
    UNITED STATES of America, Appellee, v. Humberto Antonio GAVIRIA, a/k/a Chicky, a/k/a Alberto Bustamonte, a/k/a Antonio Gaviria Alvarez, a/k/a Pablo Vargas, a/k/a Radamas Perez, Appellant.
    Nos. 95-3124, 95-3125, 95-3151, 96-3018.
    United States Court of Appeals, District of Columbia Circuit.
    Argued April 17, 1997.
    Decided June 27, 1997.
    
      Stephen C. Leckar, Joseph Virgilio, Neal Goldfarb, Washington, DC, and Howard F. Bramson, E. Brunswick, NJ, all appointed by the Court, argued the causes and filed the joint and individual briefs for appellants. Zachary Williams, Chicago, IL, appearing pro se, also filed a brief.
    William D. Weinreb, Assistant United States Attorney, Washington, DC, argued the cause for appellee, with whom Eric H. Holder, Jr., United States Attorney, Washington, DC, John R. Fisher, Mary-Patriee Brown, and Jeanne M. Haueh, Assistant United States Attorneys, Washington, DC, were on the brief. Barbara A. Grewe and Elizabeth Trosman, Assistant United States Attorneys, Washington, DC, entered appearances.
    Before: WALD, GINSBURG and TATEL, Circuit Judges.
   Opinion for the Court filed Per Curiam.

PER CURIAM:

In these consolidated appeals, the appellants are four individuals convicted of various drug conspiracy and distribution offenses arising out of an undercover investigation of a multikilogram drug-dealing operation in Miami and the District of Columbia. Appellants challenge their convictions and sentences, raising numerous claims, one jointly and the rest individually. In Part I of this opinion, we summarize the basic facts of the ease. In Part II, we address the challenge to the jury instruction on the conspiracy charge, an argument raised jointly by all four appellants. In Part III, we address the challenges raised individually by appellant Humberto Gaviria, in Part IV, those raised by appellant Regulo Zambrano, in Part V by appellant Zachary Williams, and in Part VI, by appellant Jose Naranjo. We affirm on all issues and uphold all of the appellants’ convictions, except that we remand appellant Gaviria’s claim of ineffective assistance of counsel to the district court for an evidentiary hearing, and we vacate the forfeiture portion of appellant Williams’s sentence.

I. Background

The convictions at issue arose out of a joint Federal Bureau of Investigations (FBI)-Metropolitan Police Department (MPD) investigation of appellant Jose Naranjo, a federal prison inmate who, with the help of his wife Gloria Naranjo and various other individuals, continued his cocaine business while he was incarcerated at the Federal Correctional Institute (FCI) in Petersburg, Virginia. During the course of his prison term, Naranjo was introduced to David Sanders, himself an experienced drug dealer who was visiting a friend at FCI. At that initial meeting, Nar-anjo introduced Sanders to Naranjo’s wife, Gloria, who was also in the FCI visiting room at the time. Subsequently, Naranjo arranged for his wife to supply Sanders with multi-kilogram quantities of cocaine to be resold in the District of Columbia. However, this arrangement failed when Gloria Naranjo was arrested and imprisoned on a federal drug conspiracy charge during the summer of 1992. In order to maintain his cocaine business after that, Naranjo had to find a new drug connection on the outside.

Consequently, during the fall of 1992, Nar-anjo put in several telephone calls from FCI to Humberto Gaviria, a convicted drug dealer residing in Colombia, to find out whether Gaviria would be willing to supply drugs for resale in the United States. In these phone calls, which like many others in the case were conducted in code, Naranjo asked Gaviria for details about the price, availability, and quality of cocaine that Gaviria would be able to acquire in Colombia. Gaviria informed Naranjo in Spanish that “one of those ears here cost[s] around $800.00 pesos,” that “there is a whole, whole, whole bunch for everyone,” and that “it is the best.” GovEx 102292 at 12-13. Per Gaviria’s request, Naranjo confirmed this conversation with a letter written in Spanish code that, among other things, provided a New Jersey telephone number for “El Perrito,” Naranjo’s “connection” for the drugs. In a November 20, 1992 telephone call, Gaviria told Naranjo that he had found a drug supplier in Colombia (“Pachito”). Subsequently, Naranjo arranged for Gaviria to come to the United States and directed Sanders to help Gaviria in the drag-selling endeavor. However, unbeknownst to Naranjo or Gaviria, Sanders was arrested on an unrelated charge sometime between the original phone calls between Naranjo and Gaviria and the time of Gaviria’s arrival in the United States. Following his arrest, Sanders agreed to cooperate with the FBI in the investigation of Nar-anjo.

After Gaviria’s illegal immigration, the Naranjo/Gaviria conspiracy planned four shipments of drags that figured in the FBI/ MPD investigation. Arrangements for the first shipment, which was “lost” before arrival in this country, occurred three weeks after Gaviria’s arrival. Sanders gave Gaviria $17,-500 as a downpayment on five kilograms of cocaine, but after the money was sent, Nar-anjo and Gaviria spent months unsuccessfully tracking the shipment through South and Central America. The drags had not entered the United States by the time the two men were arrested in November 1993.

The second and third shipments of drags arose out of a surprise phone call received by Gaviria on October 27, 1993, from appellant Regulo Zambrano in Miami, where Zambra-no, a Colombia native and old acquaintance of Gaviria’s, had been residing illegally since March 1993. One month prior to this phone call, Gaviria was introduced to Detective Jesus Gonzales, an undercover officer who called himself “Carlos.” Upon receiving Zambrano’s phone call, Gaviria told Sanders and Gonzales that Zambrano could provide them with drags, and Gaviria introduced them to him over the phone. Both Gaviria and Naranjo vouched for Zambrano’s trustworthiness and ability to get drags. After several more phone calls between Gaviria and Zambrano, Naranjo instructed Sanders to get Gaviria a plane ticket to Miami, and Sanders did so. Gaviria flew to Miami on November 2,1993, spending several nights at Zambrano’s house. In a three-way phone conversation in which Gonzales, Gaviria, Zambrano, Naranjo, and Sanders participated, the group talked in code about the possibility of arranging a drug deal.

The next day, Friday, November 5, 1993, after receiving a message from a man calling himself “the Panamanian” via Martha Gavi-ria, Humberto Gaviria and Zambrano went to a Burger King in Coral Gables, Florida, to receive a shipment of drags from the Panamanian. Because Zambrano had to leave the Burger King meeting early, before the Panamanian’s arrival, in order to go to work, Gaviria requested that his sister Martha pick him up in her car. After she appeared at the Burger King, Gaviria requested that she wait a little while to see if the Panamanian would arrive. When the Panamaniam did arrive, he used Martha’s car to pick up an eight-kilogram package of drugs, which Gaviria then hid in Martha’s house. Two days later, on Sunday, November 7, 1993, Gonzales and Sanders flew down to Miami. In a rented hotel room that served as a meeting place, Gaviria and Martha gave them the eight kilograms of cocaine in exchange for $8,000 in transportation costs. Upon leaving the hotel where that exchange took place, Gaviria and Martha met Zambrano at a restaurant in another location and gave him a thick stack of cash. Gaviria asked Zambrano to meet with Gonzales and Sanders to “pressure them so they would pay him part of the money” for the drugs.

Further negotiations followed — and Gonzales and Gaviria ultimately agreed on November 9, 1993, that Gonzales would fly to Miami and pick up the third cocaine shipment (seven kilograms) from Zambrano or Martha, and that Sanders would at the same time deliver the money still owed on the first eight kilogram shipment to Gaviria (in D.C.). In accordance with this plan, on Wednesday, November 10,1993, Zambrano first met Gonzales at a hotel. Zambrano then drove to Martha Gaviria’s house in Gonzales’s car, spent approximately ten minutes inside, drove back to the hotel to meet Gonzales, indicated to Gonzales that the drugs were hidden behind the driver’s seat, and accepted $7,000 in transportation costs from Gonzales in exchange for the seven kilograms. At that point, uniformed officers arrested Zambrano; around the same time, back in Washington, D.C., Gaviria was arrested, and the $148,000 payment he had received from Sanders, the balance of money still owed on the first shipment of cocaine, was found on his person.

The fourth and final shipment of cocaine (five kilograms) occurred on November 16, 1993, after months of arrangements and planning, involving several additional participants. The events leading to the sale began in July 1993, when appellant Zachary Williams became Naranjo’s FCI cellmate. On October 15, 1993, Williams contacted Jocelyn and David Johnson from FCI and told them he had made some friends who could help obtain drugs. On October 26, 1993, Gaviria told Gonzales that Naranjo had directed Gaviria to send a friend’s [Williams’s] money — which Johnson had obtained by selling off some of Williams’s jewelry — to Colombia for another shipment of cocaine. On October 29, 1993, Naranjo gave Gaviria two telephone numbers to contact David Johnson. When Gaviria and Gonzales flew to Miami a few days afterwards, Gaviria called Johnson from the airport, and Gonzales told Johnson that he and Gaviria were preparing to purchase some cocaine. Johnson said that he wanted to set up a meeting with Gonzales and Gaviria when they returned to Washington. On November 5, 1993, Williams and Johnson had a telephone conversation in which Williams indicated that he wanted Johnson to find out whether they could get drugs on credit. On November 9, 1993, Gavi-ria suggested that six kilograms from the next shipment of drugs be sold to Johnson. On November 12, 1993 — two days after the arrests of Gaviria and Zambrano — Gonzales met with Johnson and Johnson’s friend Ulysses Bobby Wilson at a Washington restaurant. After some negotiation, Johnson and Wilson told Gonzales that they would try to get money together and call him with an “order.” Then, on November 16,1993 — after various phone calls and meetings involving Williams, David Johnson, Jocelyn Johnson, Naranjo, Gonzales, and Wilson, during which the deal was organized — Johnson and Wilson met Gonzales on a D.C. street corner and drove to an apartment. Johnson brought $13,900, $7,000 of which had been contributed by Wilson, to purchase cocaine. They agreed that Gonzales would give Johnson five kilograms of cocaine in exchange for the downpayment, and that Johnson would be allowed one week in which to sell the cocaine and pay the remainder of the purchase price. As Wilson and Johnson, who was carrying the five kilograms of cocaine in a bag, walked out of the apartment, they were arrested by police officers.

The four appellants were indicted on charges of conspiracy to distribute and possess with intent to distribute five or more kilograms of cocaine, in violation of 21 U.S.C. §§ 841(a)(1) and (b)(l)(A)(ii) (Count One), and with obtaining or using approximately $44,409 in connection with that conspiracy, in violation of 21 U.S.C. § 853 (Count Three). Appellant Gaviria was also charged with illegally entering the United States following arrest and deportation, in violation of 8 U.S.C. § 1326 (Count Four). The appellants were tried before a jury. Appellants Gaviria, Naranjo, and Zambrano claimed that they had been entrapped and challenged various aspects of the government’s evidence. Appellant Williams denied any knowledge of or involvement in the conspiracy, and argued that he was “indicted and charged in this case because of a cultural misunderstanding of what [he had said] on the tapes.” On April 28, 1995, the jury returned guilty verdicts against all four appellants on all charged counts. On July 24,1995, Naranjo and Gaviria were sentenced to life in prison without parole on Count One. Gaviria also received a concurrent sentence of 180 months on Count Four. On September 13, 1995, Williams received a sentence of 188 months of incarceration. On February 5, 1996, the court sentenced Zambrano to 188 months in prison. In addition, each appellant was ordered to forfeit $44,409 pursuant to 21 U.S.C. § 853.

II.Joint Issue: The Conspiracy Instruction

Each appellant contends that the district court’s instruction to the jury included a sentence that might have led the jury to believe that it could convict a defendant of conspiracy without the Government having proven all the elements of the crime. Because none of the appellants objected to the instruction before the district court, our review is for plain error. Therefore, we can reverse only if (1) the jury instruction was in error, (2) the error was plain or obvious, and (3) the error affected the defendant’s substantial rights. United States v. Olano, 507 U.S. 725, 732-34, 113 S.Ct. 1770, 1776-77, 123 L.Ed.2d 508 (1993). We conclude that the disputed sentence, read in isolation, is capable of bearing two meanings — one legally erroneous and one legally correct; however, read in context, including the rest of the instructions and the lawyers’ closing statements to the jury, it is clear that the correct understanding of the instruction was conveyed to the jury. Accordingly, the instruction as a whole is not plainly erroneous.

The 1,100-word conspiracy instruction included the following sentence:

It is not necessary [that] the Government prove that a particular defendant was aware of the common purpose, had knowledge that the conspiracy existed, or was aware of the conspiracy from its beginning.

Tr. 4981 (4/25/95). The appellants argue that the prepositional phrase “from its beginning” modifies only the last of the three verb phrases in the sentence (“was aware of the conspiracy”). So read, the sentence would imply that the Government need not prove that a particular defendant was (ever) aware of the common purpose of the conspiracy and that the Government need not prove that a particular defendant (ever) had knowledge that the conspiracy existed. The Government concedes that such would not be a correct statement of the law. See United States v. Tarantino, 846 F.2d 1384, 1393 (D.C.Cir.1988) (Government must prove that defendant shared common goal with other conspirator); United States v. Falcone, 311 U.S. 205, 210, 61 S.Ct. 204, 206, 85 L.Ed. 128 (1940) (“Those having no knowledge of the conspiracy are not conspirators.”).' The Government contends, however, that the prepositional phrase “from its beginning” modifies all three verb phrases. So read, the sentence would state that the Government need not prove that a particular defendant was aware' of the common purpose of the conspiracy from its beginning, had knowledge that the conspiracy existed from its beginning, or was aware of the conspiracy from its beginning. The appellants concede that such would be a correct statement of the law. See United States v. Miller, 895 F.2d 1431, 1440 (D.C.Cir.1990) (Government need not show defendant was part of conspiracy from its inception); United States v. Stewart, 104 F.3d 1377, 1382 (D.C.Cir.1997) (defendant can be held liable for conspiracy even if he did not join conspiracy until final crime).

