building. Gutierrez testified that, earlier that day, she had seen Soto and Rodriguez with these same items.

Still later that night, Gutierrez observed Carmen Quinones’s car and a minivan parked outside Gutierrez’s apartment building. From the street, Gutierrez saw Quinones pushing a shopping cart out of her building and loading the bundled contents into the van.

Gutierrez testified that, when Quinones and Rodriguez arrived at Soto’s apartment sometime later, Quinones happily announced that they had “burned the guy.” Id. at 1939. He told Gutierrez that he had used her comforter and shopping cart in the process and promised to reimburse her for these items. Gutierrez further recalled Quinones bragging that “if it would have been Lefty he would have screamed.” Id. at 1940.

Hector Vega testified that, soon after these events, when he told Quinones that one of Vega’s workers, “Chupacabra,” was cooperating with the police, Quinones offered to kill the worker, stating that “he got rid of one snitch already and he would like to get rid of another one.” Id. at 1493.

(3) The Discovery of Santiago’s Burned Body

On June 28, 1999, the charred dead body of Eddie Santiago was found in a vacant lot in the Bronx. Remnants of a comforter remained around the body, which was hogtied, with duct tape covering the nose and mouth. A medical examiner determined the cause of death to be asphyxiation.

3. Verdict and Sentencing

At the conclusion of the prosecution’s case, the defendants elected not to present any evidence. On July 27, 2004, the jury found them guilty of five of the seven counts charged, including the capital charge of murder in furtherance of a continuing criminal drug enterprise.

At the ensuing penalty phase, the jury, after hearing from three prosecution witnesses and forty-four defense witnesses, unanimously voted not to impose the death penalty. On September 27, 2004, the district court sentenced each defendant, principally, to life imprisonment.

II. Discussion

A. The District Court Acted Within Its Discretion in Em/paneling an Anonymous Jury

Defendants submit that the district court erred in empaneling an anonymous jury. We are not persuaded.

It is well settled that, “ ‘when genuinely called for and when properly used, anonymous juries do not infringe a defendant’s constitutional rights.’ ” United States v. Thai, 29 F.3d 785, 800-01 (2d Cir.1994) (quoting United States v. Vario, 943 F.2d 236, 239 (2d Cir.1991)); see also United States v. Tutino, 883 F.2d 1125, 1132-33 (2d Cir.1989). In reviewing an anonymous jury challenge, we “balance the defendant’s interest in conducting meaningful voir dire and in maintaining the presumption of innocence, against [the jury’s] interest in remaining free from real or threatened violence and the public interest in having the jury render a fair and impartial verdict.” United States v. Amuso, 21 F.3d 1251, 1264 (2d Cir.1994).

Where we find evidence to support the district court’s conclusion that the jury needed protection, and where the court took reasonable precautions to minimize any prejudice to the defendant and to ensure the protection of the defendant’s fundamental rights, “the decision to empanel an anonymous jury is reviewed only for abuse of discretion.” United States v. Thai, 29 F.3d at 801; United States v. Paccione, 949 F.2d 1183, 1192 (2d Cir.1991). We have identified strong reasons to believe that a jury needed protection in situations where the government demonstrated a defendant’s willingness to tamper with the judicial process. See, e.g., United States v. Gotti, 459 F.3d 296, 345-46 (2d Cir.2006); United States v. Aulicino, 44 F.3d 1102, 1116 (2d Cir.1995); United States v. Thai, 29 F.3d at 801; United States v. Amuso, 21 F.3d at 1264-65; United States v. Paccione, 949 F.2d at 1192. In reviewing such evidence, we are not limited to the facts available at the time of actual empanelment; rather, we may consider any relevant evidence in the record. See United States v. Wong, 40 F.3d 1347, 1376-77 (2d Cir.1994); see also United States v. DeLuca, 137 F.3d 24, 31 (1st Cir.1998).

Defendants submit that there was no basis for the district court’s finding that they posed a substantial risk to the judicial process. The record is plainly to the contrary. The indictment specifically charged defendants with murdering a confidential informant in retaliation for his cooperation with law enforcement authorities. Indeed, trial evidence showed the defendants’ dogged determination in pursuing this homicidal objective, both directly and through various confederates. Although defendants assert that their conduct did not actually threaten the judicial process, see Rodriguez Br. at 10-11 (describing defendants as “low-level drug dealers” who killed Santiago because he “sold Quinones to narcotics detectives for $500 and nothing more”), we disagree. The murder of Eddie Santiago threatened the judicial process both by eliminating a witness who could have provided incriminating evidence against defendants and by sending a powerfully frightening message to others of the terrible consequences awaiting anyone who cooperated in defendants’ prosecution. Under these circumstances, the district court acted well within its discretion in concluding that the defendants posed a substantial risk to the integrity of the judicial process warranting empanelment of an anonymous jury. See United States v. Gotti 459 F.3d at 345-46 (holding that district court did not abuse its discretion in empaneling anonymous jury where defendants were alleged members of powerful organized crime family and indictment charged them with witness tampering); United States v. Thai, 29 F.3d at 801 (holding anonymous jury was warranted where there was evidence, inter alia, of defendants’ acts of intimidation towards their crime victims, including attempts to kill certain victims, and murder of individual who refused to withdraw complaints to police). Indeed, that conclusion finds further support in trial evidence indicating Quinones’s expressed willingness to kill other persons whom he perceived to be “snitches.” Trial Tr. at 1493 (offering to kill informant “Chupacabra” and boasting that “he got rid of one snitch [Santiago] already and he would like to get rid of another one”); see id. at 1940 (hypothesizing that cooperator “Lefty” would not have been able to tolerate torture Quinones had inflicted on Santiago).

Two other grounds cited by the government — the seriousness of the crime and the likelihood of pre-trial publicity- — -reinforce the district court’s decision to empanel an anonymous jury. See United States v. Persico, 832 F.2d 705, 717 (2d Cir.1987) (upholding anonymous jury in light of defendant’s history of violence and obstruction of justice together with reasonable expectation of publicity); United States v. Thomas, 757 F.2d 1359, 1364-65 (2d Cir.1985) (upholding anonymous jury where defendants were alleged to have participated in several “ ‘mob-style’ killings” and to have made past attempts to interfere with judicial process); see also United States v. Vario, 943 F.2d at 240 (noting that “[p]retrial publicity may militate in favor of an anonymous jury because it can enhance the possibility that jurors’ names would become public and thus expose them to intimidation by defendants’ friends or enemies, or harassment by the public” (internal quotation marks omitted)). We need not here decide whether these grounds would, by themselves, have supported the challenged decision. See id. at 241 (concluding that evidence linking defendant to “organized crime” does not, by itself, warrant anonymous jury); United States v. Mansoori, 304 F.3d 635, 651 (7th Cir.2002) (concluding that charges exposing defendant to lengthy prison terms do not, by themselves, support anonymous jury).

Defendants do not contend that the district court failed to take adequate procedural precautions to ensure that they were not prejudiced by the selection of an anonymous jury, nor would the record support such an argument. The district court’s voir dire was sufficiently detailed to compensate for jury anonymity, see United States v. Aulicino, 44 F.3d at 1116, and the court couched its jury instruction regarding anonymity in such a way as to avoid intimating that defendants posed any risk to persons or to the judicial process, see United States v. Paccione, 949 F.2d at 1192. On this record, we reject defendants’ anonymous jury challenge as without merit.

B. The District Court’s Removal for Cause of Prospective Jurors Opposed to the Death Penalty Based Solely on Responses to a Questionnaire Does Not Warrant Reversal of Defendants’ Convictions

Although the jury decided not to impose the death penalty, defendants appeal their convictions on the ground that the removal for cause of certain jurors opposed to capital punishment violated their Sixth Amendment right to trial by a fair and impartial jury. See U.S. Const, amend VI; Witherspoon v. Illinois, 391 U.S. 510, 88 S.Ct. 1770, 20 L.Ed.2d 776 (1968) (holding that, in capital cases, Sixth Amendment prohibits systematic removal of venireper-sons opposed to death penalty). Specifically, defendants contend that the district court erred by relying only on prospective jurors’ responses to a written questionnaire to determine whether a person’s opposition to the death penalty would, in fact, “prevent or substantially impair the performance of his duties as a juror in accordance with [the court’s] instructions and [the juror’s] oath.” Wainwright v. Witt, 469 U.S. 412, 424, 105 S.Ct. 844, 83 L.Ed.2d 841 (1985) (internal quotation marks omitted). Defendants submit that oral inquiry is essential to any removal for cause under Witt-Witherspoon.

At the outset, we commend the practice of some oral examination of prospective jurors in capital cases preliminary to any removal for cause based on their views about the death penalty. At a minimum, oral examination permits a trial court to assess an individual’s responses in light of demeanor, an important factor in commanding appellate deference to the ultimate Witt-Witherspoon determination. See generally Uttecht v. Brown, — U.S. -, 127 S.Ct. 2218, 2223, 167 L.Ed.2d 1014 (2007) (collecting cases and noting need to defer to trial court in jury selection “because so much may turn on a potential juror’s demeanor”); cf. Mu’Min v. Virginia, 500 U.S. 415, 425, 111 S.Ct. 1899, 114 L.Ed.2d 493 (1991) (observing that written answers to questionnaire “would not give counsel or the court any exposure to the demeanor of the juror in the course of answering the content questions”). We are not convinced, however, that oral examination is a constitutional prerequisite to every for-cause removal pursuant to WittWitherspoon. More important, even if defendants could demonstrate that, on the particular facts of this case, further oral inquiry was necessary to support the challenged removals, they would not be entitled to the relief they seek on this appeal: reversal of their convictions. A WittWitherspoon error precludes imposition of the death penalty, a punishment already rejected by the jury in defendants’ case. It does not warrant reversal of the underlying conviction. To explain this conclusion, we begin with a review of the questionnaire process that is the subject of defendants’ challenge.

1. The Questionnaire Inquiry in this Case

To facilitate the examination of the hundreds of persons summoned for possible jury service in this capital case, the district court employed a questionnaire submitted jointly by the parties. Of the five questions posed to prospective jurors, the first, inquiring as to the personal hardship of service, is not here at issue. Accordingly, we focus attention on the remaining four.

Question 2 asked jurors to use a scale of 1 to 7 to indicate how strongly they generally favored or opposed the death penalty, with 1 indicating “strongly oppose” and 7 indicating “strongly favor.” Questionnaire at 2.

Question 3 solicited similar information by asking jurors to check one of the following choices:

• Favor the death penalty in every case where someone has committed an intentional murder
• Favor the death penalty in most but not all intentional murder cases
• Favor the death penalty in some intentional murder cases but not all intentional murder cases
• Oppose the death penalty in most but not all intentional murder cases
• Oppose the death penalty in every case even where someone has been intentionally murdered

Id.

Question 4 asked prospective jurors whether a person who committed intentional murder in circumstances involving particular aggravating factors should “necessarily” receive the death penalty. The jurors were asked to indicate “Yes” or “No” as to each of the following factors: (a) “[tjorture of the victim,” (b) “[kjilling of a witness,” (c) “[a] drug conspiracy,” (d) “[pjayment or promise of payment,” (e) “[obstruction of justice,” (f) “[a] defendant with a prior murder conviction,” and (g) “[a] defendant with a prior record of violence other than murder.” Id.

Finally, Question 5 asked for similar “Yes” or “No” responses to whether the following mitigating facts “could ... support a sentence of life imprisonment instead of the death penalty for a person who commits an intentional murder of a police informant”: (a) “[t]he person had an abusive, neglectful or chaotic childhood,” (b) “[t]he person had a mental illness or emotional disturbance,” (c) “[t]he person has below normal intelligence,” (d) “[t]he murder was committed under duress,” (e) “[ojthers equally guilty will not be punished by death,” and (f) “[t]he victim himself engaged in criminal conduct leading to his death.”