A reader or listener of English is not infrequently puzzled by what a linguist calls “syntactic ambiguity.” For example, the appellants point out that if one were to say, “We discussed running with Bob” the listener would not know for sure whether the prepositional phrase “with Bob” modifies the verb “discussed” or the gerund “running.” The sentence before us is similar. Drawing upon the often abstruse work of a phalanx of philologists, the appellants argue that the jury listening to (or reading, for the jurors were given a copy of the instructions to consult during their deliberations) the instruction would be more likely to resolve the syntactic ambiguity in the disputed sentence by concluding that “in the beginning” modifies only the last and not the first two verb phrases.

The appellants concede, however grudgingly, that “one can find a lurking ambiguity"’ in the sentence. Joint Brief for Appellants, at 14. It is precisely because such ambiguity stalks many an utterance, judicial and otherwise, that we review a jury instruction in its entirety, not by looking only to the “supposedly erroneous snippets.” United States v. Whoie, 925 F.2d 1481, 1485 (D.C.Cir.1991). Of particular relevance to this case, we have long recognized that one ambiguous part of an instruction may be made clear by another unambiguous part of the same instruction. United States v. Lemire, 720 F.2d 1327, 1339-41 (D.C.Cir.1983). See United States v. Eltayib, 88 F.3d 157, 170-71 (2d Cir.1996) (although particular part of instruction ambiguous with regard to need to find that defendant participated in conspiracy, instruction as a whole not plainly erroneous because another part clarifies ambiguity).

Just as the ambiguity in the appellant’s example (‘We discussed running with Bob”) would disappear in context (depending upon whether the preceding sentence was, say, “What did you and Bob talk about?” or “Have you chosen a running partner yet?”), the ambiguity in the disputed sentence in the instruction disappears when one considers the entire instruction. The instruction makes it clear at least twice that in order to “find a defendant guilty of conspiracy, the Government must prove each of the following things beyond a reasonable doubt ... that a particular defendant knowingly and willfully participated in the conspiracy, with the specific intent for the conspiracy to distribute or possess with intent to distribute cocaine.”' Tr. 4979 (4/25/95); see also Tr. 4982 (4/25/95). Any doubt that the jury might have been misled by the ambiguous sentence into thinking that the Government did not have to prove that a defendant was aware of the common purpose of the conspiracy, or that the Government did not have to prove that a defendant had knowledge that the conspiracy existed, is dispelled by these commands to the contrary.

The appellants claim, however, that the arguably erroneous sentence uses simple terms that a juror can readily understand whereas the various formulations in the instruction that clearly set forth the Government’s burden use arcane legal terms such as “knowingly” and “willfully.” This argument is not convincing. The instruction defines the supposed arcana in simple English: “An act is done knowingly if done voluntarily and purposely, and not because of mistake, inadvertence, or accident. An act is done willfully if done knowingly, intentionally, and deliberately.” Tr. 4980 (4/25/95). The appellants also argue that to the extent that other parts of the jury instruction make it clear that the jury must find that each defendant was aware at some time of the purpose of the conspiracy and knew at some time that the conspiracy existed, those sections of the instruction merely contradict, rather than cure, the erroneous sentence. Were the disputed sentence clearly rather than only possibly wrong, we might agree, but if a sentence can mean either A or B and another sentence in the instruction clearly says A, then one does not say that the first sentence must mean B; one says, rather, that the first sentence must therefore also mean A.

In addition, the court considers the lawyers’ arguments and the evidence in deciding whether a jury instruction is plainly erroneous. Whoie, 925 F.2d at 1485; United States v. Levi 45 F.3d 458, 456 (D.C.Cir.1995). In his closing argument counsel for Zambrano enumerated for the jury what the government must show in order to prove a count of conspiracy:

The Government is required to prove beyond a reasonable doubt that there was a criminal conspiracy ... with a common goal to distribute cocaine in Washington, D.C. The Government must prove beyond a reasonable doubt that Mr. Zambrano knowingly and willfully became a member of this conspiracy.

Tr. 4863 (4/24/95). The prosecutor also told the jury that a defendant could be convicted of conspiracy only if the jury found “beyond a reasonable doubt that the conspiracy existed and that the defendant knowingly participated in the conspiracy with the intent to encourage, advise, or assist other conspirators.” Tr. 4768 (4/24/95). Having been told by the judge, by defense counsel, and by the prosecutor that it could not find a defendant guilty of conspiracy unless the Government proved that the defendant knew that the conspiracy existed and knew what its purpose was, the jury could not have misunderstood the disputed sentence to have said the opposite.

III. Appellant Gaviria

Several defendants, including appellant Gaviria, spoke little English. Concerned that they would not understand the plea negotiation process, the district court requested at . a November 1994 status conference that each outstanding plea offer be put on the record. With his lawyer and the prosecutor present, each defendant approached the bench separately. Gaviria went first. The prosecutor put on the record that under the plea offer tendered to Gaviria, the Government would not file repeat-offender or life enhancement papers if Gaviria pled guilty to a count of conspiracy to distribute cocaine, a criminal forfeiture count, and a charge of unlawful re-entry into the United States following deportation. The prosecutor added, “That plea, like all of the pleas still existing in the case, is wired to the acceptance of pleas by the codefendants,” meaning that the Government would not accept a plea from Gaviria unless all defendants pled. Tr. 26 (11/17/94).

In response to a question from the district court as to what sentence Gaviria would face if he were to accept the plea, Gaviria’s attorney answered:

Mr. Gaviria, with two prior felony drug convictions, would be considered under [section 4B1.1 of] the [Federal Sentencing] guidelines to be a career offender, which would automatically take him to a category VI under the criminal history category and, I believe in his case, at least an offense level 37, which separate from the amount of drugs involved, as I recall, would require a sentence that starts, I believe, at about 36 years and goes up.

Tr. 27 (11/17/94). When the district court responded, “360 months to life.... That’s with the plea,” defense counsel agreed: “That is with the plea. Without the plea, he faces a mandatory sentence of life.” Id. at 27-28.

Defense counsel was wrong. More than a year before the November 1994 status call, we held in United States v. Price, 990 F.2d 1367, 1370 (D.C.Cir.1993), that a defendant convicted of conspiracy could not be sentenced as a career offender because the statute under which the Guideline career offender provision was initially promulgated did not list conspiracy as a crime warranting career offender treatment. If Gaviria had accepted the Government’s plea offer, his Guideline range would therefore have been 188-262 months (fifteen to twenty-two years), assuming all other contributing factors remained the same and that he received a two- or three-point downward adjustment for acceptance of responsibility. Having been advised by his lawyer that he faced thirty years to life in prison under the plea agreement, Gavi-ria instead rejected the offer. Following Gaviria’s conviction and as required by the “three-strikes” rule of 21 U.S.C. § 841(b) (1994), the district court imposed a mandatory sentence of life imprisonment.

Gaviria now argues that had counsel advised him correctly at the November 1994 status call, instead of risking life imprisonment upon conviction, he would have accepted the Government’s offer and received a fifteen-to-twenty-two-year sentence. With the misinformation his lawyer gave him, Gav-iria contends, he had little to lose by going to trial.

For an ineffective-assistance claim to succeed under the familiar Strickland standard, a defendant must show two things: that his lawyer made errors “so serious that counsel was not functioning as the ‘counsel’ guaranteed the defendant by the Sixth Amendment,” Strickland v. Washington, 466 U.S. 668, 687, 104 S.Ct. 2052, 2064, 80 L.Ed.2d 674 (1984); and that counsel’s deficient performance was prejudicial, i.e., that there is a “reasonable probability that, but for counsel’s unprofessional errors, the result of the proceeding would have been different.” Id. at 694, 104 S.Ct. at 2068. Because ineffective assistance of counsel claims usually require an evidentiary hearing, we normally do not resolve them on direct appeal, instead remanding to the district court. See United States v. Fennell, 53 F.3d 1296, 1303-04 (D.C.Cir.1995); see also United States v. Morrison, 98 F.3d 619, 626 n. 7 (D.C.Cir.1996), cert. denied, - U.S.-, 117 S.Ct. 1279-80, 137 L.Ed.2d 355 (1997). This rule has two exceptions: “when the trial record alone conclusively shows that the defendant is entitled to no relief,” and when the record “conclusively shows the contrary.” Fennell, 53 F.3d at 1303-04. Because this case falls within neither exception, we will remand Gaviria’s ineffective-assistance claim for an evidentiary hearing.

Gaviria satisfies Strickland’s first prong. His counsel’s representation that Gaviria would be sentenced as a career offender following a plea and that his Guideline range would be from 360 months to life was plainly incorrect. Because we issued Price a year and a half prior to the November 1994 status conference, Gaviria’s counsel should have been aware of the decision and its implications for his client. Cf. United States v. Day, 969 F.2d 39, 43 (3d Cir.1992) (“[Fjamiliarity with the structure and basic content of the Guidelines (including the definition and implications of career offender status) has become a necessity for counsel who seek to give effective representation.”).

Not so clear is whether Gaviria satisfies Strickland’s prejudice requirement; that is, whether there was a “reasonable probability” that he would have entered a guilty plea had his lawyer correctly advised him of his sentence exposure. As the Government reiterated many times at the status conference, Gaviria’s plea offer was “wired” to the offers to his codefendants. For Gaviria to succeed on his ineffective-assistance claim, therefore, he must establish not only that he would have taken the plea offer if his lawyer had advised him correctly, but also either that each of his co-defendants would have accepted their respective plea offers, or that the Government would have offered Gaviria an unwired plea.

We think it quite likely that Gaviria would have accepted the plea offer. After all, fifteen to twenty-two years for a man in his mid-forties is significantly less than life imprisonment, and Gaviria himself admits that the prosecution’s case against him was quite strong. Reply Brief for Appellant Gaviria, at 2. Gaviria does not claim that each of his codefendants would have accepted their offers, arguing instead that his wired plea offer was just Government “posturing,” and that the Government was clearly willing to accept individual pleas. In support of this contention, he points out that in January 1995, one day before trial began, the Government accepted Ulysses Wilson’s plea even though at the status conference the Government insisted, as it did with each of the other defendants, that Wilson’s plea offer was wired. Tr. 89 (11/17/94) (“[T]his plea is wired; that is, it would require the guilty pleas of [Wilson’s] codefendants before the government would accept Mr. Wilson’s plea.”). Gaviria also points to the prosecution’s statement that it would consider counteroffers from individual defendants. See, e.g., id. at 30 (‘We’ve always, I should say, entertained counteroffers, and [counsel for Zambrano] has made a counteroffer which we’ve rejected.”).

Gaviria’s arguments have merit. Although we do not suggest that the prosecution would have followed the exact same course in dealing with Gaviria that it did with Ulysses Wilson, the fact remains that the Government accepted an unwired plea from Wilson despite its contention that Wilson’s offer, like other offers, was wired. Coupled with the Government’s consideration of counteroffers as of the status conference, this supports Gaviria’s contention that the Government would have been willing to accept an unwired plea from him had he, aware of his true exposure under the plea, begun negotiating.

Not denying that it accepted counteroffers from individual defendants, the Government argues that the Wilson plea, like pleas from other co-defendants taken prior to November 1994, was “not without a price” — the Government required Wilson to meet with FBI agents and police detectives to answer questions about his transactions with “Kiki.” Brief for Appellee, at 46. If anything, however, this argument supports Gaviria because it shows that the prosecution’s initial plea offer to Wilson, containing no mention of cooperation with the FBI or local police, was not set in stone but was later modified, presumably to counterbalance the unwired nature of Wilson’s plea and to sweeten the prosecution’s end of the bargain.

Claiming that the length of Gaviria’s sentence would not change even if he prevails in the district court and claims the benefit of the initial plea, offer, the Government argues that Gaviria cannot satisfy Strickland’s prejudice requirement. As the Government points out, because the Sentencing Guidelines were amended in 1994 in response to Price, a defendant with two or more prior felonies now convicted on a drug conspiracy charge is treated as a career offender. According to the Government, the current Guidelines would apply to Gaviria and his Guideline range would be thirty years to life. We disagree.

The premise underlying the Government’s argument is incorrect: if Gaviria prevails on his ineffective-assistance claim, he cannot be resentenced under the current Guidelines because to do so would violate the Constitution’s Ex Post Facto Clause. U.S. Const, art. I, § 10. Long ago, the Supreme Court explained:

It is settled, by decisions of this Court so well known that their citation may be dispensed with, that any statute which punishes as a crime an act previously committed, which was innocent when done; which makes more burdensome the punishment for a crime, after its commission, or which deprives one charged with crime of any defense available according to law at the time when the act was committed, is prohibited as ex post facto.

Beazell v. Ohio, 269 U.S. 167, 169-70, 46 S.Ct. 68, 68-69, 70 L.Ed. 216 (1925). Accordingly, the Sentencing Guidelines state: “If the court determines that use of the Guidelines Manual in effect on the date that the defendant is sentenced would violate the ex post facto clause of the ... Constitution, the court shall use the Guidelines Manual in effect on the date that the offense of conviction was committed.” U.S.S.G. § 1B1.11(b)(l) (1995). Because applying the Current Guidelines to Gaviria would, in Beazell’s words, “make[] more burdensome the punishment for a crime, after its commission,” should Gaviria prevail on his ineffectiveness claim, he will be resenteneed under the Guidelines as they existed prior to the 1995 amendment. See United, States v. Booze, 108 F.3d 378, 381 n. 3 (D.C.Cir.1997) (resentencing occurs under version of Guidelines in effect at time of resentencing unless to do so would violate Ex Post Facto Clause); United States v. Clark, 8 F.3d 839, 844 (D.C.Cir.1993) (same).

The Government contends that because Gaviria joined the conspiracy prior to Price, he should have recognized his potential exposure to the Guidelines’ career-offender provision. But Price held that a defendant convicted of conspiracy and sentenced under the Guidelines’ career-offender provision had been illegally sentenced. Price, 990 F.2d at 1370. Because the career-offender provision was initially promulgated under a statute making no reference to drug conspiracy as a predicate crime for career-offender status, the provision was not lawfully applicable to drug conspiracy defendants — before or after Price — until the Sentencing Commission remedied its error in 1995. See U.S.S.G. § 4B1.1 (1995); id. App. C, amend. 528 (1995). Cf. Rivers v. Roadway Express, Inc., 511 U.S. 298, 312-13, 114 S.Ct. 1510, 1519-20, 128 L.Ed.2d 274 (1994) (“A judicial construction of a statute is an authoritative statement of what the statute meant before as well as after the decision of the case giving rise to that construction.”); United States v. McKie, 73 F.3d 1149, 1153 (D.C.Cir.1996) (same).

We also disagree with the Government that sentencing Gaviria under the old version of the Guidelines would give him an unearned “windfall.” Brief for Appellee, at 48. Gavi-ria was not, as the Government would have it, merely “ ‘deprived ... of the chance to have the ... court make an error in his favor.’ ” Lockhart v. Fretwell, 506 U.S. 364, 371, 113 S.Ct. 838, 122 L.Ed.2d 180 (1993) (quoting brief for United States as Amicus Curiae at 10). If Gaviria had been sentenced following a timely plea, he would not have been taking advantage of a court’s erroneous construction of the law. See Fretwell, 506 U.S. at 371, 113 S.Ct. at 843. Instead, he would have been sentenced according to the then-existing Guidelines. Gaviria gets no windfall; he gets instead the sentence for which he would have been eligible had he timely pled.

We thus remand Gaviria’s ineffective-assistance claim to the district court for an evi-dentiary hearing on two issues: whether Gaviria would have taken the Government’s plea offer had he known of his true exposure under the Guidelines; and whether the Government would have entertained an unwired plea from Gaviria. While recognizing the inherent difficulty in reconstructing events long past and in determining what might have been had counsel given his client correct information on his sentencing exposure, we emphasize that Strickland requires reasonable probability, not certainty. Strickland, 466 U.S. at 694, 104 S.Ct. at 2068 (“A reasonable probability is a probability sufficient to undermine confidence in the outcome.”). Because we remand Gaviria’s ineffective assistance claim on these grounds, we have no need to address his separate contention that the district court had an obligation to correct counsel’s error sua sponte.

IV. Appellant Zambrano

All five of Regulo Zambrano’s challenges— one to his conviction and five to his sentence — rely on the fundamental premise that he did not become involved in the charged conspiracy until November 10, and that his involvement was limited to his purportedly coerced personal delivery on that date of seven kilograms of cocaine to Gonzales in exchange for a $7,000 deposit from Gonzales. Because the record evidence amply supports the conclusion — by the jury at the conviction stage, and by the district court judge at the sentencing phase — that Zambrano’s involvement predated the November 10 delivery, and the district court’s conclusion at the sentencing phase that Zambrano was dishonest in his trial testimony about the extent of his involvement in the conspiracy, all of his challenges must fail.

A. Sufficiency of Evidence to Support Conspiracy Conviction

Appellant Zambrano cites three reasons why there was insufficient evidence to convict him of conspiring to possess cocaine with intent to distribute pursuant to 21 U.S.C. § 846 and § 841(a)(1). First, he argues that there was insufficient evidence that he knowingly participated in the charged conspiracy at all. Second, he contends that even if he was involved in a conspiracy, it was separate from and smaller than the charged conspiracy, and was limited to a one-time distribution on November 10 in Florida. Finally, Zambrano claims that because the conspiracy in which he was allegedly involved was limited to transactions in Florida, the district court did not have subject matter jurisdiction over his trial. We conclude that none of Zambrano’s three challenges to his conviction has merit.

1. Insufficient Evidence that Zambrano Participated in Any Conspiracy

Zambrano’s first challenge must fail because there is ample evidence on the record to support his conviction for conspiring to distribute cocaine. Zambrano’s conspiracy conviction should be reversed for insufficient evidence only if, “viewing [the evidence] in the light most favorable to the government, a reasonable trier of fact could not have found guilt beyond a reasonable doubt.” United States v. Lam Kwong-Wah, 924 F.2d 298, 302 (D.C.Cir.1991). At trial, the government was required to prove beyond a reasonable doubt that Zambrano purposefully “entered into an agreement with at least one other person and that the agreement had as its objective a violation of the law.” Id. at 303 (internal quotation marks omitted). In proving that an agreement to violate the law existed, “the government need only show that the conspirators agreed on the essential nature of the plan, not that they agreed on the details of their criminal scheme.” United States v. Gatling, 96 F.3d 1511, 1518 (D.C.Cir.1996).

Under this standard, Zambrano’s conviction must be upheld if the government produced sufficient evidence for the jury to find beyond a reasonable doubt that Zambrano intended to and did in fact conspire with Gaviiia to distribute at least one shipment of cocaine in Miami. The government clearly met its burden here. Although Zambrano claims that the evidence is insufficient because he “did not participate in any discussions between Humberto Gaviria and Detective Gonzales about quantity or price” and “[h]e was not present when the day, time or location of the transaction was fixed,” Brief for Appellant Zambrano, at 17, these details are insignificant in light of the overwhelming direct and circumstantial evidence against Zambrano, including numerous telephone conversations, meetings, and actions. Construed in the light most favorable to the government, this evidence demonstrates that the conspiracy in which Zambrano participated encompassed both the November 7 and the November 10 transactions. In addition to delivering personally the seven kilograms of cocaine on November 10, a fact which Zambrano concedes, the record shows the following facts: a week after first speaking to Zambrano, Gaviria, a key player in the conspiracy, traveled from Colombia to Miami, moved into Zambrano’s house, and received 15 kilograms of cocaine on credit three days later from a complete stranger; then, after delivering the first shipment of eight kilograms of cocaine to undercover agents in exchange for $8,000, Gaviria was observed giving Zambrano a thick stack of cash. After the November 7 transaction had taken place, Zambrano pressured government agents for the remainder of the price of the first shipment of cocaine, stating that future deliveries were contingent upon full payment. Finally, after hearing that the balance of the payment had been received by Gaviria in Washington, Zambrano personally delivered the second shipment of cocaine to Gonzales on November 10. All of this evidence in combination is more than adequate to support the jury’s decision to convict Zambrano for conspiring to distribute or possess with intent to distribute cocaine.

2. Variance Between Evidence and Indictment

Zambrano’s second argument alleging “multiple conspiracies” and a variance between the evidence and the indictment is similarly unpersuasive and certainly does not constitute plain error. In order to show that the indictment varied improperly from the evidence, appellants must demonstrate

(1) that the evidence at trial established the existence of multiple conspiracies, rather than the one conspiracy alleged in the indictment, and (2) that because of the multiplicity of defendants and conspiracies, the jury was substantially likely to transfer evidence from one conspiracy to a defendant involved in another.

United States v. Tarantino, 846 F.2d 1384, 1391 (D.C.Cir.1988) (as amended). Zambra-no’s argument fails because the evidence demonstrates that he did participate in the charged conspiracy.

Zambrano concedes his involvement in the seven kilogram transaction that occurred on November 10, but as explained above he asserts that this was the only transaction in which he was involved or, at the very least, that he was not involved in any of the parts of the charged conspiracy that transpired in Washington, D.C. In contrast to his assertions, the government asserted, both at trial and on appeal, that all the codefendants participated in a single conspiracy with the goal of distributing large quantities of cocaine. According to the government’s theory, Naranjo and Gaviria initiated the importation of drugs from Colombia and sought customers who would buy the drugs in order to resell them. Zambrano’s role was to supply the conspiracy with large quantities of cocaine. Williams, Johnson, and Sanders — until he was arrested and became an informant — were potential buyers of the cocaine. See Brief for Appellee, at 66.

To prove the existence of a single conspiracy in which Zambrano participated, the Government was not required to prove that Zam-brano knew all the other participants in that conspiracy. We have previously stated “that participants in a continuous drug distribution enterprise can be parties to a single conspiracy even if they do not all know one another, so long as each knows that his own role in the distribution of drugs and the benefits he derives from his participation depend on the activities of the others.” Childress, 58 F.3d at 709-10. To determine whether defendants who did not all know one another were nevertheless co-conspirators, this court examines “whether the defendants ‘shared a common goal,’ any ‘interdependence between the alleged participants,’ and ‘any overlap among alleged participants,’ such as the presence of core participants linked to all the defendants.” Gatling, 96 F.3d at 1520 (quoting United States v. Graham, 83 F.3d 1466, 1471 (D.C.Cir.1996)).

The Government amply met its burden in this case. As already explained, the record contains overwhelming evidence indicating that Zambrano was an integral participant in both the November 7 and 10 drug transactions. Moreover, although Zambrano may not have known the specific identity of the buyers for the drugs he was supplying, he must have known that those buyers existed, and that he was connected to those buyers by Gaviria and Naranjo, the core participants in the conspiracy. Indeed, as the Government persuasively argues, the sheer quantities of drugs involved and the speed with which the first eight kilograms of cocaine were converted into cash indicated that the drugs were being sold to others for retail distribution.

3. Lack of Jurisdiction/Venue

Finally, Zambrano’s third argument alleging “lack of jurisdiction” in the district court is also meritless. The Government was correct to point out that the district court’s jurisdiction in this case, premised on 18 U.S.C. § 3231, was not conditioned on the location of the criminal conduct charged. Thus, Zambrano’s “jurisdictional” claim is more properly identified as a challenge to venue. However, Zambra-no waived this challenge when he failed to raise it below. See United States v. Wilson, 26 F.3d 142, 151-52 (D.C.Cir.1994). In any event, the court did not commit plain error by allowing the case to be tried in D.C. Because overt acts in furtherance of the conspiracy did occur within the District of Columbia, venue was proper notwithstanding Zambrano’s claim to the contrary. Lam Kwong-Wah, 924 F.2d at 301 (“It is a well-established rule that ‘a conspiracy prosecution may be brought in any district in which -some overt act in furtherance of the conspiracy was committed by any of the co-conspirators.’ ”) (quoting United States v. Rosenberg, 888 F.2d 1406, 1415 (D.C.Cir.1989)).

B. Sentencing Issues

At Zambrano’s sentencing, the district court found that he was responsible for all 15 kilograms of cocaine that were sold in Miami on November 7 (eight kilograms) and November 10 (seven kilograms). Accordingly, his base offense level was 34. The court then added two levels for obstruction of justice because Zambrano perjured himself. The court also found that Zambrano was not entitled to a downward adjustment based on the minimal or minor nature of his role in the offense, or on acceptance of responsibility. Finally, the court concluded that he was not eligible for the safety valve provision of the Sentencing Guidelines. Zambrano’s total offense level was 36, which meant that the applicable sentencing range given his criminal history category of I was 188 to 235 months. The court ultimately gave Zambra-no a sentence at the bottom of the range— 188 months.

We review the district court’s findings of fact during the sentencing phase for clear error. United States v. Broumas, 69 F.3d 1178, 1180 (D.C.Cir.1995) (citing United States v. Kim, 23 F.3d 513 (D.C.Cir.1994)). The district court’s application of the Sentencing Guidelines to the facts is entitled to “due deference.” See id. Legal questions relating to sentencing are reviewed de novo. See id.

1. Obstruction of Justice

Under the Sentencing Guidelines, a defendant commits perjury and obstructs justice under U.S.S.G. § 3C1.1 if he “gives false testimony concerning a material matter with the willful intent to provide false testimony, rather than as a result of mistake or faulty memory.” United States v. Dunnigan, 507 U.S. 87, 94, 113 S.Ct. 1111, 1116, 122 L.Ed.2d 445 (1993). A defendant also obstructs justice if he “provides] materially false information to a probation officer in respect to a presentence or other investigation for the court.” U.S.S.G. § 3C1.1, cmt. n.3(h). The district court must find willful perjury by clear and convincing evidence. United States v. Montague, 40 F.3d 1251, 1254 (D.C.Cir.1994) (as amended). In the present case, the district court did find by clear and convincing evidence that Zambrano willfully provided false testimony when he testified that (1) he did not know about or engage in the cocaine conspiracy until November 10,1993; and (2) he was coerced into participating in the conspiracy on November 10 by pressure from Gonzales and his concern for the safety of Martha Gavina. The court additionally found that Zambrano had furnished the same materially false information to the U.S. Probation Office.

Zambrano claims that the district court erred in three respects when it found that Zambrano obstructed justice. First, he claims that none of the testimony that the district court cited as perjurious was false. Second, he contends that, even if some of the testimony was false, none of it was material. Third, he asserts that there was no showing that any of the purported falsehoods were willful. None of these three arguments is persuasive.

First, the district court did not commit clear error in finding that Zambrano testified falsely. Although Zambrano makes much of the fact that his testimony at trial (regarding the November 7 meeting with Gonzales and Sanders) was internally consistent, see Brief for Appellant Zambrano, at 1-4, he fails to account for the fact that the district court found credible testimony offered by Gonzales and Martha Gaviria — which directly contradicted Zambrano’s testimony. Moreover, the district court did not commit clear error when it found that Zambrano had lied by testifying that he did not “discuss any business” with Gonzales during their November 8, 1993, telephone call. The conversation was conducted in code, and Zambrano contends that there is therefore no basis for finding that Zambrano understood that Gonzales was talking about drugs. However, Zambrano never stated during the conversation that he did not understand what the conversation was about, and two days later, Zambrano referred back to the conversation, stating that he “understood that [Gonzales] ... had told [Zambrano] that it had been brought down, that it wasn’t putting out what it was supposed to be_” GovEx 111093-2, at 8. The district court also did not commit clear error when it found by clear and convincing evidence that Zambrano lied to the jury and the Probation Office by claiming that he was coerced into participating in the conspiracy by threats against the safety of Martha Gaviria. Any of these three findings of false testimony would serve to support the district court s finding that Zambra-no obstructed justice.