In proposing these questions to the court, counsel for Rodriguez represented that they would be helpful in identifying jurors with views so extreme that they could be readily excused for cause:

Ms. BaRrett: ... [T]hey are helpful in term[s] of, for instance weeding out th[ose] jurors who answer either the very top, I will never impose the death penalty under any circumstances or at the very bottom, I believe that the death penalty should be imposed in all cases— Court: The only for cause exclusions are those two[?]
Ms. Barrett: Exactly.

Tr. of Conference at 33 (May 13, 2004). Counsel for Quinones, however, indicated that, even in such circumstances, individual questioning would be appropriate “because jurors will check 7 [ (strongly favor) ] when they mean 1 [ (strongly oppose) ].” Id. at 35. Such an error, if one had occurred, would have been at least partially corrected by the fact that the district court indicated that extreme answers on both ends of the spectrum (ie., those who checked 1 and those who checked 7) would result in removal of jurors. The risk of an erroneous removal for cause was minimal because only jurors who provided equally extreme answers to all four questions were excused for cause on the basis of their questionnaire responses. See e.g., Tr. of Conference at 27 (June 15, 2004) (noting with respect to jurors who expressed support for death penalty that court would automatically excuse only those jurors who responded to each of the questions about the death penalty as follows: “who answered] question No. 2 with a 7 [i.e., ‘strongly favor’ the death penalty], who answer[ed] question No. 3 with the top check [ie., would ‘[flavor the death penalty in every case where someone has committed an intentional murder’], who answer [ed] ‘yes’ to all parts of No. 4 [ie., that every specified aggravating factor would ‘necessarily’ warrant the death penalty], and who answer[ed] ‘no’ to each part of No. 5 [ie., that no mitigating factor ‘could’ support a sentence of life imprisonment rather than death].”). A juror whose answers were at all equivocal or inconsistent would have been brought in for further questioning.

2. The Use of Questionnaires in the Voir Dire Process

Although the Constitution makes no mention of voir dire, the law recognizes the important role this process plays in ensuring the fair and impartial criminal jury mandated by the Sixth Amendment. See Morgan v. Illinois, 504 U.S. 719, 729, 112 S.Ct. 2222, 119 L.Ed.2d 492 (1992) (observing that “part of the guarantee of a defendant’s right to an impartial jury is an adequate voir dire to identify unqualified jurors”). Voir dire helps the trial court and the parties identify those persons who, for various reasons, cannot evaluate the evidence impartially or follow the court’s legal instructions. See Rosales-Lopez v. United States, 451 U.S. 182, 188, 101 S.Ct. 1629, 68 L.Ed.2d 22 (1981); United States v. Stewart, 433 F.3d 273, 303 (2d Cir.2006). That being said, it has long been the rule that “judges have been accorded ample discretion in determining how best to conduct the voir dire,” Rosales-Lopez v. United States, 451 U.S. at 189, 101 S.Ct. 1629; see United States v. Lawes, 292 F.3d 123, 128 (2d Cir.2002); accord Fed.R.Crim.P. 24(a) (describing court’s authority to examine prospective jurors or permit parties to do so), and that “an appellate court will not interfere with the manner in which it has been conducted absent a clear abuse of discretion,” United States v. Salameh, 152 F.3d 88, 121 (2d Cir.1998) (internal quotation marks omitted); see generally Zervos v. Verizon New York, Inc., 252 F.3d 163, 169 (2d Cir.2001) (observing that, when matters are left to district court discretion, law does not require it to follow single procedure or to reach particular decision; rather, discretion empowers court to act within permissible range of choices).

Applying these principles to this case, we observe at the outset that a district judge does not abuse his discretion simply by using a written questionnaire in the voir dire process. Although voir dire ordinarily contemplates seeing the jurors and hearing them speak, see generally Cardinal v. Gorczyk, 81 F.3d 18, 20 (2d Cir.1996) (referencing a defendant’s right to “see and hear” prospective jurors during voir dire ), any court-supervised examination of prospective jurors is reasonably understood to be part of voir dire. District courts routinely employ questionnaires to facilitate voir dire in a number of circumstances, e.g., where a large number of prospective jurors must be screened, see, e.g., United States v. Rahman, 189 F.3d 88, 121 (2d Cir.1999) (approving court’s use of comprehensive questionnaire in case involving over 500 prospective jurors); where an anonymous jury is to be empaneled, see, e.g., United States v. Thai, 29 F.3d at 801; where there has been extensive pre-trial publicity, see, e.g., United States v. Stewart, 433 F.3d at 303; or where the death penalty is sought, see, e.g., United States v. Wilson, 493 F.Supp.2d 537, 544 (E.D.N.Y.2007) (observing, in a capital case, that “[n]early 600 potential jurors came to this courtroom to fill out 56-page questionnaires prepared by the parties and by the court”); see also United States v. McVeigh, 153 F.3d 1166, 1181 (10th Cir.1998). The use of such a procedure as a preliminary screening tool falls well within the district court’s broad discretion in conducting voir dire. See generally United States v. Rahman, 189 F.3d at 121-22 (holding, where district court removed some potential jurors for cause based on responses to questionnaires while conducting oral voir dire of remaining ven-irepersons, that court’s “voir dire skillfully balanced the difficult task of questioning such a large jury pool with the defendants’ right to inquire into the sensitive issues that might arise in the case”); United States v. Contreras, 108 F.3d 1255, 1269-70 (10th Cir.1997) (sanctioning removal of prospective jurors for cause in non-capital cases based on questionnaire responses); United States v. Parodies, 98 F.3d 1266, 1277-81 (11th Cir.1996) (same).

3. Removals for Cause Based on Questionnaire Responses

Defendants submit that a district court nevertheless abuses its discretion when it relies only on questionnaire responses in removing a prospective juror for cause, particularly in a capital case. We are not convinced.

As a corollary to the Sixth Amendment right to trial by a fair and impartial jury, the Supreme Court has ruled that prospective jurors may be removed “for cause” only on “narrowly specified, provable, and legally cognizable bas[es] of partiality.” Swain v. Alabama, 380 U.S. 202, 220, 85 S.Ct. 824, 13 L.Ed.2d 759 (1965); see United States v. Torres, 128 F.3d 38, 43 (2d Cir.1997) (“[T]he category of challenges for cause is limited.”). In a capital case, removal for cause based on a person’s views about the death penalty is warranted only where it can be determined that “the juror’s views would ‘prevent or substantially impair the performance of his duties as a juror in accordance with his instructions and his oath.’ ” Wainwright v. Witt, 469 U.S. at 424, 105 S.Ct. 844 (quoting Adams v. Texas, 448 U.S. 38, 45, 100 S.Ct. 2521, 65 L.Ed.2d 581 (1980)); cf. Witherspoon v. Illinois, 391 U.S. at 522, 88 S.Ct. 1770 (holding that opposition to the death penalty is not enough, by itself, to support removal for cause).

While these standards necessarily delineate the boundaries within which a district court may exercise its removal discretion, “the Constitution lays down no particular tests” or procedures for determining when these standards are satisfied. United States v. Wood, 299 U.S. 123, 145-46, 57 S.Ct. 177, 81 L.Ed. 78 (1936); accord United States v. Haynes, 398 F.2d 980, 983 (2d Cir.1968) (observing that there is no “rigid formula” for determining impartiality). Thus, we identify no general Sixth Amendment proscription on the removal of jurors for cause based on questionnaire responses. Defendants nevertheless invite us to hold that, in capital eases, some oral questioning is constitutionally necessary to a Witt-Witherspoon determination of partiality warranting removal. We decline this invitation.

Preliminary to explaining our conclusion, we observe that this case appears to present a rare exception to the general practice of district courts in this circuit, which, in selecting capital juries, have routinely employed some oral voir dire in resolving disputed Witt-Witherspoon challenges. The practice is commendable. The bluntness or hesitancy, confidence or discomfort displayed by prospective jurors as they respond to questions about the possibility of returning a capital verdict often reveals as much about bias as the actual answers given. Mindful of this fact, the Supreme Court, in virtually every capital voir dire case from Witt through Uttecht, has emphasized a trial court’s opportunity to observe demeanor in according deference to removal decisions. See, e.g., Uttecht v. Brown, 127 S.Ct. at 2224 (“Deference to the trial court is appropriate because it is in a position to assess the demeanor of the venire.”); Darden v. Wainwright, 477 U.S. 168, 178, 106 S.Ct. 2464, 91 L.Ed.2d 144 (1986) (noting trial court’s removal decision was “undoubtedly” aided “by its assessment of the potential juror’s demeanor”); Wainwright v. Witt, 469 U.S. at 426, 428, 105 S.Ct. 844 (noting trial court’s finding of bias “is based upon determinations of demeanor and credibility that are peculiarly within a trial judge’s province” and “this is why deference must be paid to the trial judge who sees and hears the juror”). Thus, simply to maximize their claim on our deference, district courts are well advised to employ some oral voir dire in making Witt-Witherspoon decisions.

However strongly we recommend some oral voir dire in capital cases, we do not conclude that the procedure is constitutionally mandated. Cf. Mu’Min v. Virginia, 500 U.S. at 425-26, 111 S.Ct. 1899 (“To be constitutionally compelled ... it is not enough that such [voir dire ] questions might be helpful. Rather, the trial court’s failure to ask these questions must render the defendant’s trial fundamentally unfair.”). As the Supreme Court has made clear, in capital cases, no less than in non-capital cases, the Constitution does not dictate a particular voir dire process; it demands only that the process be “adequate ... to identify unqualified jurors.” Morgan v. Illinois, 504 U.S. at 729, 112 S.Ct. 2222 (“The Constitution ... does not dictate a catechism for voir dire, but only that the defendant be afforded an impartial jury.”). To be adequate, voir dire need not establish juror partiality with “unmistakable clarity.” Wainwright v. Witt, 469 U.S. at 424, 105 S.Ct. 844 (internal quotation marks omitted). Rather, it must be sufficient to permit a trial judge to form “a definite impression that a prospective juror would be unable to faithfully and impartially apply the law.” Id. at 426, 105 S.Ct. 844.

Whether questionnaire responses, without more, can convey the impression necessary to removal for cause admits no easy answer applicable to all cases. Juror partiality can, after all, take various forms: actual, implied, or inferred. See United States v. Torres, 128 F.3d at 43. Actual bias is “bias in fact,” id., generally evidenced by “express proof,” such as a juror’s admission to “a state of mind prejudicial to a party’s interest.” United States v. Haynes, 398 F.2d at 984. Implied bias is “bias conclusively presumed as a matter of law” from circumstances in which an average person in the position of the prospective juror would be prejudiced. United States v. Torres, 128 F.3d at 45. Inferred bias exists “when a juror discloses a fact that bespeaks a risk of partiality sufficiently significant to warrant granting the trial judge discretion to excuse the juror for cause, but not so great as to make mandatory a presumption of bias.” Id. at 47. As the fluidity of these categories suggests, some facts may reveal juror partiality more obviously than others. While blunt acknowledgment of bias may support removal without further inquiry, the more ambiguous a prospective juror’s responses, the more useful demeanor, and thus oral inquiry, become in allowing a trial judge to identify partiality warranting removal for cause. See generally Uttecht v. Brown, 127 S.Ct. at 2223 (recognizing importance of demeanor in allowing trial court to resolve ambiguity in prospective juror’s responses).

In the non-capital context, we would be loath to conclude that a trial judge had violated the Sixth Amendment or exceeded his discretion when, without oral inquiry, he removed for cause a prospective juror who, on a written questionnaire, demonstrated bias by, e.g., revealing that he was the defendant’s brother or the prosecutor’s uncle, stating that he thought all persons of the defendant’s ethnicity were criminals, or pronouncing that he had already concluded from the nature of the charges that the defendant must be guilty. Irrevocable bias would be so evident from these written responses as to render superfluous further oral inquiry about the juror’s ability to follow legal instructions and to serve impartially. See generally United States v. Torres, 128 F.3d at 47 (observing that, once facts are elicited permitting finding of bias, “juror’s statements as to his or her ability to be impartial become irrelevant”).

The same logic applies in capital cases. See generally United States v. Moore, 149 F.3d 773, 780 (8th Cir.1998) (upholding removal of juror who indicated that he would consider death penalty only if defendant had murdered 100 people, notwithstanding juror’s assurance that he could follow rule of law). The Supreme Court has recognized that when a prospective juror indicates that he will “automatically vote” for or against the death penalty “in every case,” that is sufficient to conclude that the person “will fail in good faith to consider the evidence of aggravating and mitigating circumstances as the [relevant legal] instructions require him to do,” and to support his removal for cause. Morgan v. Illinois, 504 U.S. at 729, 733, 112 S.Ct. 2222. There is no reason to think that any different conclusion obtains when such irrevocable partiality is elicited in response to a questionnaire rather than to oral examination.

4. Defendants Demonstrate No Error Warranting Relief a. Deferential Review of Removal Decisions

The fact that, even in capital cases, we do not categorically reject the possibility of removals for cause based on questionnaire responses, does not resolve the issue of whether the questionnaire responses in this case were sufficient to support the challenged removals. In arguing that they were not, defendants urge us to apply de novo review. At the outset, we note a circuit split as to the degree of appellate deference properly accorded removal decisions made without oral inquiry in capital cases. Compare United States v. Chanthadara, 230 F.3d 1237, 1269-70 (10th Cir.2000) (applying de novo review in capital case to removals for cause based solely on questionnaire responses), with United States v. Purkey, 428 F.3d 738, 750 (8th Cir.2005) (reviewing removals for cause in capital case based solely on questionnaire responses only for abuse of discretion, observing that “[ojther reasons, such as respect for the trial process, the expertise developed by trial judges, and the desire to conserve judicial resources” made de novo review inappropriate). While our court has not previously addressed this question, we are disinclined to adopt a dual standard of removal review in capital cases depending on whether juror bias manifests itself orally or in writing. The fact that it may be easier for us to conclude that there has been no abuse of discretion when a trial court’s removal decisions are informed by demeanor is insufficient to persuade us that bias findings based on questionnaire responses are subject to de novo review.

As the Supreme Court observed in Waimoright v. Witt, the identification of juror bias is a factual finding “concerning the venireman’s state of mind” that is decidedly the “province of the trial judge.” Wainwright v. Witt, 469 U.S. at 428, 105 S.Ct. 844. The Court has expressly instructed “appellate courts ... not to decide” such questions of fact “de novo,” Maine v. Taylor, 477 U.S. 131, 145, 106 S.Ct. 2440, 91 L.Ed.2d 110 (1986), and we see no reason to create an exception to this rale for bias findings based on written responses to questionnaires. Although Witt emphasized the value of credibility and demeanor assessments in the selection of a capital jury, 469 U.S. at 428, 105 S.Ct. 844, those were not the exclusive reasons for according deference to the trial court’s removal decisions. The Court cited with approval Judge Higginbotham’s special concurrence in O’Bryan v. Estelle, 714 F.2d 365, 392 (5th Cir.1983), which “artfully discusses those factors, in addition to the trial court’s advantage of having seen and heard the juror, which dictate deference to the trial judge’s decision under these circumstances.” Wainwright v. Witt, 469 U.S. at 428 n. 10, 105 S.Ct. 844; see O’Bryan v. Estelle, 714 F.2d at 396 (identifying factors to include finality as well as “the values of comity and of respect for trial court integrity with its sometime superior opportunity for accurate decisionmaking”). We note that Judge Higginbotham, in discussing a district court’s decision-making competency, implicitly acknowledged that removal decisions would not involve oral examination in every instance:

A trial court’s decision to sustain a challenge for cause because the venireman would automatically vote against the death penalty sometimes presents questions of fact in the sense that the trial court must choose from permissible inferences. That choice is often aided by the opportunity to observe and sometimes cannot be made without that opportunity. If we really mean that the review is wholly afresh [i.e., de novo review], one can wonder if we are telling the trial judge not to make the choice.

O’Bryan v. Estelle, 714 F.2d at 393 (emphasis added).

Thus, while the importance of demeanor to a determination of juror bias cannot be gainsaid, see, e.g., Uttecht v. Brown, 127 S.Ct. at 2229, other compelling reasons justify appellate deference to a trial court’s factual findings of bias even when made on the basis of questionnaire responses. As the Supreme Court has explained:

The rationale for deference ... is not limited to the superiority of the trial judge’s position to make determinations of credibility. The trial judge’s major role is the determination of fact, and with experience in fulfilling that role-comes expertise. Duplication of the trial judge’s efforts in the court of appeals would very likely contribute only negligibly to the accuracy of fact determination at a huge cost in diversion of judicial resources. In addition, the parties to a case on appeal have already been forced to concentrate their energies and resources on persuading the trial judge that their account of the facts is the correct one; requiring them to persuade three more judges at the appellate level is requiring too much.

Anderson v. City of Bessemer City, N.C., 470 U.S. 564, 574-75, 105 S.Ct. 1504, 84 L.Ed.2d 518 (1985). This court has similarly observed that the deferential standard of review for factual findings based on oral testimony and documentary evidence is grounded in the “belief that district courts have a good deal of ‘expertise’ when it comes to fact-finding.” Zervos v. Verizon New York, Inc., 252 F.3d 163, 168 (2d Cir.2001). The observation is particularly apt in the context of factual findings made during jury selection, a process with which trial judges are intimately familiar and in which appellate courts have no opportunity to participate. Cf. Illinois v. Abbott & Associates, 460 U.S. 557, 564 n. 8, 103 S.Ct. 1356, 75 L.Ed.2d 281 (noting special deference due trial judge who “had acquired a unique familiarity with” the supervision of grand juries).

In sum, because a finding of juror bias is a factual determination uniquely within the province of the trial court, see Wainwright v. Witt, 469 U.S. at 429, 105 S.Ct. 844; Uttecht v. Brown, 127 S.Ct. at 2231 (describing trial court as “in a superior position to determine the demeanor and qualifications of a potential juror” (emphasis added)), we conclude that, whether the finding is made on the basis of written responses to a questionnaire, oral responses to in-court examination, or some combination of the two, it is properly reviewed under our precedent for abuse of discre-tion. See United States v. Morales, 185 F.3d 74, 84 (2d Cir.1999).

b. Bias Evidenced by the Questionnaire Responses

Applying this standard of review to the challenged removal decisions in this case, we focus first on three questionnaire inquiries. Each person whose removal is here at issue described himself, in response to question two, at the highest-offered numerical level of opposition to the death penalty. See supra at Part II.B.l. Presented with a list of possible aggravating and mitigating circumstances for intentional murder at questions four and five, see id., each such person identified no aggravating factor that would necessarily warrant imposition of the death penalty, but identified each possible mitigating factor as one that could support a sentence of life imprisonment in lieu of the death penalty.

While these three responses plainly reveal strong opposition to the death penalty, it is not clear that, by themselves, they suffice to support removal for cause under Supreme Court precedent. In Adams v. Texas, the Supreme Court ruled that opposition to the death penalty, even when grounded in religious conviction, does not by itself support removal for cause because such views might indicate “only that the potentially lethal consequences of their [sentencing] decision-would invest [these prospective jurors’] deliberations with greater seriousness and gravity or would involve them emotionally.” 448 U.S. at 49, 100 S.Ct. 2521. Such reasoning presumes that a person who did not think that any listed aggravating factor necessarily warranted a death sentence might, on further inquiry, indicate an ability to conceive of some circumstances in which an aggravating factor could prompt him to vote for the death penalty. Similarly, a person who thought that any of a list of mitigating factors could support a life sentence rather than death might, upon further questioning, indicate that not all circumstances involving these mitigating factors would necessarily support that conclusion.

In this case, however, the district court did not rely solely on these three responses in removing certain persons for cause. It ordered removal only if, in response to question three, see supra at Part II.B.l, a prospective juror also indicated opposition to the death penalty in every case of intentional murder. This response, viewed together with the other three, is certainly more indicative of absolute opposition to the death penalty that could “prevent or substantially impair the performance” of a juror’s duties “in accordance with his instructions and his oath.” Wainwright v. Witt, 469 U.S. at 424, 105 S.Ct. 844; cf. Morgan v. Illinois, 504 U.S. at 729, 112 S.Ct. 2222 (“A juror who will automatically vote for the death penalty in every case will fail in good faith to consider the evidence of aggravating and mitigating circumstances as the instructions require him to do.”). Nevertheless, we are reluctant to reach that conclusion on the record before us, which fails to indicate what, if any, preliminary instructions were given by the district court to the jury panel about the questionnaire generally or question number three in particular as it bore on the openmindedness necessary for capital service. See generally Darden v. Wainwright, 477 U.S. at 178, 106 S.Ct. 2464 (noting the removal decision was properly informed by juror’s presence throughout process that “made the purpose and meaning of the Witt inquiry absolutely clear”). We have not pursued that point with the parties, however, because, as we explain in the next section, even if defendants had been able to persuade us that the challenged removals were error, that would not entitle them to any relief in this case in which the jury did not impose the death penalty.

c. A Witt-Witherspoon Error Does Not Support Reversal of a Conviction

The law is clear that a Witt-Wither-spoon error precludes the government from imposing the death penalty. It does not, however, mandate reversal of the underlying conviction. Witherspoon itself makes this point. At the same time that the Supreme Court therein ruled that “[n]o defendant can constitutionally be put to death at the hands of a tribunal” from which persons were excluded simply because they expressed some objection to the death penalty, Witherspoon v. Illinois, 391 U.S. at 522-23, 88 S.Ct. 1770, it pointedly observed that such an error does not “affect the validity of any sentence other than one of death [or] ... render invalid the conviction, as oppose[d] to the [death] sentence, in this or any other case,” id. at 523 n. 21, 88 S.Ct. 1770 (emphasis in original). The Court reiterated this distinction in Morgan v. Illinois, reversing a death sentence based on inadequate voir dire, but noting that this decision had “no bearing on the validity of petitioner’s conviction,” 504 U.S. at 739 n. 11, 112 S.Ct. 2222; see also Gray v. Mississippi, 481 U.S. 648, 650, 668, 107 S.Ct. 2045, 95 L.Ed.2d 622 (1987) (observing that Witherspoon error means “a death sentence imposed by the jury cannot stand,” and reversing judgment only “insofar as it imposes the death sentence”); Adams v. Texas, 448 U.S. at 51, 100 S.Ct. 2521 (observing that Wither-spoon error “disentitles the State to execute a sentence of death” and reversing judgment “to the extent that it sustains the imposition of the death penalty”); Davis v. Georgia, 429 U.S. 122, 123, 97 S.Ct. 399, 50 L.Ed.2d 339 (1976) (holding that, where venireman is improperly excluded from jury for opposition to capital punishment, “subsequently imposed death penalty cannot stand”).