Second, the district court did not err in finding that Zambrano’s false testimony was material. Under the Sentencing Guidelines, information is material when, “if believed, [it] would tend to influence or affect the issue under determination.” U.S.S.G. § 3C1.1, emt. n.5. The false testimony Zambrano gave was clearly material because it was crucial to the Government’s ability to defeat Zambrano’s entrapment defense, which asserted that Gonzales entrapped Zambrano on November 10 by pressuring him into delivering the seven kilogram shipment of cocaine. If the jury found that, contrary to his false testimony, Zambrano participated in the conspiracy prior to November 10, his entrapment claim would fail.

Third, the district court did not err in concluding that Zambrano’s false statements were willful. Indeed, Zambrano does not claim that the statements resulted from “mistake or faulty memory.” Dunnigan, 507 U.S. at 94, 113 S.Ct. at 1116. He only claims that they were not false. Because the record overwhelmingly supports the court’s finding that the statements were in fact false, and because there is no evidence in the record that Zambrano was confused, mistaken or forgetful about the scope of his participation in the conspiracy, the finding of willfulness should be affirmed.

2. Minor or Minimal Participant Reduction

Zambrano claims that he should have received a reduction in his base offense level because he was either a “minor” or “minimal” participant in the charged conspiracy under U.S.S.G. § 3B1.2. He argues that, in addition to the fact that he had no prior criminal record, he was not involved in “initiating the conspiracy, attempting to locate suppliers, arranging finances for Humberto Gaviria’s return to the United States, negotiation of the quantity or price of the cocaine sold to the undercover officer, or transferring the initial 8 kilograms.” Brief for Appellant Zambrano, at 7. Moreover, Zambrano claims that the district court failed to consider his blameworthiness relative to his co-conspirators as required by the Guidelines, and that he was far less culpable than Gavi-ria, Naranjo, or Williams.

We are not persuaded by Zambrano’s argument that the district court erred in ruling that Zambrano’s role in the conspiracy was not “minor.” The district court found:

[Zambrano’s] role here is very clear from the evidence and his conversations with the undercover agent and his spending the afternoon and evening with him essentially for the final delivery and discussions he had with the agent at that time, accepting the $7000, being entrusted to accept that money by whoever owned the drugs, and his first meeting with him, his request to get the money down, his instructions that he wouldn’t release the rest of the drugs until the first payment had been received by Mr. Gaviria in Washington, all take him out of the role of a minor or minimal player. He’s not just a courier.

Hrg. Tr. 19-20 (2/5/96). These findings were supported by the record, and the district court was justified in concluding that this level of active participation in the conspiracy made Zambrano ineligible for the downward departure under section 3B1.2. Under this circuit’s precedent, even a so-called “courier” may not qualify for a downward departure as a “minor” participant because, depending on the specific circumstances involved, “a courier can play as active and culpable a part in a drug offense as another participant.” United States v. Caballero, 936 F.2d 1292, 1299 (D.C.Cir.1991).

Zambrano’s argument that the district court failed to consider his culpability in relation to his co-conspirators is similarly meritless. Although in cases of joint criminal activity, a district court should examine a defendant’s culpability in relation to his co-conspirators’ culpability, “a defendant is not entitled to a reduction ... simply because he is the least culpable among several participants in a jointly undertaken criminal enterprise.” United States v. Lockhart, 37 F.3d 1451, 1455 (10th Cir.1994). Rather, a court may find that none of the co-conspirators qualify as “minor” participants because even the “least culpable” participants in the conspiracy — although they might not have played the roles of organizers or supervisors within the chain of command — nevertheless were active participants and were equally culpable vis-a-vis each other. In so concluding, “the district court need not make express findings of relative culpability so long as it is clear that the court assessed the defendant’s ‘role in-the specific criminal conduct’ and did not ‘gauge his culpability ge-nerieally.’ ” Washington, 106 F.3d at 1018 (quoting United States v. Edwards, 98 F.3d 1364, 1370 (D.C.Cir.1996)). Here, it is clear that the district court examined Zambrano’s role in relation to the conspiracy in which he participated, and that the record as a whole supports the court’s conclusion that Zambra-no played far more than a “minor” role in the conspiracy. As we have previously explained, “the district court is in the best position to assess the defendant’s relative culpability vis-a-vis other participants in the offense.” United States v. Williams, 891 F.2d 921, 926 (D.C.Cir.1989); see also United States v. Caballero, 936 F.2d 1292, 1299 (D.C.Cir.1991) (“The application of section 3B1.2 is inherently factbound and largely committed to the discretion of the trial judge.”). We conclude that the district court correctly applied the Sentencing Guidelines as they pertain to the downward adjustment for a minor or minimal role; therefore, we affirm the court’s denial of this adjustment to Zambrano.

3. Downward Departure for Acceptance of Responsibility

Appellant Zambrano next asserts that the district court erred when it refused to grant him a downward departure for accepting responsibility for transferring the November 10 shipment to Gonzales in exchange for $7,000, despite the fact that he denied any involvement in the conspiracy prior to November 10 and claimed that his delivery of the seven kilograms was coerced. During the sentencing phase, the court found that — both at trial and in his presentence memorandum to the Probation Office — Zambrano “admitted only to a limited role, which he said he was forced into, in his delivery on November 10, and that certainly is not acceptance for [sic] responsibility under [U.S.S.G. § ] 3E1.1, and normally, certainly when he obstructs justice, it would be difficult to find that in any event.” Sentencing Transcript 36. Zambrano claims that, because he accepted full responsibility for his involvement in the conspiracy and the trial court erroneously found that he perjured himself, the corat also erred when it denied him the departure.

We reject this argument because we have already rejected Zambrano’s claim that the district court erred in finding that he committed perjury. To receive the downward adjustment raider § 3E1.1, a defendant must “truthfully admit[ ] or not falsely deny[ ] any additional relevant conduct for which [he] is accountable under § 1B1.3 (Relevant Conduct).” U.S.S.G. § 3E1.1, cmt. n.l(a). In almost all cases, a defendant who denies guilt and goes to trial, or who receives an obstruction of justice enhancement under § 3C1.1, is not eligible for a downward adjustment for acceptance of responsibility. Id., cmt. nn.2, 4. Zambrano clearly failed to accept responsibility for his full participation in the charged conspiracy, and so he is not entitled to the departure.

4. Downward Departure Under the Safety Valve Provision

Since we conclude that the district court did not err in finding that Zambrano perjured himself, we also affirm the court’s determination that Zambrano was not entitled to a downward departure under the safety valve provision of 18 U.S.C. § 3553(f) and U.S.S.G. § 5C1.2. Five criteria must be satisfied for the district court to grant an adjustment under this provision. The fifth criterion is that:

(5) not later than at the time of the sentencing hearing, the defendant has truthfully provided to the Government all information and evidence the defendant has concerning the offense or offenses that were part of the same course of conduct or of a common scheme or plan, but the fact that the defendant has no relevant or useful information to provide or that the Government is already aware of the information shall not preclude a determination by the court that the defendant has complied with this requirement.

18 U.S.C. § 3553(f)(5) (1994). The fifth element of the safety valve provision requires full and candid disclosure by the defendant of all information in his possession concerning the charged offense, see, e.g., United States v. DeJesus-Gaul, 73 F.3d 395, 397 (D.C.Cir.1996), and Zambrano clearly failed to meet this requirement when he perjured himself during the trial and presentencing proceedings. Accordingly, the district court was justified in denying Zambrano a downward departure under the safety valve provision.

5. Accountability for Entire 15 Kilograms of Cocaine

During sentencing, the district court found that Zambrano had lied about his involvement in the drug” transaction that took place on November 7 and that he therefore was responsible for all 15 kilograms involved in both the November 7 and November 10 transactions. In his brief, Zambrano contests the district court’s conclusion, stating:

Because the record does not support a finding that appellant lied about his involvement as to the November 7th transaction, the record cannot and does not support a finding that the sale of the total 15 kilograms was reasonably foreseeable to or in furtherance of appellant’s agreement with the co-conspirators. Rather, although appellant knowingly participated in the November 10th transaction of 7 kilograms, a preponderance of the evidence in the record does not indicate his foreseeability with respect to the November 7th transaction. The fact that appellant was convicted of conspiracy does not end the analysis.

Brief for Appellant Zambrano, at 14-15.

Similar to Zambrano’s other sentencing challenges, this one relies on his assertion that his involvement in the conspiracy was much more limited than the district court found that it was. Zambrano’s argument fails because, as explained above, the district court did not err in concluding that he in fact participated in the November 7 drug transaction. The record indicates that, after Gavi-ria transacted the November 7 sale, he gave Zambrano a large stack of cash and requested that Zambrano pressure the undercover “buyers” to pay the remaining balance for the cocaine. Following this directive, Zam-brano met with the undercover agents, told them that he did not like to be kept waiting, and informed them that more drugs would not be forthcoming until they paid the balance on the first shipment. He also refused to make the November 10 delivery of seven additional kilograms until assured that the balance of $148,000 on the previous shipment was paid. Even if — giving Zambrano the benefit of every doubt — he was not in fact responsible for initially “supplying” the drugs, the record evidence amply supported the district court’s conclusion that he participated in the November 7 sale; at the very least, he aided and abetted the transaction, and such action is clearly covered by the “relevant conduct” definition of U.S.S.G. § lB1.3(a)(l)(A).

V. Appellant Williams

A. Failure to Allow Recall of Government Witness

One of the primary prosecution witnesses against Williams, David Johnson, a former eo-defendant, pled guilty in September 1994 to possession with intent to distribute cocaine. A long-time Williams friend and a fellow drug dealer, Johnson testified that Williams and his cellmate Naranjo arranged two drug deals for him: to purchase heroin from “KiM,” and to buy cocaine from undercover Detective Gonzales, who in turn had purchased it from Gaviria. Johnson’s testimony against Williams included “decoding” several phone calls placed by Williams to him from the jail, since Williams, like the other defendants, spoke of drug dealing in code.

Because it placed Williams in the role of intermediary and facilitator of several drug transactions, Johnson’s testimony was quite damaging to Williams. Williams’s attorney accordingly cross-examined Johnson thoroughly, establishing, among other things, that Johnson had dealt drugs for many years prior to his arrest and had initially lied to police officers when arrested. When Williams’s attorney questioned Johnson on the details of his plea .agreement with the Government, the following exchange occurred:

Q. (Williams’s attorney) So you want to do everything you can to make certain [the prosecutors] are happy with what you say; isn’t that right?

A. (Johnson) I want to do whatever I can to make the truth prevail.

Q. And [the truth] matters to you now, because you know even with the plea agreement ... you could get 40 years, and you had a tough time doing a year in the D.C. Jail?

A. I’ve never been arrested before.

Q-That gives [you] further impetus to why you would want to cooperate, because you had never been arrested before, right?

[The Interpreter:] I’m sorry?

A. That’s not why I’m cooperating.

QI’m sorry. It would give further impetus to why he would want to cooperate, because he had never been arrested.

A. That’s not why I’m cooperating.

Tr. 2339-40 (3/9/95). Williams’s attorney continued the cross-examination throughout the day, concluding the next morning.

Nearly a month later, after the close of the Government’s case and after two defendants had put on their evidence, Williams’s attorney asked permission to recall Johnson for further cross-examination, arguing that he wanted to impeach Johnson’s prior statement that he had never before been arrested with evidence that he had once been arrested in Maryland. Although Williams’s attorney conceded that he had possessed information on Johnson’s arrest record when initially cross-examining Johnson a month earlier, he claimed that when Johnson volunteered that he had never before been arrested, he was “caught off guard” and failed to pursue the issue. Tr. 3709 (4/6/95). The prosecutor objected, pointing out that Johnson’s arrest record had been provided in discovery and that the court had the discretion to refuse to recall Johnson to the stand. Agreeing with the prosecutor, the district court declined to allow Williams to recall Johnson.

District courts enjoy “ “wide discretion to control cross-examination.’ ” United States v. Thorne, 997 F.2d 1504, 1513 (D.C.Cir.1993) (quoting Harbor Ins. Co. v. Schnabel Found. Co., 946 F.2d 930, 935 (D.C.Cir.1991)). We will reverse a trial court’s decision to limit cross-examination only where it resulted in substantial prejudice to the appellant. Id.; see also United States v. Mitchell, 49 F.3d 769, 780 (D.C.Cir.), cert. denied, - U.S. -, 116 S.Ct. 327, 133 L.Ed.2d 228 (1995); Fed. R. Evid. 611(a). Applying this highly deferential standard, we find no abuse of discretion in the district court’s refusal to permit Williams to recall Johnson.

We are unconvinced by Williams’s contention that Johnson’s statement “caught counsel ... by surprise.” Brief for Appellant Williams, at 14. Because Williams’s trial counsel conceded that he had information on Johnson’s prior arrest record when he first cross-examined Johnson, counsel surely could have reviewed the discovery materials on Johnson after the first day of cross to check for any inconsistencies or further fruitful avenues of cross-examination and followed up the next morning while Johnson was still on the stand.