Bumper v. North Carolina, 391 U.S. 543, 88 S.Ct. 1788, 20 L.Ed.2d 797 (1968), decided in the same year as Witherspoon, lends further support to this conclusion. Like the defendants in this case, Bumper was found guilty of a capital crime but, on the jury’s recommendation, sentenced to life imprisonment. He argued for reversal of his conviction on the ground that the removal for cause of prospective jurors opposed to the death penalty violated his right to an impartial jury. In a single sentence, the Supreme Court dismissed the argument, noting that “[o]ur decision in Witherspoon does not govern the present case, because here the jury recommended a sentence of life imprisonment.” Id. at 545, 88 S.Ct. 1788. The same reasoning applies in this case: even if the defendants could demonstrate a Witt-Witherspoon error in the removal for cause of certain jurors, they would not be entitled to reversal of their convictions.

d. Defendants Fail to Demonstrate Other Prejudice Supporting Reversal

To the extent defendants attempt to avoid this conclusion by framing a Sixth Amendment challenge to their convictions in non-capital terms, such an alternative effort hardly lightens their appellate burden. Where the death penalty is not at issue, a defendant seeking reversal of his conviction based on alleged defects in jury selection must demonstrate more than error; he must establish the actual partiality of the jury that convicted him. See United States v. Rubin, 37 F.3d 49, 54 (2d Cir.1994) (holding that, for defendant to prevail on claim that court erred in failing to remove certain jurors for cause, he must “establish that the jury that eventually convicted him was not impartial”); accord United States v. Martinez-Salazar, 528 U.S. 304, 307, 120 S.Ct. 774, 145 L.Ed.2d 792 (2000) (observing that defendant “convicted by a jury on which no biased juror sat ... has not been deprived of any rule-based or constitutional right”). Defendants submit that the erroneous removal for cause of a category of persons, i.e., those strongly opposed to the death penalty, necessarily means that their guilt was adjudicated by a jury that was not impartial. The argument is unconvincing for several reasons.

First, the fact that the Supreme Court has never reversed a conviction upon a finding of a Witt-Witherspoon error strongly indicates that there is no merit to the claim that such an error necessarily produces a jury that is not impartial in determining guilt. See generally Lockhart v. McCree, 476 U.S. 162, 183, 106 S.Ct. 1758, 90 L.Ed.2d 137 (1986) (“[T]he Constitution presupposes that a jury selected from a fair cross section of the community is impartial, regardless of the mix of individual viewpoints actually represented on the jury, so long as the jurors can conscientiously and properly carry out their sworn duty to apply the law to the facts of the particular ease.”).

Second, United States v. Salamone, 800 F.2d 1216 (3d Cir.1986), the sole case cited by defendants to support their argument, is readily distinguishable. In Salamone, the defendants were charged with firearms offenses. The Third Circuit concluded that removal for cause of prospective jurors based on group affiliation, such as the National Rifle Association, deprived the defendant of an impartial jury because it was, in essence, based upon an unsubstantiated presumption of bias resulting from connection to a particular organization. See id. at 1226-27. Without deciding whether we would reach the same conclusion on similar facts, we note that the removals in the instant case were not based simply on bias inferred from group affiliation or even from any general opposition to the death penalty. Rather, removal was based on specific views expressed by individual jurors indicating such automatic opposition to the death penalty in every case as to suggest that partiality prevented or at least substantially impaired the particular juror’s ability to render good faith service consistent with the law. See Wainwright v. Witt, 469 U.S. at 424, 105 S.Ct. 844. Such circumstances do not demonstrate that defendants were convicted by a partial jury. See generally Lockhart v. McCree, 476 U.S. at 183-86, 106 S.Ct. 1758 (rejecting argument that process of qualifying a jury to consider death penalty produces a biased jury at the guilt phase of trial); see also Wainwright v. Witt, 469 U.S. at 423, 105 S.Ct. 844 (defining impartial jury as one that “will conscientiously apply the law and find the facts” and adding that “we do not think, simply because a defendant is being tried for a capital crime, that he is entitled to a legal presumption or standard that allows jurors to be seated who quite likely will be biased in his favor”).

Finally, the verdicts rendered by the jury demonstrate its impartiality. The fact that, at the penalty phase, the jury did not vote to impose the death penalty conclusively refutes defendants’ suggestion that it was composed of persons “uncommonly willing to condemn a man to die.” Witherspoon v. Illinois, 391 U.S. at 521, 88 S.Ct. 1770. Further, the fact that, at the culpability phase, the jury voted to acquit defendants on two of the most serious charges demonstrates that the panel was not predisposed to convict. Cf. United States v. Qamar, 671 F.2d at 732, 737 (2d Cir.1982) (observing that acquittals on certain counts belie claim that jury could not fairly adjudicate the case).

Accordingly, we reject the defendants’ argument that alleged errors in the jury selection process require reversal of their convictions.

C. The Challenged Evidentiary Rulings

Defendants further urge reversal on the ground that their convictions were procured through inadmissible evidence. Specifically, they contend that (1) evidence that they had purchased cocaine from Joseph Sapia should have been excluded pursuant to Fed.R.Evid. 404(b), (2) evidence that Quinones had threatened to kill informants other than Santiago should have been excluded pursuant to Fed.R.Evid. 403 and 404(b), (3) Santiago’s statement of concern about being exposed as an informant was inadmissible hearsay, and (4) cooperating witnesses should not have been allowed to testify as to their expectations that prosecution counsel would discover if they lied at trial.

We review a trial court’s evidentiary rulings deferentially, and we will reverse only for abuse of discretion. See United States v. Khalil, 214 F.3d 111, 122 (2d Cir.2000); United States v. Naiman, 211 F.3d 40, 51 (2d Cir.2000). To find such abuse, we must conclude that the challenged evidentiary rulings were “arbitrary and irrational.” United States v. Dhinsa, 243 F.3d 635, 649 (2d Cir.2001) (internal quotation marks omitted); United States v. Salameh, 152 F.3d at 110. That is not this case.

1. Defendants’ Cocaine Purchases from Sapia

Defendants submit that testimonial and recorded evidence of their cocaine purchases from Joseph Sapia was improperly received to prove their propensity to commit drug crimes in violation of Fed. R.Evid. 404(b). We disagree.

While Rule 404(b) identifies various rationales&emdash;notably excluding propensity&emdash; for which evidence of bad acts other than those charged in the indictment may be admitted at trial, the rule has no bearing on the admissibility of acts that are part of the charged crime. See United States v. Concepcion, 983 F.2d 369, 392 (2d Cir.1992) (“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.”). Defendants’ cocaine purchases from Sapia were clearly part of a crime charged in the indictment, specifically, the narcotics conspiracy charged in Count Five, a stated objective of which was defendants’ distribution and possession with intent to distribute of five or more kilograms of cocaine. The Sapia purchases, as acts in furtherance of the charged conspiracy, were obviously relevant to proof of the existence of that conspiracy. See, e.g., United States v. Alaga, 995 F.2d 380, 382 (2d Cir.1993) (holding that evidence that defendant initiated and participated in purchase of one kilogram of heroin supported conviction for conspiring to possess heroin with intent to distribute).

The government’s use of the disputed testimony in its summation was thus entirely proper. No different conclusion is warranted by the fact that the government mistakenly referenced heroin rather than cocaine in describing defendants’ drug dealing with Sapia. A review of the summation, in its entirety, indicates that the misstatement was inadvertent and neither intended nor understood to suggest that uncharged evidence demonstrated defendants’ propensity to commit drug crimes. That conclusion is reinforced by defendants’ failure to raise a contemporaneous objection. See United States v. Walker, 191 F.3d 326, 337 (2d Cir.1999) (observing that, where prosecutor’s misconduct “did not prompt a contemporaneous objection,” omission was “an indication that the incident did not affect the trial atmosphere in a manner disadvantageous to [defendant]”).

Accordingly, we conclude that this part of defendants’ evidentiary challenge is without merit.

2. Quinones’s Statements Regarding Other Informants

a. Rule I0Jp(b)

Defendants assert that the district court erred in allowing the jury to hear evidence of statements attributed to Qui-nones purportedly threatening the lives of two informants, “Lefty” and “Chupaca-bra.” Defendants submit that the statements “served only to demonstrate a ... propensity to kill informants” and, thus, were inadmissible under Fed.R.Evid. 404(b). Quinones Br. at 9, 40-41.

We have previously held that evidence of uncharged criminal conduct is not evidence of “other crimes, wrongs, or acts” under Rule 404(b) if that conduct is “inextricably intertwined with the evidence regarding the charged offense.” United States v. Towne, 870 F.2d 880, 886 (2d Cir.1989). In such circumstances, the uncharged crime evidence is necessary to “complete the story of the crime on trial,” id., and, thus, appropriately treated as “part of the very act charged,” or, at least, proof of that act, United States v. Concepcion, 983 F.2d at 392.

The record plainly demonstrates that the challenged statements constituted important proof of the charged crimes: they contained Quinones’s admissions to the Santiago murder. Indeed, the statement, “if it had been Lefty, he would have screamed,” makes no sense except as an admission to that crime. Its meaning becomes clear only in light of evidence showing that Quinones had spent the better part of the day abusing a bound and gagged Eddie Santiago who, like “Lefty,” had informed on Quinones to the police. Further, when Quinones made the challenged statement, he had just announced that he had “burned” Santiago. In this context, the statement that “[‘Lefty’] would have screamed,” is reasonably understood as a boast by Quinones to the particularly brutal way that he had killed Santiago, inflicting so much pain that, if “Lefty” had been subjected to similar abuse, he could not have endured it silently. When a statement of hypothetical harm to a third person is thus inextricably linked with the evidence offered to prove the charged offense, it is admissible without reference to Rule 404(b). See United States v. Towne, 870 F.2d at 886.

The same is true of Quinones’s offer to help rid Vega of the informant “Chupaca-bra.” The fact that Quinones phrased this homicidal offer with specific reference to having “got rid of one snitch already,” permitted the jury to conclude that Qui-nones was — again—boasting of the Santiago murder, inextricably linking the proposed uncharged crime to the charged crime. See id. Moreover, the boastful nature of both statements, with Quinones even asserting that he would “like to get rid of another [informant],” fairly supported an inference that Santiago’s death was no accident, but rather intentional murder. It is well established that intent is a permissible ground for the admission of uncharged crime evidence. See, e.g., United States v. Paulino, 445 F.3d 211, 221-23 (2d Cir.2006) (noting admissibility of prior bad acts on issue of intent); see also United States v. Livoti, 196 F.3d 322, 326 (2d Cir.1999) (holding that evidence of defendant choking another arrestee was properly admitted under Rule 404(b) to rebut suggestion that defendant had unintentionally choked victim of charged crime).

b. Rule Í03

Quinones asserts that the district court nevertheless erred in failing to exclude the challenged statements as unduly prejudicial under Rule 403.

Pursuant to Rule 403, a trial judge retains discretion to exclude plainly relevant evidence “if its probative value is substantially outweighed by the danger of unfair prejudice.” Fed.R.Evid. 403; see Huddleston v. United States, 485 U.S. 681, 687-88, 108 S.Ct. 1496, 99 L.Ed.2d 771 (1988); United States v. Reifler, 446 F.3d 65, 91 (2d Cir.2006). No stricter standard applies to death threats. See United States v. Tracy, 12 F.3d 1186, 1195 (2d Cir.1993) (“Evidence of threats of death is subjected to the same Rule 403 balancing test as other relevant evidence”)- While “the government must have an important purpose for [such] evidence in order to satisfy the Rule 403 balancing test[,] ... death threats, just as other potentially prejudicial evidence, are to be judged by the normal process of Fed.R.Evid. 403 balancing.” United States v. Qamar, 671 F.2d 732, 736 (2d Cir.1982). In reviewing Rule 403 challenges, we “accord great deference” to the district court’s assessment of the “relevancy and unfair prejudice of proffered evidence, mindful that it sees the witnesses, the parties, the jurors, and the attorneys, and is thus in a superior position to evaluate the likely impact of the evidence.” United States v. Paulino, 445 F.3d at 217 (internal quotation marks omitted). Applying these principles to this case, we identify no abuse of discretion.

As already noted, the challenged evidence, containing Quinones’s admissions to the Santiago murder, was highly probative of the charged capital crimes. To the extent these admissions were made in the context of threats to other informants (hypothetically with respect to “Lefty” and prospectively with respect to “Chupaca-bra”), these threats were no more inflammatory than the charged murder itself. See generally United States v. Livoti, 196 F.3d at 326 (rejecting Rule 403 challenge where other-act evidence “did not involve conduct more inflammatory than the charged crime”). The government placed no undue emphasis on the threats, and, with respect to the one relating to “Chupa-cabra,” the district court minimized any possible prejudice by carefully instructing the jury that this evidence was received only against Quinones and could be considered only as to his mental state at the time of Santiago’s death. See United States v. Qamar, 671 F.2d at 736-37 (noting that district court limited potential prejudice from death threat evidence by instructing jury that it could be used only for specified purposes).

The relevance of the challenged evidence to the charged crimes lays to rest defendants’ argument that death threats are admissible only when the threat is directed against the witness who testifies to it. In upholding the admissibility of evidence that a defendant threatened a testifying witness, see id. at 736, we have emphasized the witness’s relationship to the threat simply to demonstrate the probative value of that evidence, see United States v. Tracy, 12 F.3d at 1195 (“[Ejvidence of death threats may be extremely probative when the threats were directed against the witness. ...”). Thus, in Qamar we observed that “the threat evidence was useful to explain the demeanor of Uttam [the witness against whom the threat had been directed], who testified in an almost inaudible voice.” 671 F.2d at 736 (internal quotation marks omitted). Further, because “the threat would be likely to make a lasting impression on those present when it was made, [it explained] Uttam’s vivid recollection of the events surrounding the threat.” Id. Where, as in this case, death threat evidence constitutes a defendant’s admissions to the charged crimes, the relevancy of the threat is established without regard to its bearing on witness credibility.

Accordingly, we conclude that there is no merit in defendants’ Rule 404(b) and 403 challenges to the admission of Qui-nones’s statements.

3. Santiago’s Statement Following Quinones’s Arrest

Defendants fault the district court for allowing an undercover officer to testify to out-of-court statements made by Santiago at the scene of Quinones’s arrest. Santiago used an expletive to express that he was now in serious trouble, observing that Quinones was “going to know” Santiago was responsible for the arrest. Trial Tr. at 264. In admitting this testimony, the district court instructed the jury that Santiago’s statements “were not offered for their truth. They were offered for what Mr. Santiago was thinking, and only then to the extent that they may have or may not have influenced his subsequent conduct.” Id. at 264-65. Defendants submit that the district court erred because (1) Santiago’s state of mind was not relevant to any material issue in dispute, and (2) the statements constituted inadmissible hearsay. Neither argument is persuasive.

a. Relevancy

A district court has “broad discretion to determine the relevancy of evidence,” United States v. Amaso, 21 F.3d 1251, 1263 (2d Cir.1994), and we will not reverse its ruling absent abuse of discretion indicative of arbitrariness or irrationality, see United States v. Reifler, 446 F.3d at 91; United States v. Southland Corp., 760 F.2d 1366, 1375 (2d Cir.1985) (observing that “[particular deference” is accorded “ruling of the trial judge with respect to relevancy” because judge “has a familiarity with the development of the evidence and the jury’s reaction to it which an appellate court cannot equal”). Defendants cannot make such a showing in this case.

The district court determined that Santiago’s statement was relevant because his fearful state of mind helped to explain why he made himself scarce after Quinones’s arrest. This, in turn, explained why it took defendants months to locate Santiago and why they had to develop a ruse to lure him to his death. The district court voiced concern that, absent this chain of evidence, the jury might have been inclined to engage in unwarranted speculation as to why, if Quinones was bent on revenge, Santiago was not murdered within days of Quinones’s release from custody. Mindful that the district court’s observation of the trial proceedings placed it “in a superior position to evaluate the likely impact of the evidence” on the jury, we cannot conclude that its relevancy assessment was arbitrary or irrational. United States v. Paulino, 445 F.3d at 217; see United States v. Southland Corp., 760 F.2d at 1375. Thus, we reject defendants’ relevancy challenge as without merit.

b. Rule 803(8)

Equally unavailing is defendants’ contention that Santiago’s out-of-court statements did not qualify for admission pursuant to Fed.R.Evid. 803(3). Defendants submit that Rule 803(3) creates a hearsay exception only for statements evincing a declarant’s existing state of mind and not for statements of memory or belief contributing to that state of mind. Defendants are correct that Rule 803(3) does not permit statements of memory or belief to be admitted for their truth. But where, as in this case, a district court plainly instructs the jury that the out-of-court statements cannot be considered for their truth, no hearsay concern arises requiring a rule exception. See Fed.R.Evid. 801(c) (defining hearsay as an out-of-court statement “offered in evidence to prove the truth of the matter asserted”); see also United States v. Paulino, 445 F.3d at 216-17.

The district court reasonably recognized that, regardless of the truth of Santiago’s declaration about Quinones’s knowledge of Santiago’s status as an informant, the statement was admissible because it established Santiago’s then-fearful state of mind, which explained Santiago’s future actions and, in turn, those of the defendants. This court has recognized that “the mere utterance of a statement, without regard to its truth,” may circumstantially evidence “the state of mind of the declar-ant,” and, as such, does not constitute “hearsay.” Smith v. Duncan, 411 F.3d 340, 346 n. 4 (2d Cir.2005) (internal quotation marks omitted); see United States v. Detrich, 865 F.2d 17, 21 (2d Cir.1988) (same). Indeed, we have observed that “[w]hen a declaration is admitted only to prove a relevant state of mind, it does not appear to matter ... whether admissibility is predicated on the declaration not being hearsay ... or under the [Rule 803(3)] hearsay exception for declaration of states of mind ... [because u]nder either theory, a state of mind can be proved circumstantially by statements which are not intended to assert the truth of the fact being proved.” United States v. Southland Corp., 760 F.2d at 1376 (internal quotation marks omitted). In United States v. Harris, we held that out-of-court statements, such as “the Government and people were after him and trying to set him up,” and “Mr. Steward had brought an agent to him,” were admissible because they were offered “not for their truth, but instead as circumstantial evidence of [the declarant’s] state of mind” with respect to “his knowledge” of Steward’s status as a cooperator. 733 F.2d 994, 1004 (2d Cir.1984). In this case, because Santiago’s statements as to what Quinones had likely deduced were not received for their truth, we conclude that the district court acted within its discretion in allowing these statements to be considered by the jury as circumstantial evidence of Santiago’s state of mind, which helped to explain his and the defendants’ future actions.

c. Harmless Error

Even if we had identified any error in the admission of the challenged Santiago statement, defendants would not be entitled to any relief on this appeal. Other trial evidence, notably the eyewitness accounts of Hector Vega, Louis Malave, and Nilsa Gutierrez, as well as Quinones’s own admissions, so overwhelmingly proved defendants’ protracted search for, and eventual murder of, Eddie Santiago as to render the alleged error harmless. See United States v. Dukagjini, 326 F.3d 45, 61-62 (2d Cir.2003) (holding reversal required in case of erroneously admitted evidence only when error had “substantial and injurious effect or influence in determining the jury’s verdict” (internal quotation marks omitted)); see also Fed. R.Crim.P. 52(a) (“Any error ... that does not affect substantial rights must be disregarded.”).

4. Cooperating Witnesses

Defendants assert that the district court impermissibly allowed the government to bolster the testimony of various witnesses testifying pursuant to cooperation agreements by inquiring as to their expectation that prosecutors would find out if they lied at trial. While it is well-settled that, “absent an attack on the veracity of a witness, no evidence to bolster his credibility is admissible,” United States v. Gaind, 31 F.3d 73, 78 (2d Cir.1994) (internal quotation marks omitted), once such an attack has been launched, a district court enjoys broad discretion in admitting rehabilitative evidence of credibility, see id.; United States v. Cosentino, 844 F.2d 30, 33 (2d Cir.1988).

In this case, from opening statements through summation, defense counsel argued not only that government witnesses were lying when they implicated defendants in narcotics trafficking and in the murder of Eddie Santiago, but that their relationships with the prosecutors provided them with a particular motive to do so. In his opening statement, Quinones’s counsel stated:

[T]hose witnesses are likely to do or say anything on the witness stand as long as they believe it pleases the prosecutors. Why would they do that? Because they have signed these cooperation agreements .... They sign agreements with the prosecutors, prosecutors who at the end of the day will decide whether or not they will write a letter to the sentencing judge for those cooperators which will help those cooperating witnesses get reduced sentences or obtain their freedom. So who do you think those cooperating witnesses want to please?

Trial Tr. at 23-24. Rodriguez’s counsel similarly urged the jury to “[k]eep in mind what a strong motivation [the cooperating witnesses] have to please the government and to please these particular prosecutors because it’s these particular prosecutors that are their ticket out of jail.” Id. at 35.

In light of this attack, which was pursued throughout trial, it was within the district court’s discretion to allow the government to elicit from the witnesses not only their knowledge that they could be prosecuted for perjury if they lied at trial, see United States v. Smith, 778 F.2d 925, 928 (2d Cir.1985); United States v. Cosentino, 844 F.2d at 34; United States v. Ricco, 549 F.2d 264, 274 (2d Cir.1977), but their expectation that prosecutors would uncover any such lies. A cooperating witness’s expectation as to how his testimony will be viewed by prosecutors or the court, whether realistic or not and whether characterized as fact or as opinion, is relevant to demonstrating his motive to lie or to tell the truth and, thus, may properly be explored by the government no less than the defense once the witness’s credibility has been put in issue.

In sum, we conclude that defendants’ various evidentiary challenges are uniformly without merit.

D. The Challenged RICO Charge

Defendants submit that their racketeering convictions must be reversed because the district court lessened the government’s burden of proof in charging these crimes by reference to only three elements. We are not persuaded.

To secure reversal based on a flawed jury instruction, a defendant must demonstrate both error and ensuing prejudice. See United States v. Aina-Marshall, 336 F.3d 167, 170 (2d Cir.2003); see also United States v. Amuso, 21 F.3d at 1260-61 (concluding that harmless error in jury instruction did not warrant reversal). While we review a claim of error in jury instructions de novo, see United States v. Quattrone, 441 F.3d 153, 177 (2d Cir.2006), we will reverse only where the charge, viewed as a whole, “either failed to inform the jury adequately of the law or misled the jury about the correct legal rule,” United States v. Ford, 435 F.3d 204, 209-10 (2d Cir.2006); see United States v. Goldstein, 442 F.3d 777, 781 (2d Cir.2006); United States v. Scarpa, 913 F.2d 993, 1018 (2d Cir.1990) (“Often isolated statements taken from the charge, seemingly prejudicial on their face, are not so when viewed in the context of the entire record of the trial.” (internal quotation marks omitted)).

Defendants’ claim fails at the first step of analysis. They cannot establish any error in the assignment of the government’s burden of proof because the district court’s three-element RICO charge required the jury to make the identical factual findings beyond a reasonable doubt as the standard five-element substantive RICO charge. A comparison of the challenged charge with the five-element substantive charge recommended in Modem Federal Jury Instructions makes this point.

The challenged charge identified as the first RICO element requiring proof beyond a reasonable doubt “that a racketeering enterprise existed that affected interstate commerce.” Trial Tr. at 2669. Modern Federal Jury Instructions charges the identical factual requirement in two elements: “First, that an enterprise existed,” and “Second, that the enterprise affected interstate or foreign commerce.” See Leonard B. Sand, et al, 3 Modem Federal Jury Instructions: Criminal, Instruction 52-19 (2003).

The challenged charge identified the second RICO element requiring proof beyond a reasonable doubt as “that the defendant you are considering was associated with that enterprise.” Trial Tr. at 2669. Modem Federal Jury Instructions states the same requirement as its recommended third element: “Third, that the defendant was associated with or employed by the enterprise.” Instruction 52-19.