Claiming that his attorney’s failure to attack Johnson’s statement immediately amounted to ineffective assistance of counsel, Williams also argues that the district court should have allowed the attorney to remedy the situation a full month later. We disagree. As the district court recognized, Williams’s attorney used Johnson’s statement — “I had never been arrested before”— to his advantage, asking, “That gives [you] further impetus to why you would want to cooperate, because you had never been arrested before, right?” Given that Williams’s counsel had initially used Johnson’s allegedly false statement to support his theory that Johnson would willingly lie on the stand to gain favor with the Government, the district court was well within its discretion in refusing to allow counsel to switch tactics and cross-examine Johnson on his alleged perjury.

This leaves Williams with the argument that “the rules of evidence did not compel the trial court to preclude Williams from examining Johnson during his defense case about Johnson’s prior arrest.” Brief for Appellant Williams, at 11. This is certainly true, but neither do the rules compel the court to allow further cross-examination of witnesses long since dismissed from the stand.

B. Sentencing Challenges

1. Enhancement Based on Prior Convictions

Williams begins his challenge to his sentence by arguing that the Government and the district court failed to abide by 21 U.S.C. § 851(a)’s prohibition against enhancing a drug defendant’s sentence based on prior convictions “unless before trial, or before entry of a plea of guilty, the United States attorney files an information with the court (and serves a copy of such information on the [defendant] or counsel for the [defendant] ) stating in writing the previous convictions to be relied upon.” 21 U.S.C. § 851(a)(1) (1994). We disagree.

By filing an enhancement information against Williams on August 31,1994, approximately four months before trial, the Government complied with section 851(a). The information identified two 1990 convictions supporting enhancement: conspiracy to distribute heroin and use of a communications facility to distribute narcotics. Although Williams claims he never received personal notice of the enhancement information filed against him, he does not deny that his lawyer was properly served, which is all section 851(a) requires.

Moreover, at a November 17, 1994, status hearing at which Williams was present, the district court made a point of asking Williams’s lawyer whether he had discussed the enhancement papers with his client. The Government had offered to withdraw the enhancement filing if Williams would plead guilty to the cocaine conspiracy charge on which he had been indicted. At the end of the colloquy, the court stated, “I just want to make sure what the situation was because ... Mr. Williams is facing a very drastic sentence if convicted with the enhancement papers.” Williams’s lawyer responded, “Right. Mr. Williams is aware of that your honor.” Tr. 48 (11/17/94).

Williams also argues that the district court violated section 851(b), which imposes two duties on the court:

If the United States attorney files an information under this section, the court shall after conviction but before pronouncement of sentence inquire of the person with respect to whom the information was filed whether he affirms or denies that he has been previously convicted as alleged in the information, and shall inform him that any challenge to a prior conviction which is not made before sentence is imposed may not thereafter be raised to attack the sentence.

21 U.S.C. § 851(b). By giving Williams an opportunity to question the accuracy of the prior convictions, the district court carried out the first of its section 851(b) duties. As the Government concedes, however, the court neglected to inform the defendant that a failure to challenge his prior convictions would constitute a waiver. Brief for Appellee, at 152. Although failure to comply strictly with the statute’s requirements is error, see United States v. Jordan, 810 F.2d 262, 269 (D.C.Cir.1987) (requiring strict compliance); United States v. Ramsey, 655 F.2d 398, 400 n. 7 (D.C.Cir.1981) (same), here the error was harmless, cf. United States v. Brown, 921 F.2d 1304, 1308 n. 5 (D.C.Cir.1990) (excusing less than complete compliance). Cf. United States v. Gonzalez-Lerma, 71 F.3d 1537, 1541 n. 4 (10th Cir.1995) (citing decisions from 1st, 4th, 7th, 9th, and 11th Circuits applying harmless-error analysis to § 851(b)), cert. denied, - U.S. -, 116 S.Ct. 1341, 134 L.Ed.2d 490 (1996).

Not until his reply brief does Williams suggest the bases for challenging his prior convictions. Because all three are constitutional challenges — -vindictive or selective prosecution, double jeopardy, and a Batson violation, Reply Brief for Appellant Williams, at 1 — had he' raised these challenges before the district court, he would have had to comply with section 851(c)(2)’s requirement to set forth “with particularity” any constitutional challenge to a prior conviction and “the factual basis therefor.” 28 U.S.C. § 851(c)(2). Even on appeal, however, Williams fails to offer any factual basis for his claims. The closest he comes to complying with section 851(c)(2) is his claim, based on his own trial testimony, that he used the proceeds from pawning some jewelry to hire an Ohio law firm to file a section 2255 petition on his behalf. Because even now Williams cannot satisfy the requirements of section 851(e)(2), the district court’s failure to comply with section 851(b) was not prejudicial. See United States v. Olano, 507 U.S. 725, 734-35, 113 S.Ct. 1770, 1777-78, 123 L.Ed.2d 508 (1993) (explaining centrality of prejudice to harmless-error inquiry); cf. United States v. Fragoso, 978 F.2d 896, 902 (5th Cir.1992) (finding § 851(b) error harmless because of defendant’s failure to comply with § 851(c)).

2. Drug Quantity

Relying on the presentence report, the district court found Williams responsible for two of the five kilos of cocaine that David Johnson and Ulysses Wilson purchased from Detective Gonzales on November 16, 1993. According to the presentence report, during a November 14, 1993, conversation at the federal prison at Petersburg, Williams and Johnson agreed on a two-kilo purchase. Williams explained that Johnson could buy one kilo for cash and one on credit. Williams now claims he should have been held responsible for only one kilo, which would have made his base offense level 26 instead of 28. He makes two arguments to support his contention, neither of which has merit.

The first, that he was a victim of indirect sentencing entrapment, rests on his claim that Johnson, intending to buy only one kilo, was entrapped by Detective Gonzales into buying more. Since the amount of drugs for which Williams was held responsible derives from Johnson’s purchase, Williams argues, he too was a victim of Gonzales’s insistence that Johnson buy more than one kilo.

Although recognizing the possibility of indirect entrapment claims of the sort maintained by Williams, we have held that such claims may be raised only if the defendant

was induced by an unknowing intermediary at the instruction or direction of a government official or third party acting on behalf of the government (e.g., an informant). The defense should not apply if, in response to pressure put on him by the government, the unknowing intermediary on his own induces the defendant to engage in criminal activity.

United States v. Layeni, 90 F.3d 514, 520 (D.C.Cir.1996), cert. denied, - U.S. -, 117 S.Ct. 783, 136 L.Ed.2d 726 (1997); see also United States v. Spriggs, 102 F.3d 1245, 1261-62 (D.C.Cir.1996). Even assuming Johnson’s request to Williams amounted to inducement, that inducement did not flow from the direction or insistence of Government agents. Although Johnson’s conversation with Williams about securing credit to buy a second kilo took place after Gonzales’s conversation with Johnson urging him to buy more than one kilo, Johnson did not seek out Williams’s help at Gonzales’s direction. Before his conversation with Gonzales, Johnson had already discussed buying on credit with Williams, and it was Williams who suggested that Johnson ask Gonzales about buying on credit.

Williams also argues that the district court failed to make a specific finding that the two kilos were within the scope of the conspiratorial agreement into which he entered. In support of this argument, Williams relies largely on United States v. Saro, 24 F.3d 283 (D.C.Cir.1994), where we stated:

The extent of a defendant’s vicarious liability under conspiracy law is always determined by the scope of his agreement with his co-conspirators. Mere foreseeability is not enough: someone who belongs to a drug conspiracy may well be able to foresee that his co-venturers, in addition to acting in furtherance of his agreement with them, will be conducting drug transactions on the side, but he is not automatically accountable for all those side deals.

Saro, 24 F.3d at 288; see also, e.g., United States v. Graham, 83 F.3d 1466, 1478-79 (D.C.Cir.1996), cert. denied, - U.S. -, 117 S.Ct. 993, 136 L.Ed.2d 874 (1997); United States v. Childress, 58 F.3d 693, 723 (D.C.Cir.1995), cert. denied, - U.S. -, 116 S.Ct. 825, 133 L.Ed.2d 768 (1996).

Contrary to Williams’s assertion, however, the district court did not rely only on foreseeability, instead making specific findings that the two kilos satisfied both elements for vicarious liability:

There’s ample evidence [that] the 2 kilograms was reasonably foreseeable and was in furtherance of the conspiratorial agreement: the discussion that Mr. Johnson testified to of obtaining 2 kilograms, with one to be purchased and one [to be] fronted, the discussion that he had been given a letter that he was supposed to deliver to Carlos that came through Mr. Williams that was going to arrange for this fronting correctly, and the discussions in the tapes reflecting that.

Tr. 29 (9/13/95). The record bears out the district court’s, statement. Williams twice acknowledged on the stand that Johnson explained to him that he intended to purchase two kilos and that he needed Williams’s help in getting financing for the second kilo. Williams denied that he gave Johnson the assistance he requested, but Johnson’s own testimony, notably his description of Naran-jo’s note that Williams gave him to take to Detective Gonzales, supports the district court’s conclusion that Williams could reasonably foresee that Johnson would purchase two kilos. Although Williams denied that he had agreed to assist Johnson in buying two kilos, the district court reasonably credited Johnson’s testimony to the contrary. That Johnson brought his friend Ulysses Wilson into the deal without Williams’s knowledge in no way suggests that Williams was not a party to the agreement or that the purchase represented a “side deal” involving only Johnson and Wilson. According to Johnson, he brought Wilson along because, feeling insecure as a negotiator, he wanted the support of a friend.

3. Reverse Sting Downward Departure

Williams argues that even if the district court properly used two kilos in setting his base offense level, he should have received a downward departure based on the “reverse sting” provision of U.S.S.G. § 2D1.1, which provides:

If, in a reverse sting (an operation in which a government agent sells or negotiates to sell a controlled substance to a defendant), the court finds that the government agent set a price for the controlled substance that was substantially below the market value of the controlled substance, thereby leading to the defendant’s purchase of a significantly greater quantity of the controlled substance than his available resources would have allowed him to purchase except for the artificially low price set by the government agent, a downward departure may be warranted.

U.S.S.G. § 2D1.1, cmt. n.15 (1995). Refusals to depart are reversible only if the district court failed to recognize its authority to depart or if it made a clearly erroneous factual finding that the factor potentially justifying departure was not present. See United States v. Sammoury, 74 F.3d 1341, 1343-44 (D.C.Cir.1996); see also United States v. Washington, 106 F.3d 983, 1016 (D.C.Cir.1997). The district court committed neither error.

When Williams first raised the reverse-sting issue at his sentencing hearing, the district court acknowledged the possible applicability of note 15: “I’m applying what the guidelines says about the reverse sting, but I didn’t find that it made a difference in the 2 kilograms that applies to you, that’s all.” Tr. 34 (9/13/95). To have reached this conclusion, the district court must have found either that Gonzales did not set the price at an artificially low level, or that Johnson did not buy more than he otherwise would have because of the depressed price. Neither of those findings would have been clearly erroneous. In support of his argument that the $18,500/kilo price was “substantially below the market value,” Williams offers no evidence other than that Gaviria originally offered to sell at $24,000/kilo. Nor does anything in the record suggest that Johnson bought more than he otherwise would have because the price was $18,500 rather than the $24,000 originally suggested by Gaviria, or that he would have purchased less than the two kilos ultimately attributable to Williams. Most of the purchase was on credit. Even assuming Johnson had a fixed amount to spend (5 x $18,500 = $92,500), he still would have purchased nearly four kilos if the price had been $24,000/kilo.

4. Denial of Motion To Allow Witnesses and Evidence at Sentencing Hearing

Williams next challenges the district court’s denial of his motion to call two FBI agents, three co-defendants, and an employee of the Pretrial Services Agency at his sentencing hearing. The court also prohibited him from introducing a videotape of David Johnson’s and Ulysses Wilson’s November 16 drug buy and an audio tape of a November 16 phone conversation between Williams and Jocelyn Johnson.

According to the district court, Williams gave three principal reasons for his request: to impeach trial testimony; to show that he was not involved in the conspiracy for which he had been convicted; and to dispute the two kilograms for which the presentence report held him responsible. The court reasonably rejected the first two justifications:

The function of the sentencing hearing is not to re-try issues which have been fully explored at trial. Here, three of the six witnesses which the defendant presently seeks to call ... previously testified at trial and were fully available to be cross-examined by the defendant. Moreover, the question of whether the defendant was “involved in the conspiracy” is a question that the jury explicitly answered when it found [the] defendant guilty....
As for the other witnesses the defendant requests, ... the defendant has not made even a minimal showing to this Court why their testimony is relevant to sentencing. The defendant’s failure to offer proffers as to what these witnesses’ testimony might be flies in the face of the Court’s request ... to demonstrate why such testimony would be relevant. As for the videotape and tape recordings that defendant requests, these recordings are part of the trial record, and the Court is familiar with them. The defendant is free to call the Court’s attention to specific portions of these recordings ... during oral allocution at sentencing.

Order, at 2-3 (9/6/95).

With respect to Williams’s argument that he needed the testimony to challenge the attribution to him of two kilos of cocaine, the district court found Williams’s request deficient in two respects: it failed to identify the portion of the drugs attributed to him that he wished to dispute; and it “failed to explain the nature of the witnesses’ potential testimony, and why it is relevant to sentencing.” Id. at 3. Although Williams now challenges one of the two kilograms of cocaine for which he was held responsible, he still has not explained the relevance of the witnesses or the tapes to that challenge. His brief simply refers to the defendant’s bearing the burden of proof on mitigating factors at sentencing. The drug quantity that determines the base offense level, however, is not a “mitigating factor.” See, e.g., United States v. Booze, 108 F.3d 378, 381 (D.C.Cir.1997). In his reply brief, Williams makes a series of claims about how the excluded testimony (and a number of documents not requested in his motion) would have demonstrated his innocence. Williams also mentions the drug quantity issue, suggesting that testimony from the two FBI agents would have supported his contention that he should have been held responsible for only one kilo. Reply Brief of Appellant Williams, at 2 & n.3. One of the agents, however, testified at trial and was subject to cross-examination. As the Government pointed out in its opposition to Williams’s motion, the other agent’s role was limited to her presence at the November 16, 1993, cocaine purchase. Under these circumstances, the district court’s conclusion that Williams had failed to explain how the agent’s testimony was relevant to the question of drug quantity was perfectly reasonable. See Fed.R.Crim.P. 32(c)(1) (decisions about admission of evidence at sentencing hearings entrusted to district court’s discretion).

5. Upward Adjustment for Managing or Supervising Criminal Activity

Equally reasonable was the district court’s decision to add two points to Williams’s offense level under U.S.S.G. § 3Bl.l(c) for being “an organizer, leader, manager, or supervisor” in a criminal activity. In applying this adjustment, the district court relied on two aspects of Williams’s conduct: his service in linking together Nar-anjo and his confederates in the drug supply network, on the one hand, and David Johnson as a buyer and reseller, on the other; and his supervision of Johnson. At the sentencing hearing, the district court explained:

The Court recognizes that Mr. [Williams] was not the proponent originally of all this operation. ■ Hé was brought in apparently by Mr. Naranjo to assist with further distributions of both heroin and cocaine and did so, introducing Mr. Johnson, and arranged through this introduction for the multiple heroin deals with Kiki and then attempted to arrange the cocaine deal.
He organized or helped the organization of Mr. Naranjo in making the phone calls and trying to assist in the distribution of these drugs, as I’ve said, bringing Mr. Johnson and Mr. Wilson, whom he didn’t know, when Mr. Johnson recruited Mr. Wilson to assist,in the distribution of these drugs. He obviously played an integral role in linking the Naranjo people and their access to drugs with Mr. Johnson and his people to arrange for the distribution and resale of these drugs, both the heroin and the cocaine, and as such, I believe under 3Bl.l(c), 2 points are appropriate to add, as he is a supervisor and director of Mr. Johnson in the other matters I referred to in the conspiracy.

Tr. 27-28 (9/13/95).

The district court did not clearly err in making these findings. See, e.g., United States v. Baylor, 97 F.3d 542, 548 (D.C.Cir.1996) (adjustments under § 3B1.1 reviewed for clear error). As the Government acknowledges, the district court’s conclusion that Williams recruited Johnson to buy cocaine from the Naranjo group rests on an inference that Williams was the one who supplied Naranjo with Johnson’s phone number. Brief for Appellee, at 169. We think this inference is reasonable, both in light of Williams’s position — as Naranjo’s cellmate and Johnson’s de facto brother-in-law — and his earlier heroin transactions with Johnson, as well as his later involvement with Johnson in the cocaine transaction. Although Williams claims that Naranjo got Johnson’s phone number from another inmate named “fat Sam,” he gives no record citation for this claim, and the transcript excerpt in his brief does not bear it out. See Brief for Appellant Williams, at 21.

The district court’s conclusion that Williams supervised or managed Johnson in his cocaine purchase likewise finds support in the record. Although Johnson did state on cross-examination that buying the full five kilos was his idea, Williams served as Johnson’s financial advisor and, ultimately, as conveyor of the financial backing Johnson needed to consummate the deal.

6. Upward Adjustment for Obstruction of Justice

Finding that Williams lied on the stand, the district court also added two points to his offense level for obstruction of justice under U.S.S.G. § 3C1.1. Williams challenges this adjustment, claiming that he misunderstood the prosecutor’s questions and that the evidence supporting the court’s finding of perjury was insufficient. See, e.g., Washington, 106 F.3d at 1016-17 (adjustments under § 3C1.1 reviewed for clear error).

Drawing on the definition of perjury under the federal perjury statute, the Supreme Court has held that an enhancement under U.S.S.G. § 3C1.1 based on perjury must rest on a finding that the defendant gave “false testimony concerning a material matter with the willful intent to provide false testimony, rather than as a result of confusion, mistake, or faulty memory.” United States v. Dunnigan, 507 U.S. 87, 94, 113 S.Ct. 1111, 1116, 122 L.Ed.2d 445 (1993). The Court has also directed trial judges to “review the evidence and make independent findings necessary to establish a willful impediment to or obstruction of justice.” Id. at 95, 113 S.Ct. at 1116. Interpreting the instruction in section 3Cl.l’s first application note — that a defendant’s testimony “should be evaluated in a light most favorable to the defendant,” U.S.S.G. § 3C1.1, cmt. n.l — we have held that district courts’ findings must rest on clear and convincing evidence, not a mere preponderance. See United States v. Montague, 40 F.3d 1251, 1253-56 (D.C.Cir.1994); see also United States v. Onumonu, 999 F.2d 43, 45 (2d Cir.1993). We have also held that the closer the issue, the more detailed the district court’s findings must be. Montague at 1256; see also United States v. Sobin, 56 F.3d 1423, 1429 (D.C.Cir.), cert. denied, 116 S.Ct. 348 (1995).

This case was not particularly close, and the district court made sufficient findings to support the enhancement. In particular, the district court found that Williams lied when he denied any involvement in the conspiracy; when he claimed to have told Johnson not to deal drugs; and when he denied talking in code about drug deals with Johnson. The district court reached these conclusions because it credited Johnson’s testimony and because taped conversations— between Williams and Johnson on November 5, 1993, and between Johnson and Detective Gonzales on November 12, 1993 — contradicted Williams’s assertions. Williams argues that he initially denied using drug trafficking code because he misunderstood the prosecutor’s question, claiming that he later acknowledged using “slang,” not “code.” Near the end of his testimony, however, Williams again denied that his conversations with Johnson, whether characterized as code or slang, concerned drug transactions.

We do agree with Williams that because the perjury supporting a section 3C1.1 enhancement must concern the offense of conviction, see United States v. Barry, 938 F.2d 1327, 1332-35 (D.C.Cir.1991), the district court should not have relied, even in part, on perjury concerning the heroin transactions Williams helped arrange between Johnson and “Kiki.” However, because the district court identified in the record plenty of perjury directly related to the offense of conviction, this error, which the Government attempts to gloss over by treating the heroin and cocaine conspiracies as one and the same, was harmless.

7. Downward Adjustment for Minimal Role

Relying on the principle that adjustments under U.S.S.G. § 3B1.2 should be based on “a defendant’s culpability relative to that of his comrades,” Washington, 106 F.3d at 1018; see also United States v. Caballero, 936 F.2d 1292, 1298-99 (D.C.Cir.1991), Williams claims that he was entitled to a downward adjustment for being a minor or minimal participant because Ulysses Wilson received an adjustment for being a minor participant and Williams’s own role was less significant than Wilson’s. In support of his argument, Williams offers two pieces of evidence: that Wilson was held responsible for the entire five Míos he and David Johnson bought from Detective Gonzales, whereas Williams was held accountable for only two kilos; and that Wilson actually put up half the cash used for the purchase. Reasonably viewing these considerations as not dispositive, the district court focused instead on essentially the same factors it relied on in giving Williams an upward adjustment for being a manager or supervisor: that Williams served as “a crucial link between the sellers and the buyers of [the] cocaine,” Tr. 27 (9/13/95); that he supervised Johnson, who only brought Wilson in at the tail end of the conspiracy; and that he arranged for the purchase of most of the cocaine on credit, an arrangement worth much more than Wilson’s small cash contribution. The district court’s denial of the downward adjustment was not an abuse of discretion. See, e.g., Spriggs, 102 F.3d at 1263 (refusals to grant downward adjustments under § 3B1.2 reviewed for abuse of discretion).

C. Forfeiture

For his final challenge, Williams argues that the record contains insufficient evidence to support his criminal forfeiture conviction, claiming he contributed none of the money David Johnson and Ulysses Wilson used to buy cocaine from Detective Gonzales. Acknowledging that the $44,409 subject to forfeiture represents the amount of money that other conspirators derived from or used in the cocaine trafficking conspiracy, the Government argues that Williams is subject to forfeit this amount because co-conspirators bear joint and several liability under the criminal forfeiture statute, 21 U.S.C. § 853.

We have never considered the scope of liability under 21 U.S.C. § 853. Although every circuit addressing the issue has approved joint and several liability, see United States v. Hurley, 63 F.3d 1, 22 (1st Cir.1995) (collecting cases), cert. denied, - U.S.-, 116 S.Ct. 1322, 134 L.Ed.2d 474 (1996), the question is not simple, as the First Circuit recently observed. Id. We need not decide the issue, however, because the Government concedes that the district court, contrary to Fed.R.CrimP. 43(a), failed to announce the forfeiture portion of Williams’s sentence in his presence. The Government requests that the court vacate the forfeiture count, however, rather than remand the proceedings, telling us that if we were to remand, it would simply seek dismissal of the charge rather than bear the expense of bringing Williams back to court. Thus, we will simply vacate the forfeiture portion of Williams’s sentence.

YI. Appellant Naranjo

Naranjo raises a number of objections to his conviction and to his sentence, none of them persuasive. He claims that the district court erred when it denied his request to present a defense of duress to the jury and when it admitted evidence of his involvement in heroin transactions. He also claims that the evidence showed multiple conspiracies rather than a single conspiracy. Finally, Naranjo complains that the conduct of the Government in this case was so outrageous that the court must reverse his conviction as a matter of due process. As to sentencing, Naranjo argues that the statutory provision under which he received a life sentence does not apply to a conspiracy conviction, and that the district court erred in determining the quantity of drugs attributable to him as a member of the conspiracy.

A. Duress

When Naranjo’s wife was arrested in June 1992, Naranjo placed his teenaged daughter Carolina in Sanders’s custody. She lived with Sanders until March 1993 when she moved to California and began living with her aunt, Naranjo’s sister. According to Naranjo, Sanders, who had on three occasions struck Carolina when she did something that he considered disobedient, threatened Naranjo by reminding him that Carolina was “in his hands.” Naranjo claims that he agreed to help Sanders obtain cocaine only because he feared that otherwise Sanders would harm the girl. After a three-day hearing the district court ruled that Naranjo’s defense of duress was insufficient as a matter of law and refused to allow Naranjo to make the duress argument to the jury. We review this ruling de novo.

A defendant may assert duress as an affirmative defense only if he shows that he acted under the threat of immediate death or serious bodily injury. United States v. Bailey, 444 U.S. 394, 409, 100 S.Ct. 624, 634, 62 L.Ed.2d 575 (1980). In addition, he must show that he had no reasonable legal alternative to committing the crime. United States v. Jenrette, 744 F.2d 817, 820-21 (D.C.Cir.1984) (Congressman who claims that he agreed to accept bribe only because he feared that he was dealing with mobsters may not raise duress defense because he had opportunity to notify law enforcement officials during two days between agreeing to take bribe and actually taking it). A defendant “cannot claim duress when he had, but passed up, an opportunity to seek the aid of law enforcement officials.” United States v. Rawlings, 982 F.2d 590, 593 (D.C.Cir.1993). Because Naranjo failed to show that he had no reasonable alternative but to engage in a drug conspiracy with Sanders, the district court properly rejected his defense of duress.

Naranjo’s argument that he was not able to inform anybody of the threat to his daughter during the 13 months in which he participated, allegedly unwillingly, in the drug distribution conspiracy with Sanders borders upon the frivolous. Naranjo had ample opportunities to inform his daughter, his sister, his or his wife’s lawyer, or prison officials about Sanders’s alleged threat.' His excuses for failing to take advantage of a single opportunity over the course of the conspiracy do not withstand scrutiny. First, Naranjo could have warned his sister or Carolina herself about the threat to her safety. Although Naranjo claims that he was concerned about upsetting his daughter, that is not a sufficient justification for continuing to participate in a major criminal conspiracy. Nor, when the principal of his daughter’s school spoke to Naranjo about his concern for her well-being, did Naranjo inform the principal of the alleged threat to Carolina. Second, Naranjo could have told a prison guard or a more senior prison official of his dilemma. Naranjo claims that he could not have reported Sanders’s threats to a prison guard because many of the guards were corrupt but he provides no concrete evidence in support of this assertion. He also claims that had he reported Sanders’s threat to a prison official he would have been placed in protective custody, which Sanders would have interpreted as an indication that Naran-jo had squealed. This speculation is belied by the record; on several occasions diming the conspiracy Naranjo was placed in isolation; he so informed Sanders yet Sanders never betrayed any concern that Naranjo might have informed prison officials of their scheme. Cf. United States v. Merchant, 992 F.2d 1091, 1096-97 (10th Cir.1993) (prisoner who agreed to help smuggle cocaine into prison and claimed that he did so only out of fear of fellow prisoners could not raise duress defense because he could have sought protective custody). Finally, Naranjo could have told somebody other than a family member or a prison employee about Sanders’s alleged threats. Naranjo points out that (again, allegedly corrupt) prison employees monitored most of his calls, but he was free to make unmonitored calls to his lawyer and he actually did speak, unmonitored, to his wife’s lawyer during the course of the conspiracy.

Naranjo claims that his case is analogous to that of the defendant in United States v. Contento-Pachon, 723 F.2d 691 (9th Cir.1984). In that case the defendant proffered that he agreed to transport cocaine from Colombia to the United States only because he was told that if he did not do so then his wife and child would be killed. The defendant testified that he did not inform authorities in Colombia of his plight because the Colombian police were corrupt. As soon as he reached the United States he consented to an x-ray that revealed the balloons of cocaine that he had swallowed. Under these eircum-stances, the court held that Contento-Pachon could argue duress to the jury. Id. at 693-94. But that case does not help Naranjo. The conspiracy in this case lasted for 13 months, in contrast to the single flight at issue in Contento-Pachon. See United States v. Alicea, 837 F.2d 103 (2d Cir.1988) (defendant who had 20-minute period in which she was free to inform authorities about threat to her life precluded from raising duress defense); cf. United States v. Jennell, 749 F.2d 1302, 1306 (9th Cir.1984) (refusing to follow Contento-Pachon where conspiracy “dragged on for a period of more than a year”). In addition, Naranjo, unlike Contento-Pachon, had access to a number of prison officials, relatives, and lawyers, not simply to allegedly corrupt Colombian police officers.