The challenged charge identified the third RICO element requiring proof beyond a reasonable doubt as “that on or about the dates charged the defendant unlawfully, intentionally, and knowingly participated in the conduct of the affairs of the enterprise through a pattern of two or more specified racketeering activities.” Trial Tr. at 2669. Modem Federal Jury Instructions states the same proof requirement in two elements: “Fourth, that the defendant engaged in a pattern of racketeering,” and “Fifth, that the defendant conducted or participated in the conduct of the enterprise through the pattern of racketeering activity.” Instruction 52-19.

In short, this case is not at all akin to United States v. Howard, 506 F.2d 1131 (2d Cir.1974), and United States v. Fields, 466 F.2d 119, 120 (2d Cir.1972), relied on by defendants. In those cases, reversal was required not because of the number of elements assigned to the required factual findings, but because the district courts completely omitted an essential factual finding from the jury instructions. See United States v. Howard, 506 F.2d at 1133-34 (reversing conviction where charge failed to instruct on need to find that bank victim was federally insured and that robbery was accomplished through force or violence); United States v. Fields, 466 F.2d at 120 (reversing conviction where charge failed adequately to explain requisite degree of knowledge).

Courts and commentators have long disagreed in assigning a number of elements to the factual findings required to support a RICO conviction. While some circuit courts adhere to the same five elements referenced in Modem Federal Jury Instructions for substantive RICO charges, see United States v. Keltner, 147 F.3d 662, 668 (8th Cir.1998); United States v. To, 144 F.3d 737, 747 (11th Cir.1998), others are inclined to identify four RICO elements, either by combining the enterprise and interstate commerce requirements into a single element, see United States v. Richardson, 167 F.3d 621, 625 (D.C.Cir.1999); United States v. Parise, 159 F.3d 790, 794 (3d Cir.1998); United States v. Posada-Rios, 158 F.3d 832, 855 (5th Cir.1998); United States v. Shifman, 124 F.3d 31, 35 (1st Cir.1997), or by combining the pattern and conduct requirements into a single element, see United States v. Palumbo Bros., Inc., 145 F.3d 850, 877 (7th Cir.1998). The Ninth Circuit, like the district court in this case, makes both these combinations in delineating three RICO elements. See Ninth Circuit Pattern Jury Instructions (Criminal) § 8.129.

As Modem Federal Jury Instructions observes, none of these alternative formulations is erroneous. Instruction 52-19, emt. Wfiiile the five-element formulation “preferred” by Modem Federal Jury Instructions, id., and followed by many district courts in this circuit has much to commend it in explaining the particularly complicated crime of racketeering to a jury, it is not surprising that the district court in this case chose to employ a three-element model, see Jed S. Rakoff & Howard W. Goldstein, RICO: Civil and Criminal Law and Strategy, § 10.05[4] (2005) (recommending three-element RICO instruction).

Our concern on appellate review of a RICO charge is not, however, with the number of elements assigned to the required factual findings, but with whether those elements, when viewed as a whole, adequately instructed a jury as to all factual findings required to support conviction. See United States v. Quattrone, 441 F.3d at 177. Just as a defendant “does not have the right to dictate the precise language of a jury instruction,” United States v. Imran, 964 F.2d 1313, 1317 (2d Cir.1992); see United States v. Stantini, 85 F.3d 9, 21 (2d Cir.1996), he has no right to demand that required factual findings be stated in any particular number of elements, see generally United States v. Conway, 73 F.3d 975, 980 (10th Cir.1995) (“A trial judge retains extensive discretion in tailoring jury instructions, provided that they correctly state the law and fairly and adequately cover the issues presented.”); United States v. Casto, 889 F.2d 562, 565-66 (5th Cir.1989) (rejecting argument that instruction did not “adequately delineate the elements of the crime,” noting that “framing of jury instructions is a matter within the broad discretion of the trial judge”).

In this case, the record shows that the district court not only included within its three-element formulation all the factual findings necessary to support a substantive or conspiratorial RICO conviction, it explained the government’s burden of proof with respect to those findings in some detail. As to the first element, the district court defined the term “enterprise” and explained that the government had to prove beyond a reasonable doubt both the existence of the charged enterprise and its effect on interstate commerce. With respect to the second element, the court explained the need for proof beyond a reasonable doubt that a defendant “not only knew the existence of the criminal enterprise, and the general nature of its activities, but also that he purposely associated himself with it and played some discretionary role, however modest, in its operation, management, or direction.” Trial Tr. at 2669-70. As to the third element, the district court explained that to establish the requisite “pattern” of racketeering activity beyond a reasonable doubt, the government had to prove “at least two specified racketeering acts that, rather than being isolated, are related [in] the sense of having the same or similar purposes, results, participants, victims, or methods of commission and that pose a threat of continued racketeering activity in that they were committed as part of the enterprise’s ongoing criminal purposes.” Id. at 2670. The court then explained that the government relied on two acts to establish this pattern, the narcotics conspiracy and the Santiago murder, the elements of which had to be proved beyond a reasonable doubt.

We conclude that these instructions, read as a whole, correctly identified for the jury the factual findings necessary to support a RICO conviction and in no way lessened the government’s burden of proof.

E. Challenge to Defendants’ Life Sentences

Because defendants conceded in the district court that life sentences were mandated on the drug count of conviction relating to the murder of Eddie Santiago, we review their appellate challenge to these sentences only for plain error. See, e.g., United States v. Villafuerte, 502 F.3d 204, 207 (2d Cir.2007) (“[I]ssues not raised in the trial court ..., including sentencing issues, are normally deemed forfeited on appeal unless they meet our standard for plain error.”). To demonstrate plain error, a defendant must show (1) error, (2) that is plain at the time of appellate review, and (3) that affects substantial rights. Where these conditions are met, we have the discretion to notice a forfeited error if (4) it seriously affects the fairness, integrity, or public reputation of judicial proceedings. See United States v. Olano, 507 U.S. 725, 732, 113 S.Ct. 1770, 123 L.Ed.2d 508 (1993); United States v. Rybicki, 354 F.3d 124, 129 (2d Cir.2003) (en banc); United States v. Thomas, 274 F.3d 655, 667 (2d Cir.2001) (en banc).

The error asserted by defendants in this case is the district court’s purported misapprehension that it was required to impose a life sentence by both 21 U.S.C. § 848(e)(1)(A) and the federal Sentencing Guidelines. Defendants submit that, because this error may have resulted in the district court imposing a longer sentence than was warranted by the factors outlined in 18 U.S.C. § 3553(a), a Crosby remand is necessary to determine any effect on their substantial rights. See United States v. Crosby, 397 F.3d 103, 119 (2d Cir.2005) (providing remand procedure to determine effect of sentencing error on substantial rights). We disagree.

Crosby observed that, while a pre-Booker sentence may be erroneous insofar as it was “imposed without an understanding of sentencing law as subsequently explained” by Booker, “we cannot know whether a correct perception of law would have produced a different sentence.” Id. at 118. Here, we suffer from no such handicap. The record indicates that the challenged life sentences were dictated not by a perceived Guidelines mandate, but by a tactical concession made by defendants at the penalty phase. Specifically, to strengthen their argument to the jury against imposition of the death penalty, defendants represented (and urged the court to charge) that the single alternative sentence would require the defendants to spend the rest of their lives in prison. In light of this concession, it hardly appears that an awareness of the advisory nature of the Guidelines would have resulted in anything less than the challenged life sentences. We need not, however, conclusively resolve that issue. For reasons discussed herein, we conclude that defendants’ tactical decision at the penalty phase to concede life sentences if the jury rejected the death penalty precludes them from now complaining that those sentences constitute plain error. Thus, review pursuant to Crosby for plain error in sentences imposed before Booker was decided is not available to defendants. Id. at 116 (noting that prudential doctrines of plain error and harmless error are applied “in the customary manner” to determination of whether resentencing is warranted under Booker).

To explain this conclusion, our discussion proceeds in the following order: (1) the relevant statute and Guidelines did not mandate a life sentence in this case; (2) defendants cannot convincingly demonstrate their life sentences resulted from the district court’s misconstruction of the statute and Guidelines; (3) rather, the challenged sentences appear to derive from defendants’ tactical concession to the capital jury that, if the death penalty was not imposed, they would have to serve terms of life imprisonment; and (4) this concession precludes defendants’ claim that their life sentences constitute plain error.

1. Neither 21 U.S.C. § 81p8 Nor the Sentencing Guidelines Mandated Life Sentences in this Case

Preliminarily, we recognize that neither § 848 nor the Sentencing Guidelines, particularly when construed as advisory as required by United States v. Booker, 543 U.S. 220, 245, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005), mandated the imposition of life sentences in this case.

At the time of the challenged sentences, 21 U.S.C. § 848(e)(1)(A) provided that persons found guilty of murders related to drug enterprises might be sentenced to “a term of imprisonment, which shall not be less than 20 years, and which may be up to life imprisonment, or may be sentenced to death.” While the statute would have required the district court to follow a jury recommendation to sentence defendants to death, see id. at § 848(i) (“Upon the recommendation that the sentence of death be imposed, the court shall sentence the defendant to death.”), in the absence of such a recommendation, it afforded a district court considerable discretion to impose any other sentence “authorized by law,” id., i.e., any sentence from twenty years’ incarceration to life imprisonment without parole. See also id. at § 848(p) (noting that, if court does not impose death sentence, it “may impose a sentence of life imprisonment without the possibility of parole” (emphasis added)); United States v. Chandler, 996 F.2d 1073, 1084-85 (11th Cir.1993) (holding that, under § 848, jury has “sole power to recommend a sentence of death,” but if it does not do so, “trial judge has the responsibility to impose a sentence other than death”).

At the time of defendants’ sentences, a district court’s exercise of statutory sentencing discretion was circumscribed by what were then understood to be mandatory Sentencing Guidelines. See United States v. Mincey, 380 F.3d 102, 105-06 (2d Cir.2004) (declining to construe Blakely v. Washington, 542 U.S. 296, 124 S.Ct. 2531, 159 L.Ed.2d 403 (2004), to mandate invalidation of federal Sentencing Guidelines in the absence of further guidance from the Supreme Court), vacated sub nom., Ferrell v. United States, 543 U.S. 1113, 125 S.Ct. 1071, 160 L.Ed.2d 1053 (2005). These Guidelines identified a single non-capital penalty for premeditated murder: life imprisonment. See U.S.S.G. § 2A1.1, App. Note 2(A) (“In the case of premeditated killing, life imprisonment is the appropriate sentence if a sentence of death is not imposed.”). While the Guidelines scheme, even when mandatory, afforded district courts some discretion to depart, it strongly discouraged such departures in cases of premeditated murder. See id After the Supreme Court, in United States v. Booker, recast the Guidelines as advisory, see 543 U.S. at 245, 125 S.Ct. 738, however, this court identified potential plain error affecting substantial rights in a district court’s mandatory application of Guidelines sentences. See United States v. Crosby, 397 F.3d at 118 (observing that “sentence imposed under a mistaken perception of the requirements of law will satisfy plain error analysis if the sentence imposed under a correct understanding would have been materially different” and ordering remand for district court to indicate whether such material difference was present in case).

2. Defendants’ Claim that Their Life Sentences Were a Product of the Alleged Error

While the district court plainly viewed life sentences as required on the capital count of conviction, defendants fail to show that this view was the result of a misconstruction of § 848’s sentencing provision or of a misperception of the Sentencing Guidelines as mandatory.