B. Evidence of the Heroin Conspiracy

David Johnson, a cooperating co-defendant, testified that in October 1993 Naranjo and his cellmate Williams helped Johnson and Ulysses Wilson purchase heroin on two separate occasions from Kiki in New York. Naranjo set up the deal by giving Johnson’s telephone number to Kiki. Naranjo also urged Kiki to call Johnson and tell him that Kiki was a friend of Williams, who was related to Johnson. Johnson and Wilson made two separate purchases from Kiki. When they expressed their disappointment with the quality of the heroin in the second lot Naranjo offered to help resolve the dispute. The Government did not charge Naranjo with conspiracy to distribute heroin but the district court nevertheless allowed the Government to introduce evidence of the heroin transactions, holding that this evidence showed the relationships among the parties and was intrinsic to the cocaine conspiracy. We review the decision to admit the evidence only for an abuse of discretion. United States v. Graham, 83 F.3d 1466, 1473 (D.C.Cir.1996).

Evidence of an uncharged crime or bad act may be admitted if, as required by Federal Rule of Evidence 404(b), it is probative of a material issue other than the defendant’s character, and if, as required by Federal Rule of Evidence 403, that probative value is not substantially outweighed by the prejudicial value of the evidence. United States v. Clarke, 24 F.3d 257, 264 (D.C.Cir.1994). Naranjo argues that the evidence of the heroin purchases was introduced solely in order to taint his character: the Government had already introduced evidence showing his relationship to the other defendants. The evidence of the heroin transaction did, however, link Naranjo to Johnson and Wilson, who purchased some of the cocaine supplied by Zambrano in Miami. In this way the evidence helped tie the Miami transaction to the resulting resale of the cocaine. In addition, by showing how the appellants used code words to discuss the purchase of heroin, the evidence shed light upon the defendants’ use of code words in discussing the purchase of cocaine. Finally, the evidence tended to rebut Naranjo’s defense that he got involved with and stayed involved with the cocaine conspiracy only to benefit Sanders; Sanders played no role in the heroin deal.

The prejudicial value of the evidence of the heroin transactions is slight. Naranjo freely admitted in his testimony that he agreed with Gavina to obtain cocaine for resale. After that concession, the incremental prejudice of evidence that he also assisted a heroin purchase was not likely to be substantial. In addition, the district court instructed the jury that the evidence could be considered for certain limited purposes only, viz., “whether it shows or tends to show the existence of a relationship between the defendants, and whether it shows or tends to show the defendants had a common scheme or plan which included the offenses for which they are now charged,” and whether Naranjo was “predisposed to commit the offenses.” Tr. 4974 (4/25/95); see United States v. Moore, 732 F.2d 983, 990 (D.C.Cir.1984) (limiting instruction lessens potential prejudice of bad act evidence). The probative value of the evidence, on the other hand, was high because the heroin deal took place around the same time as the cocaine transactions and therefore tended to rebut Naranjo’s entrapment argument. See United States v. Manner, 887 F.2d 317, 321 (D.C.Cir.1989) (closeness in time and similarity of other crime to charged crime underscores relevance of evidence); Moore, 732 F.2d at 987 (evidence of other crimes properly admitted in order to rebut entrapment defense). Accordingly, because the evidence was probative of material issues other than character, and because that probative value was not substantially outweighed by the prejudicial value of the evidence, the district court did not abuse its discretion in admitting the evidence.

C. Prejudicial Variance

In his initial brief Naranjo argues that there was insufficient evidence of a single conspiracy. “At best,” he claims, “the evidence showed that Johnson, Wilson, and Williams were part of one conspiracy, that Gaviria and Zambrano were part of a second conspiracy, and [that Naranjo] and Gaviria were part of a third conspiracy.” Brief for Appellant Naranjo, at 39. To the extent that we construe this claim as a simple argument about the sufficiency of the evidence, it is ludicrous, for Naranjo admitted to conspiring with Gaviria and Sanders. To the extent that we construe this claim as one of variance between the indictment (alleging a single conspiracy) and the evidence at trial, the argument is fatally flawed.

Naranjo shows neither error nor prejudice. In order to determine whether the evidence supports the jury’s implicit finding of a single conspiracy the court looks at whether the defendants shared a common goal, any interdependence among the participants, and any overlap among the participants in the allegedly separate conspiracies. United States v. Gatling, 96 F.3d 1511, 1520 (D.C.Cir.1996). The Government showed all three in this case. The goal of the conspiracy, as charged in the indictment and as proved at trial, was the distribution of cocaine. That the participants entered the distribution chain at different levels is of no moment. See United States v. Childress, 58 F.3d 693, 710 (D.C.Cir.1995). Naranjo himself provides both the element of interdependence and the element of overlap; he oiled each cog of the conspiracy, helping to move the cocaine from Zambrano to Gaviria to Williams and Johnson.

Even assuming that there was a variance, Naranjo failed to show that he was substantially prejudiced by it. The risk of “spillover prejudice,” which may occur when a jury imputes evidence from one conspiracy to a defendant involved in another conspiracy, is less likely the fewer the defendants. United States v. Anderson, 39 F.3d 331, 348 (D.C.Cir.1994). Only four defendants were tried in this case. Cf. United States v. Alessi, 638 F.2d 466, 475 (2d Cir.1980) (10 defendants a sufficiently small number for jury to give individual consideration to each defendant). In addition, the danger of spillover prejudice is minimal when the Government presents tape recordings of individual defendants, as it did in this case, so that the jury has “no need to look beyond each defendant’s own words in order to convict.” Anderson, 39 F.3d at 348. Moreover, Naranjo played a role in all aspects of the conspiracy. Accordingly, even if there were three separate conspiracies, Naranjo would have to be deemed a member of each and could not, therefore, have been the victim of any spillover prejudice.

D. Outrageous Government Conduct

Finally, Naranjo argues that his conviction should be reversed because the Government’s conduct of the case violated his rights under the Due Process Clause of the Fifth Amendment to the Constitution of the United States. The Supreme Court has recognized that there may be situations “in which the conduct of law enforcement agents is so outrageous that due process principles would absolutely bar the government from invoking judicial processes to obtain a conviction.” United States v. Russell, 411 U.S. 423, 431-32, 93 S.Ct. 1637, 1642-43, 36 L.Ed.2d 366 (1973). But see Hampton v. United States, 425 U.S. 484, 495 n. 7, 96 S.Ct. 1646, 1653, n. 7, 48 L.Ed.2d 113 (1976) (Powell, J. concurring) (especially difficult to prevail upon ground of outrageous governmental conduct in case involving contraband offenses because they are “so difficult to detect in the absence of undercover Government involvement”). While this court, therefore, cannot rule out the possibility of finding valid a defense of outrageous governmental conduct, but see United States, v. Boyd, 55 F.3d 239, 241 (7th Cir.1995) (outrageous governmental misconduct not independent ground for ordering new trial but may support inference that without such tactics defendant might have been acquitted); United States v. Tucker, 28 F.3d 1420, 1428 (6th Cir.1994) (separation of powers principle compels court to reject outrageous conduct defense), we have limited the defense to conduct involving “coercion, violence, or brutality to the person,” United States v. Walls, 70 F.3d 1323, 1330 (1995); see also United States v. Kelly, 707 F.2d 1460 (1983).

Naranjo does not come even close to meeting that standard. He complains that the Government should have cut off his telephone privileges so that he would have been unable to continue his participation in the conspiracy; but the Government has no duty to prevent a prisoner from committing more crimes. Sounding more like an outraged taxpayer than the drug-dealer that he is, Naranjo then complains that the Government wasted money for the dubious purpose of luring a foreigner to the United States so that he could be incarcerated at public expense. How the executive branch spends (or wastes) taxpayer money is, however, not our concern. See Lincoln v. Vigil, 508 U.S. 182, 192, 113 S.Ct. 2024, 2031, 124 L.Ed.2d 101 (1993) (allocation of funds from lump-sum appropriation not subject to judicial review).

Naranjo then argues that the failure of law enforcement officers to prevent Sanders from beating Naranjo’s daughter constitutes outrageous conduct. The district court rejected Naranjo’s contention that Sanders abused Naranjo’s daughter, finding only that he disciplined her. Even assuming arguendo, however, that Sanders’s behavior constituted “coercion, violence, or brutality to [Naran-jo],” the Government’s refusal to intervene does not constitute coercion, violence, or brutality to him. See DeShaney v. Winnebago County Dep’t of Social Services, 489 U.S. 189, 109 S.Ct. 998, 103 L.Ed.2d 249 (1989) (State has no constitutional duty to protect child from his father after receiving reports of possible abuse).

E. Sentencing

Naranjo was convicted of violating 21 U.S.C. § 846, which provides that any person who conspires to commit a drug offense “shall be subject to the same penalties as those prescribed for the offense, the commission of which was the object of the ... conspiracy.” Naranjo’s underlying offenses were the distribution and the possession with intent to distribute five kilograms or more of cocaine, in violation of 21 U.S.C. § 841. That statute provides, in part, that: “If any person commits a violation of this subparagraph or of sections 849, 859, 860, or 861 of this title after two or more prior convictions for a felony drug offense have become final, such person shall be sentenced to a mandatory term of life imprisonment without release.” 21 U.S.C. § 841(b)(1)(A). Because Naranjo had (more than) twice previously been convicted of a felony drug offense the district court sentenced him to life imprisonment.

Naranjo argues that because section 841 does not expressly mention section 846, the Congress did not intend for the mandatory life provision of section 841(b) to apply to a conviction for conspiracy under section 846. Naranjo seeks support for this position from our decision in United States v. Price, 990 F.2d 1867 (1993), but to no avail. In Price we invalidated the Sentencing Commission’s inclusion of conspiracy within the meaning of a “controlled substance offense” for the purpose of the Commission’s Career Offender Guidelines. We did so, however, only because the congressional mandate upon which the Sentencing Commission expressly relied, 28 U.S.C. § 994(h), directed the Commission to establish guidelines for multiple offenders who had been convicted of an offense described in section 401 of the Controlled Substances Act, of which conspiracy is not one. Accordingly, there was no congressional authority for the Guideline insofar as it applied to a conspiracy conviction. Naranjo would have us read Price as somehow standing for the proposition that the Congress has determined “that conspiracy to commit an offense does not warrant as harsh treatment as the actual commission of the offense which is the object of the conspiracy.” Brief for Appellant Naranjo, at 32. Specifically, he argues that because the Congress did not in 28 U.S.C. § 994(h) expressly direct the Sentencing Commission to impose an enhanced penalty upon a repeat drug offender convicted of a drug conspiracy, it could not have meant to do so when it enacted 21 U.S.C. § 846. Nar-anjo provides no authority for this curious-leap of logic. The law that Naranjo violated, section 846, clearly states that a violator shall be punished as provided by section 841. This is neither complicated nor contravened by the reasoning of Price, which holds only that the Sentencing Commission may not exceed the bounds set for it by the Congress. Accordingly, we join the Tenth Circuit, see United States v. O’Brien, 52 F.3d 277, 278-79 (1995), and the Eighth Circuit, see United States v. Wessels, 12 F.3d 746, 752 (1993), in holding that the mandatory provision for a life sentence in 21 U.S.C. § 841(b)(1)(A) applies to a conviction for conspiracy.

F. Drug Quantity

Finally, Naranjo argues that there was insufficient evidence to sentence him for having distributed more than four kilograms of cocaine. The district court made express findings that Naranjo was responsible for the five kilograms of cocaine that he ordered from Colombia at the beginning of the conspiracy and for the 15 kilograms of cocaine that were delivered to government agents in Miami. Naranjo argues that these findings are erroneous, asserting that he ordered four, not five, kilograms at the beginning of the conspiracy and that he should not be held responsible for the cocaine purchase in Miami. Because the mandatory life sentence provision of section 841(b)(1)(A) applies as long as at least five kilograms of cocaine are attributed to a defendant with two or more prior drug convictions, we need determine only that Naranjo was responsible for at least five kilograms. United States v. Saro, 24 F.3d 283, 285-86 (D.C.Cir.1994) (where sentence would not be affected by disputed quantity, any error in attributing quantity to defendant is harmless). Naranjo did not timely object to the district court’s decision to attribute 20 kilograms of cocaine to him, so we review that determination for plain error only. Id. at 286.

The district court attributed the 15 kilograms of cocaine distributed in Miami to Naranjo for two independent reasons. First, the amount was reasonably foreseeable. Second, Naranjo was responsible as an aider and abettor of the sale. Naranjo argues that the 15-kilogram purchase was not foreseeable because his only agreement with his co-conspirators was to import and resell four kilograms of cocaine. The evidence showed, however, that Naranjo and Sanders had previously been involved together in deals for much greater amounts of cocaine. In addition, Naranjo directed Sanders to send Gavi-ria to Miami in order to meet with Zambra-no, whom Naranjo considered capable of producing a large amount of cocaine. Finally, Gaviria testified that while Naranjo was waiting for the initial shipment of cocaine to arrive, he tried to obtain other shipments from Colombia. Accordingly, because Nar-anjo had already ordered four or five kilograms, was aware of Zambrano’s ability to produce a large quantity of drugs, and was attempting to place new orders, it was reasonably foreseeable that his co-conspirators would purchase as much as 15 kilograms.