A careful review of the sentencing record suggests that the district court thought life sentences were required on the capital count for reasons distinct from any Sentencing Guidelines mandate. The murder Guidelines, after all, provided for life sentences on a total of three counts of conviction: the two non-capital racketeering counts (for which the Santiago murder was a predicate), as well as the capital § 848 count. The district court, however, appears to have identified some discretion with respect to the racketeering counts that did not pertain to the capital count. Compare Sentencing Tr. at 16 (observing that Guideline level of 48 for racketeering counts is “what compels the life term for the[se] counts where th[ere] is discretion”) with id. at 8 (stating that § 848 count “is not a discretionary matter”). This distinction implies that the district court understood something other than the Guidelines to mandate the challenged life sentences on the capital count. Indeed, that conclusion finds further support in the district court’s discussion of Blakely v. Washington, 542 U.S. 296, 124 S.Ct. 2531, 159 L.Ed.2d 403. While the district court expressed disappointment that this court had not construed Blakely to free federal judges from the Guidelines, it observed that Blakely made no difference to the required life sentences on the § 848 count. See id. at 7 (“Obviously, there is no, either a Blakely issue or any other kind of issue with respect to the [§ 848] count where life imprisonment is required.”).

To the extent defendants submit that the district court must have misconstrued the sentencing provision of § 848 to mandate a life sentence, we do not lightly assume that an experienced district judge has misread or misunderstood a criminal statute. See, e.g., United States v. Sweeney, 90 F.3d 55, 58 (2d Cir.1996) (applying presumption that sentencing judge is knowledgeable about available sentencing options); United States v. Rivers, 50 F.3d 1126, 1131 (2d Cir.1995) (same). Such an assumption of error is particularly unwarranted in this case because the record offers a more likely explanation for the district court’s conclusion that it was required to impose life sentences on the § 848 count. Specifically, it appears that the defendants agreed to life imprisonment as the only possible non-capital sentence to strengthen their argument to the jury, at the penalty phase of this case, that justice did not demand their deaths.

3. Defendants’ Sentencing Representations to the Jury

Even before jury selection, defendants urged the district court to instruct prospective jurors that, on the capital charges, there were only two possible sentences, life imprisonment or death, and that, if the jury rejected the latter, the court would be required to impose the former. Insofar as such an instruction correctly stated the law under the Federal Death Penalty Act, see 18 U.S.C. § 3594, which applied to the capital racketeering charges against defendants, their pre-trial request for such an instruction might not, by itself, reasonably be construed as a sentencing concession under § 848. More telling, however, is the fact that, even after the jury acquitted defendants on the capital racketeering counts, and after experienced capital defense counsel acknowledged that the death penalty was to be considered only under § 848, defendants continued to insist that the jury be charged that the only two sentencing possibilities on the capital count were life imprisonment or death. Presented with a proposed charge to this effect, defendants not only failed to object, they asked the court to emphasize the alternative life sentence would be without possibility of parole.

Consistent with these defense requests, at the penalty phase the district court framed the “ultimate question” for jury resolution as a choice between two sentencing options, i.e., “whether a defendant should be executed or imprisonfed] for life without the possibility of release.” Trial Tr. at 3985. The court explained:

[T]here are only two sentences that are legally possible under [the count involving murder in connection with the narcotics trafficking]. One is life imprisonment without release. I want to make you aware that in the federal system there is no parole. So life imprisonment means exactly that, imprisonment for life without any possibility for release. That is the sentence that will be imposed unless all of you unanimously find beyond a reasonable doubt that the death penalty must be imposed. In other words the default position in effect is life imprisonment without release and only if every one of you concludes beyond a reasonable doubt that death must be imposed, will [it] be imposed.

Trial Tr. at 2925, 3985.

Reinforcing the instruction that “the default position in effect is life imprisonment without release” was the court’s instruction on mitigating factors.

A mitigating factor is a factor that favors a punishment of life imprisonment without release rather than the death penalty.... [A] mitigating factor is a fact about the defendant’s life or character, or about other circumstances that you find relevant, that would suggest that a sentence of life in prison without any possibility of release is a more appropriate punishment than death.

Id. at 3989, 3991-92 (identifying as mitigating factor: “Life imprisonment without release is itself a very severe punishment.”).

Having successfully secured these instructions, defense counsel framed their arguments against the death penalty by emphasizing the availability of a single non-capital sentence: life imprisonment. “Now, your choice is clear. It’s life imprisonment or the death penalty.” Id. at 3975. Moreover, counsel emphasized that the jury’s decision between the two sentences would be “the final one.” Id. at 3961 (“You are the ultimate determiners of whether [the defendant] will be sentenced to death or live out his days in a federal prison.”). Indeed, when on one occasion defense counsel inadvertently referenced a jury “recommendation” of life imprisonment — a formulation that might imply the possibility of the court imposing a lesser sentence — he quickly corrected himself to urge jury “imposition” of a life sentence, signaling the finality of that decision. Id. at 3959 (“[W]e ask you to unanimously recommend and — excuse me — unanimously impose a life sentence without release.”). The singular alternative of life imprisonment was thus plainly critical to defendants’ arguments to the jury that justice did not require imposition of the death penalty. See id. at 3940 (assuring jury that “[s]ociety will be protected” by life sentences for defendants “because it’s without release”; defendants will spend the rest of their lives “in a cage,” a punishment that some think is “worse than the death penalty”); see also id. at 3960 (closing summation by stating: “Finally, it’s justice. Life in prison without release is justice in this case.”); id. at 3969 (assuring jury that, if death penalty is not imposed, “he’ll spend the rest of his life in prison”).

4. Defendants’ Tactical Decision To Agree to Mandatory Life Imprisonment as the Only Alternative to a Death Sentence Waives Their Claim of Plain Error

Defendants having thus successfully persuaded the jury that it did not need to vote for the death penalty, we decline to entertain their appellate claim that the district court committed plain error by imposing what it thus viewed as a required life sentence. The law is well established that if, “as a tactical matter,” a party raises no objection to a purported error, such inaction “constitutes a true “waiver’ which will negate even plain error review.” United States v. Kon Yu-Leung, 51 F.3d 1116, 1122 (2d Cir.1995); United States v. Coonan, 938 F.2d 1553, 1561 (2d Cir.1991) (holding that, where appeal attempts “to evade the consequences of an unsuccessful tactical decision ... we have no difficulty concluding that [appellant] has waived review” of claim); see also United States v. Krankel, 164 F.3d 1046, 1053 (7th Cir.1998) (noting particular reluctance to find plain error when defendant fails to object at trial “because of a tactical decision”). A finding of true waiver applies with even more force when, as in this case, defendants not only failed to object to what they now describe as error, but they actively solicited it, in order to procure a perceived sentencing benefit. As we observed in United States v. Ferguson, when defendants obtain “precisely what they affirmatively sought, it ill behooves [them] now to complain” of error, 758 F.2d 843, 852 (2d Cir.1985) (discussing “invited error”); cf. United States v. Chandler, 996 F.2d 1073, 1084 (11th Cir.1993) (applying “invited error” doctrine to defendant’s claim that, in § 848 case, district court erred in not permitting jury to recommend sentence other than death, and concluding the argument was foreclosed by defense position at conferences and in requested instructions that responsibility for non-death sentence rested with court).

We have no doubt that it was a tactical decision for defendants, at the penalty phase of this case, to agree that a life sentence was the only alternative to death. Indeed, the same concession was made by defendant Thomas Pitera in the first § 848 capital case tried in this circuit more than fifteen years ago. See generally United States v. Pitera, 5 F.3d 624 (2d Cir.1993). In voting against the death penalty, all twelve jurors identified as a mitigating factor “[t]hat, if not sentenced to death, defendant will serve a term of life imprisonment without parole.” Pitera v. United States, No. 90 CR 424, 2007 WL 3005791 (E.D.N.Y.), Special Findings III.4D, reprinted in Sourcebook for Judges and Counsel in Federal Capital Prosecutions, Federal Death Penalty Resource Counsel Project 13.A (1999). The tactical value of such a concession is obvious. As courts and commentators have observed, “ ‘the sooner jurors think a defendant will be released from prison, the more likely they are to vote for death....’” People v. LaValle, 3 N.Y.3d 88, 117, 783 N.Y.S.2d 485, 501, 817 N.E.2d 341, 357 (2004) (quoting William J. Bowers & Benjamin D. Steiner, Death by Default: An Empirical Demonstration of False and Forced Choices in Capital Sentencing, 77 Tex. L.Rev. 605, 703 (1999)); see Theodore Eisenberg & Martin T. Wells, Deadly Confusion: Juror Instructions in Capital Cases, 79 Cornell L.Rev. 1, 4 (1993) (noting in study of South Carolina capital cases that “misguided fears of early release generate death sentences”). Thus, while § 848 may, indeed, afford district courts considerable sentencing discretion when a jury does not impose the death penalty, a defendant might reasonably conclude that he can best avoid a death sentence by agreeing to life imprisonment as the single alternative punishment.

Sentencing agreements are not unheard of in the law. The Rules of Criminal Procedure permit parties, with the consent of the court, to agree to a specific sentence as the appropriate disposition in a case. See Fed. R. Grim P. 11(c)(1)(C). What occurred in this case might reasonably be viewed as a variation on this theme. Both defendants and the government acknowledge that they acquiesced in — and, in the case of defendants, actively solicited— Judge Rakoff s instruction to the jury that, if the death penalty were not imposed, life imprisonment was the only available alternative. Defendants can hardly complain that the district court sentenced them in accordance with this invited jury representation.

Defendants nevertheless submit that their sentencing concession cannot be binding because it was made before United States v. Booker, 543 U.S. 220, 125 S.Ct. 738, 160 L.Ed.2d 621, at a time when they understood that the district court would have little, if any, discretion to depart from the life sentence mandated by the Sentencing Guidelines. The calendar does not support defendants’ argument. At the time of their August 4, 2004 sentencing concession to the jury, defendants had the benefit of both the Supreme Court’s June 24, 2004 decision in Blakely v. Washington, 542 U.S. 296, 124 S.Ct. 2531, 159 L.Ed.2d 403, and Judge Rakoffs July 21, 2004 decision declaring the federal Guidelines unconstitutional in light of Blakely, see United States v. Marrero, 325 F.Supp.2d 453 (S.D.N.Y.2004). See also United States v. Rosen, 409 F.3d 535, 550 (2d Cir.2005) (describing Blakely as a “harbinger” of Booker). Thus, we are not persuaded that defendants’ sentencing concession was dictated by an assumption that the Guidelines were mandatory.

In any event, defendants’ argument is at odds with our holding in United States v. Morgan, 406 F.3d 185 (2d Cir.2005). In Morgan, we ruled that a pre-Booker waiver of appellate rights barred defendant from pursuing a Booker challenge to his sentence. Two observations informed our conclusion: (1) there was “no indication that the parties intended for the appeal waiver not to apply to issues arising after, as well as before, the waiver,” id. at 137; and (2) the waiver was entered as part of a “plea agreement process” that permitted the defendant and the government “to allocate risk, to obtain benefits, to achieve finality and to save resources.” Id. The same reasoning applies with even greater force in this case.

As in Morgan, the record in this case offers no indication that defendants’ sentencing representation to the jury was in any way contingent on future legal developments. The omission is significant because, while Morgan may have had no reason to suspect the invalidity of the Guidelines, defendants’ sentencing concession, as we have just shown, was made at a time when the issue was at the forefront of legal debate. More important, it is impossible to overestimate the benefit defendants derived from their representation to the jury that the only non-capital alternative in their case was life imprisonment; the argument may well have saved their lives.

In sum, because defendants, in successfully avoiding the death penalty, made a tactical decision to concede the singular non-capital alternative of a life sentence, we conclude that they cannot now argue that the imposition of such a sentence constitutes plain error. See United States v. Kon Yu-Leung, 51 F.3d at 1122; United States v. Ferguson, 758 F.2d at 852. Indeed, if we were to entertain an argument that afforded defendants the possibility of a lesser sentence than the one the jury was told would be required when it voted to spare defendants the death penalty, that ruling, and not the challenged life sentences, would raise concerns about the fairness, integrity, and repute of the capital proceeding.

III. Conclusion

To summarize, we conclude:

(1) The district court acted within its discretion in empaneling an anonymous jury-

(2) The Sixth Amendment does not necessarily preclude removals for cause based on responses to jury questionnaires although, in capital cases, some oral questioning is preferred in conducting a WitU Witherspoon inquiry. We need not decide if the challenged removals in this case, based only on questionnaire responses, comported with Witt-Witherspoon because, where the death penalty is not imposed, defendants are not entitled to relief from their convictions.

(3) None of the challenged evidentiary rulings demonstrate abuse of discretion.

(4) Charging RICO by reference to three elements does not reduce the government’s burden of proof where, as in this case, those elements are defined for the jury by detailing all factual findings necessary to support conviction.

(5) We decline to entertain a plain error challenge to life sentences imposed before Booker where defendants made the tactical decision, at the penalty phase of this capital case, to represent to the jury (both through their own arguments and the instructions they sought from the court) that, if the jury voted against the death penalty, defendants would be required to spend the rest of their lives in prison.

The judgments of conviction are hereby AFFIRMED. 
      
      . Preliminary to trial, the district court declared the federal death penalty unconstitutional, see United States v. Quinones, 205 F.Supp.2d 256 (S.D.N.Y.2002), but this court reversed that ruling in United States v. Quinones, 313 F.3d 49 (2d Cir.2002).
     
      
      . Defendants had originally faced the death penalty under three capital counts: the § 848(e)(1)(A) charge, as well as substantive and conspiratorial charges of murder in aid of racketeering, see 18 U.S.C. § 1959(a)(1), (a)(5). Defendants were acquitted on the two capital racketeering charges.
     
      
      . Other trial evidence showed that "Lefty” was a former partner of Quinones who, in 1997, had testified against the defendant in a New York State criminal trial in which Qui-nones was acquitted. Milton Rivera testified to Quinones disparaging "Lefty” as a "rat.” Id. at 458.
     
      
      . The district court instructed the jury that Vega’s testimony with respect to "Chupaca-bra” was received only against Quinones and only as to Quinones's state of mind at the time of the alleged acts respecting Santiago.
     
      
      . The district court sentenced both defendants to terms of life imprisonment on each of the racketeering counts as well as the capital § 848(e)(1)(A) charge and to a term of ten years’ imprisonment on the § 846 charge. It also sentenced Quinones to twenty years' imprisonment on a separate § 848(b)(1)(C) count. All sentences for both defendants run concurrently.
     
      
      . As discussed infra at 37-38, these statements were received into evidence at trial for relevant reasons other than Quinones's propensity for violence. A court, however, may appropriately consider a defendant’s propensity to threaten witnesses or otherwise to tamper with the judicial process in evaluating the need for an anonymous jury.
     
      
      . But see David Mellinkoff, The Language of the Law, 101-02, 106 (1963) (observing that "voir dire” derives from Old French, where it means simply "to speak the truth,” and noting “confusion results if the term is judged by the standards of modern French”).
     
      
      . In approving the use of questionnaires as part of voir dire, we do not hold that district judges are ever obligated to make use of this procedure in selecting juries. See United States v. Salameh, 152 F.3d at 120-21 (holding district court did not abuse discretion in declining to use defense questionnaire where voir dire was thorough and probing).
     
      
      . Morgan’s reference to "automatic” decision-making derives from Witherspoon. See Witherspoon v. Illinois, 391 U.S. at 522 n. 21, 88 S.Ct. 1770. Although Witt dispensed with this standard, it did so because it was inadequate to identify all persons opposed to the death penalty who might properly be removed for cause: "[I]t does not make sense to require simply that a juror not 'automatically' vote against the death penalty; whether or not a venireman might vote for death under certain personal standards, the State still may properly challenge that venireman if he refuses to follow the statutory scheme and truthfully answer the questions put by the trial judge.” Wainwright v. Witt, 469 U.S. at 422-24, 105 S.Ct. 844. The conclusion to draw from these developments, as Morgan explains, is that, if a juror would automatically vote against the death penalty in every intentional murder case, it necessarily follows that he would be seriously impaired in the good faith performance of jury service and, therefore, removable for cause. See Morgan v. Illinois, 504 U.S. at 733, 112 S.Ct. 2222; Wainwright v. Witt, 469 U.S. at 424, 105 S.Ct. 844.
     
      
      . Bumper's conviction was, however, reversed based on the failure to suppress evidence procured in an unlawful search. Bumper v. North Carolina, 391 U.S. at 548-51, 88 S.Ct. 1788.
     
      
      . The Supreme Court has clearly ruled that a non-capital defendant who is jointly tried with a capital defendant by a death-qualified jury cannot make out a claim of unconstitutional partiality. See Buchanan v. Kentucky, 483 U.S. 402, 419-20, 107 S.Ct. 2906, 97 L.Ed.2d 336 (1987).
     
      
      . Other crime evidence is admissible to prove "motive, opportunity, intent, preparation, plan, knowledge, identity, or absence of mistake or accident.” Fed.R.Evid. 404(b).
     
      
      . This same narcotics conspiracy was identified as RICO predicate act 1(A) in Counts One and Two of the Indictment. Predicate act 1(C) to these counts charged the defendants with substantive distribution or possession with intent to distribute five or more kilograms of cocaine.
     
      
      . To the extent defendants raised additional challenges to this evidence in the district court, arguing that its admission was prejudicial, inconsistent with the government’s theory of the case, and violative of their Sixth Amendment right to confrontation, see Trial Tr. at 250-51, because these issues are not pursued on appeal to this court, we deem them waived. See United States v. Pereira, 465 F.3d 515, 520 n. 5 (2d Cir.2006) (holding argument not raised on appeal waived).
     
      
      . Rule 803(3) provides that "[a] statement of the declarant's then existing state of mind, emotion, sensation, or physical condition (such as intent, plan, motive, design, mental feeling, pain, and bodily health), but not including a statement of memory or belief to prove the fact remembered or believed unless it relates to the execution, revocation, identification, or terms of declarant's will” is "not excluded by the hearsay rule even though the declarant is available as a witness.”
     
      
      . Because defendants attacked the credibility of government witnesses in their opening statements, their challenge to the elicitation of this rehabilitative testimony on direct rather than redirect examination is unavailing. See United States v. Gaind, 31 F.3d at 78 (holding that, where witness's credibility has been attacked in defense opening, evidence indicating cooperation agreement creates motive for witness to tell truth may be adduced on direct examination); United States v. Cosentino, 844 F.2d at 33 (noting that, where witness’s credibility has been attacked in opening statements, "the 'rehabilitation' stage has already been reached on direct”); United States v. Smith, 778 F.2d at 928.
     
      
      . Modern Federal Jury Instructions recommends that RICO conspiracy be charged by reference to four elements. See Leonard B. Sand, et al., 1 Modern Federal Jury Instmc-tions: Criminal, Instruction 52-28 (2003). It is unnecessary for us to discuss the reasons for this distinction because defendants' charge challenge focuses on substantive RICO and, in any event, the record shows that the argument is without merit as to both substantive and conspiratorial RICO.
     
      
      . In charging RICO conspiracy, the district court referred the jury to its instructions on substantive racketeering and conspiracy generally, explaining that "where a conspiracy is concerned, the Government is not required to prove that the given defendant ... specifically agreed to commit both specified racketeering acts or that he actually committed two such acts, but only that the defendant unlawfully, intentionally, and knowingly agreed to participate in the overall racketeering objectives of the enterprise and that at least one member of the conspiracy agreed to commit the two specified acts.” Trial Tr. at 2672-73. This is consistent with the factual findings outlined in the typical four-element RICO conspiracy charge. See Modem Federal Jury Instmctions at Instruction 52-32.
     
      
      . Judicial discretion in imposing a non-capital sentence under § 848 was repealed by 19 the USA Patriot Improvement and Reauthori-zation Act of 2005, Pub.L. No. 109-177, § 221(2), 120 Stat. 192, 231 (2006). Sentencing for capital offenses under § 848, like other federal capital crimes, is now covered by the Federal Death Penalty Act, 18 U.S.C. §§ 3591-98, which makes a jury recommendation of life imprisonment binding on the district court, see id. at § 3594 ("Upon a recommendation ,.. that the defendant should be sentenced to death or life imprisonment without possibility of release, the court shall sentence the defendant accordingly.” (emphasis added)).
     
      
      . While this commentary states that "downward departure would not be appropriate 20 in [a premeditated murder] case,” U.S.S.G. § 2A1.1, App. Note 2(A), the observation is not absolute, as evidenced by the fact that, even in cases involving "a mandatory statutory term of life imprisonment” — not then provided for in § 848 — the Guidelines recognized one circumstance in which downward departure would be "permissible,” i.e., when the government moved for consideration based on the defendant’s substantial assistance pursuant to 18 U.S.C. § 3553(e). See id.
      
     
      
      . By contrast, the failure timely to assert a claim results only in forfeiture of that claim, rather than waiver, the latter of which requires the "intentional relinquishment or abandonment of a known right." United States v. Olano, 507 U.S. 725, 733, 113 S.Ct. 1770, 123 L.Ed.2d 508 (internal quotation marks omitted).
     
      
      . The government makes essentially the same argument by reference to judicial estop-pel. That doctrine, however, applies "only when a tribunal in a prior separate proceeding has relied on a party’s inconsistent factual representations and rendered a favorable decision.” Adler v. Pataki, 185 F.3d 35, 41 n. 3 (2d Cir.1999) (emphasis in original); see also OSRecovery, Inc. v. One Groupe Int'l, 462 F.3d 87, 93 n. 3 (2d Cir.2006). As a rule, judicial estoppel does not apply on direct appeal. See Adler v. Pataki, 185 F.3d at 41 n. 3; see also 18B Wright, Miller & Cooper, Federal Practice and Procedure § 4477 ("There is much to be said for refusing to apply ‘judicial estoppel’ within the course of pretrial, trial, and appeal of a single action.”). Traditional appellate review doctrines of forfeiture, waiver, and plain error are generally adequate to address a party’s change of position between the trial and appellate courts. Because those tools permit us to reject defendants' sentencing challenge, we do not further consider the possible application of judicial estoppel in this criminal case. See generally United States v. Velez Carrero, 140 F.3d 327, 330 (1st Cir.1998) (drawing analogies between judicial es-toppel as it applies in civil cases and waiver principle applicable in criminal cases: "Just as the companion doctrines of judicial estop-pel and election of remedies preclude parties in civil litigation from asserting legal or factual positions inconsistent with the positions that they took in prior proceedings, so, too, a criminal defendant ordinarily must raise claims in a timely fashion, consistent with his prior positions in the case, or suffer the consequences.” (internal citations omitted)).
     
      
      . No different conclusion is warranted by the fact that, after the jury verdict but prior to defendants’ September 27, 2004 sentencing, this court had decided United States v. Mincey, 380 F.3d 102 (2d Cir.2004) (holding that district courts in this circuit should not rely on Blaltely to invalidate the federal Guidelines absent clearer direction from the Supreme Court). As Mincey itself noted, see id. at 103, the likelihood that further Supreme Court direction would soon be forthcoming was apparent from the fact that argument had been scheduled in United States v. Booker and United States v. Fanfan, 543 U.S. 220, 125 S.Ct. 738, 160 L.Ed.2d 621 (2004), for October 4, 2004.
     
      
      . Our ruling renders unnecessary any Crosby remand on the remaining counts of conviction, as any resentencing on those counts would not change the fact that defendants will spend the rest of their lives imprisoned pursuant to the § 848 conviction.
     