Nor did the district court clearly err in holding Naranjo responsible for the 15 kilograms as an aider and abettor. The elements of aiding and abetting an offense are (1) the specific intent to facilitate the commission of a crime by another; (2) guilty knowledge (3) that the other was committing an offense; and (4) assisting or participating in the commission of the offense. United States v. Washington, 106 F.3d 983, 1004 (D.C.Cir.1997). Much, of the evidence showing that the 15-kilogram purchase was foreseeable also supports the conclusion that Naranjo aided and abetted that purchase. Naranjo vouched for Zambrano and helped to arrange the meeting between Gaviria and Zambrano. The court permissibly inferred Naranjo’s guilty knowledge of the crime from conversations among Naranjo, Gaviria, and Zambrano while the deal was taking place and from testimony that a cut of the proceeds of the transaction was sent to Naranjo’s sister with Naranjo’s knowledge. Finally, by facilitating Gaviria’s trip to Miami, Naranjo assisted the commission of the crime. Accordingly, the district court did not err in attributing more than five kilograms of cocaine to Naranjo. 
      
      . Judge Wald authored the Introduction and Parts I and IV. Judge Ginsburg authored Parts II and VI. Judge Tatel authored Parts III and V.
     
      
      . At the time of the events leading to the convictions at issue here, Jose Naranjo was serving time at FCI for four federal drug convictions.
     
      
      . Gaviria had been deported to Colombia after being convicted of federal drug offenses in the United States.
     
      
      . The record in this case includes approximately 100 taperecorded conversations among various members of the conspiracy and undercover government agents. Many conversations were conducted in Spanish and/or in code. Several individuals at trial testified that the coded conversations were in fact discussions of planned drug transactions. Because the evidence on appeal must be construed in the light most favorable to the government, this statement of facts summarizes those conversations by assuming that the code words did refer, for example, to kilograms of cocaine. We note, however, that appellant Zambrano contests the district court’s conclusion that certain conversations showed that he was aware of and knowingly participated in the November 7 drug sale in Miami. Zambrano’s claims are based in part on his assertion, explained in more detail below, that he did not understand that the code words pertained to drug deals. On review, we find that the record evidence belies this assertion, and that it was well within the realm of the jury and the district court to discredit Zambrano’s testimony in this regard.
     
      
      . At various points during the conspiracy, the men referred in their conversations to kilograms of cocaine as "cars,” "girls,” "rooms” in an apartment, "female employees,” and "videos.” Several individuals testified at trial that all those terms were code words for drugs.
     
      
      . In April 1993, Sanders followed Naranjo's directive to wire $5,000 to Gaviria in Colombia. Gaviria used this money to enter the United States illegally. On May 14, 1993, Gaviria arrived in the United States, and Sanders took Gaviria to an apartment in McLean Gardens in Northwest Washington. As they rode from the airport, Gaviria inquired about the drug scene in Washington, including the possibility of selling cocaine, heroin, and marijuana in D.C.
     
      
      . Gaviria's sister Martha, who was also residing in Miami, had put the two men back in touch.
     
      
      . The FBI introduced Gonzales into the scheme when Gaviria, who did not speak English well, asked Sanders to find someone to act as an interpreter. Sanders told Gaviria that Gonzales was a friend who had previously traded drugs with Sanders.
     
      
      . Transcript ("Tr.”) 1637-39 (2/16/95). Zambra-no did carry out this request. He and Martha met with Gonzales and Sanders on a street in Miami. Gonzales testified that Zambrano "stated he was a businessman and he didn't like to be kept waiting,” i.e., for the money that was still owed by them for the drugs that Humberto and Martha Gaviria had delivered. Tr. 1423-25 (2/14/95); Tr.1933 (3/3/95). Martha Gaviria testified that Gonzales told Zambrano Üiat he would take the drugs to Washington and that he wanted to meet with Zambrano again to get additional drugs, to which Zambrano responded by "askflng] when could they give him the money.” Tr. 1642 (2/16/95). Zambrano explained that for them to get another shipment of drugs, “it was necessary for them to give him that money first, and then he will let them know.” Id.
      
     
      
      . Cooperating co-defendant David Johnson testified that Williams was an established drug dealer. Johnson also testified that Williams and Johnson's sister Jocelyn had parented a child together, and that Williams had helped Johnson start selling cocaine in Baltimore. Sometime after Williams was imprisoned, Johnson — at Williams's direction — pawned $10,000 of Williams’s jewelry to buy cocaine and heroin from a Spanish-speaking New York drug dealer known as "Kiki” and introduced to Johnson by Williams.
     
      
      . This conversation was surreptitiously taped by Gonzales.
     
      
      . Tr. 3899 (4/10/95). Appellant Naranjo also tried to assert a defense of duress, claiming that he feared for the safety of his daughter Carolina. However, the district court did not allow that defense to go to the jury.
     
      
      .Appellants were not indicted on Count Two, in which David Johnson and Ulysses Bobby Wilson were charged with possession with intent to distribute 500 or more grams of cocaine. Johnson, Wilson, and Martha Gaviria were indicted along with appellants, but negotiated guilty pleas prior to trial.
     
      
      . Section 846 provides that:
      Any person who attempts or conspires to commit any offense defined in this subchapter shall be subject to the same penalties as those prescribed for the offense, the commission of which was the object of the attempt or conspiracy.
      21 U.S.C. § 846(1994).
     
      
      . Section 841 provides in part:
      (a) Unlawful acts
      Except as authorized in this subchapter, it shall be unlawful for any person knowingly or intentionally—
      (1) to manufacture, distribute, or dispense, or possess with intent to manufacture, distribute, or dispense, a controlled substance....
      21 U.S.C. § 841(a)(1) (1994).
     
      
      . This argument is made for the first time on appeal, and thus is reviewed only for plain error. United States v. Sayan, 968 F.2d 55, 62 (D.C.Cir.1992).
     
      
      . Although there is no overt act requirement for a § 846 conspiracy conviction, see, e.g., United States v. Pumphrey, 831 F.2d 307, 308 (D.C.Cir.1987) (“In contrast to the general criminal conspiracy statute, 18 U.S.C. § 371, which explicitly requires proof of an overt act, § 846 makes no mention of any such requirement. Absent clearly expressed legislative intent to the contrary,this unambiguous statutory language settles the question.”), the government must prove that the defendant had the "specific intent to further the conspiracy's [unlawful] objective.” United States v. Childress, 58 F.3d 693, 708 (D.C.Cir.1995).
     
      
      . Moreover, the government's showing may be made by circumstantial evidence. Id. at 1518; Lam Kwong-Wah, 924 F.2d at 303 (“No distinction is made between direct and circumstantial evidence in evaluating the sufficiency of evidence supporting a guilty verdict.”).
     
      
      . Circumstantial evidence suggested that Zam-brano had arranged for the stranger, who called himself "the Panamanian,” to deliver the drugs to Gaviria.
     
      
      . See, e.g., Childress, 58 F.3d at 714 (fact that defendant made two 50 kilogram deliveries of cocaine to drug distribution network was "sufficient to prove his agreement to participate in the conspiracy” because "[t]wo deliveries of this magnitude suggest a continuity of relationship between [the defendant] and the [drug distribution] organization and support the inference that the defendant knew that the organization to which he was delivering such a sizeable amount of drugs must involve a substantial distribution network”).
      Circumstantial evidence also suggested that Zambrano intended to supply large quantities of drugs to the conspiracy on an ongoing basis. For example, when Zambrano was preparing for delivery of the seven kilogram shipment to Gonzales, he offered to acquire a sample of heroin for Gonzales and stated that the price would be in the range of $120,000 to $150,000 per kilogram.
     
      
      . The statute provides in relevant part that, "[t]he district courts of the United States shall have original jurisdiction, exclusive of the courts of the States, of all offenses against the laws of the United States.” 18 U.S.C. § 3231 (1994).
     
      
      . See also United States v. Miller, 111 F.3d 747, 750 (10th Cir.1997) (court applies "a more relaxed standard for finding waiver of venue rights than for finding waivers of other constitutional rights in criminal trials,” and under this standard “[a] defendant can waive venue rights by his inaction”); United States v. Meade, 110 F.3d 190, 200 (1st Cir.1997) (“We have ... recognized that venue is a waivable personal privilege designed for the benefit of the defendant. As such, the constitutional and statutory venue provisions are not restrictions on the court’s jurisdiction.”) (citation omitted); United States v. Winship, 724 F.2d 1116, 1124 (5th Cir.1984) ("[A] defendant can waive venue rights by his silence — just by his failure to lodge an objection prior to trial.").
     
      
      . Indeed, Gaviria committed numerous overt acts in furtherance of the conspiracy within D.C., "including telephoning Zambrano to discuss potential drug deals and receiving payment for the eight kilograms of cocaine that were delivered in Miami on November 7, 1993.” Brief for Appel-lee, at 75 (citations omitted).
     
      
      . The Guidelines provide that:
      If the defendant willfully obstructed or impeded, or attempted to obstruct or impede, the administration of justice during the investigation, prosecution, or sentencing of the instant offense, increase the offense level by 2 levels.
      U.S.S.G. § 3C1.1 (1995).
     
      
      . As the court very convincingly explained, “[t]he tape recordings of his own discussions with the agents, his calling the people back and talking to them in Washington, his using counter-surveillance moves to shake the tails of people who were following him in his meetings with the undercover officers, his moving the drugs around in the various cars, and his discussions of additional deals, including heroin deals, all would seem to me to belie any suggestion that the sole reason he acted was to help Martha Gaviria because he was coerced or forced into it by the threats or what he had perceived to be dangers from these other individuals, that is, the trader-cover officers.” Hearing Transcript ("Hrg. Tr.”) 44-45 (2/5/96).
     
      
      . Additionally, the scope of his involvement in the conspiracy was crucial to several sentencing issues, as discussed further below.
     
      
      .The Sentencing Guidelines provide:
      Based on the defendant's role in the offense, decrease the offense level as follows:
      (a) If the defendant was a minimal participant in any criminal activity, decrease by 4 levels.
      (b) If the defendant was a minor participant in any criminal activity, decrease by 2 levels. In cases falling between (a) and (b), decrease by 3 levels.
      U.S.S.G. § 3B1.2 (1995). The commentary to the
      Guidelines establishes that a minor participant is “any participant who is less culpable than most other participants, but whose role could not be described as minimal.” U.S.S.G. § 3B1.2(b), cmt. n.3.
     
      
      .For similar reasons we conclude that, even if — despite some circumstantial evidence to the contrary — it were true that Zambrano did not arrange for the "the Panamanian" to supply the 15 kilograms of cocaine to Gaviria, the court was correct to point out that Zambrano did not "ha[ve] to be a supplier of the drugs to not be qualified as a minor or minimal participant.” Hrg. Tr. 19 (2/5/96). Cf. United States v. Pitz, 2 F.3d 723, 733 (7th Cir.1993) (departure denied where defendant picked up and delivered 24 ounces of cocaine, collected payment, and reimbursed the supplier); United States v. Flores-Payon, 942 F.2d 556, 561 (9th Cir.1991) (downward departure denied where defendant “was not merely a courier but was an actual participant in a drug transaction who attended the negotiations and then brought the drugs to the scene" and commented on the quality of the drugs); United States v. Garcia, 920 F.2d 153, 155 (2d Cir.1990) (departure denied where defendant “was personally entrusted with and ultimately delivered” large amount of cocaine to undercover officer).
     
      
      . See, e.g., United States v. Washington, 106 F.3d 983, 1017-18 (D.C.Cir.1997) (holding that two appellants were not entitled to "minor role" adjustment despite the fact that they were not "leaders" of the conspiracy due to their active participation and relatively “ 'equal[] culpability]' ” with other non-leader members of the conspiracy).
     
      
      . The court acknowledged defense counsel’s argument that Zambrano should receive a departure “because he is the least culpable of the defendants, he was just tangentially involved and had a limited role,” Hrg. Tr. 16 (2/5/96), but rejected this argument based on Zambrano’s substantial role in the conspiracy and also noted "that both Gaviria and Naranjo vouched for Mr. Zambrano as a reliable source of drugs and a major player.” Id.
      
     
      
      . The Guidelines provide that:
      (a) If the defendant clearly demonstrates acceptance of responsibility for his offense, decrease the offense level by 2 levels.
      (b) If the defendant qualifies for a decrease under subsection (a), the offense level determined prior to the operation of subsection (a) is level 16 or greater, and the defendant has assisted authorities in the investigation or prosecution of his own misconduct by taking one or more of the following steps:
      (a) timely providing complete information to the government concerning his own involvement in the offense; or
      (b) timely notifying authorities of his intention to enter a plea of guilty, thereby permitting the government to avoid preparing for trial and peraiitting the court to allocate its resources efficiently,
      decrease the offense level by 1 additional level. U.S.S.G. § 3E1.1 (1995).
     
      
      . See also, e.g., United States v. Layeni, 90 F.3d 514, 524 (D.C.Cir.1996) (stating that "[tjhe sentencing court 'normally should deny the two-point reduction to a defendant who does not plead guilty,’ ” and explaining that, if a defendant does go to trial, "[t)he raising of an entrapment defense, in and of itself, does not constitute either an acceptance of responsibility or an expression of remorse for one’s criminal conduct”), cert. denied, - U.S. -, 117 S.Ct. 783, 136 L.Ed.2d 726 (1997).
     
      
      . See also United States v. Fletcher, 74 F.3d 49, 56 (4th Cir.) (safety valve unavailable where defendant “perjured himself at trial”), cert. denied, - U.S.-, 117 S.Ct. 157, 136 L.Ed.2d 101 (1996).
     
      
      . In rejecting Zambrano’s safety valve argument, the district court stated:
      I don’t have any demonstration to me that Mr. Zambrano made any good faith attempt to cooperate or to provide information and evidence that he has concerning this matter beyond his testimony at trial that I’ve already found to be perju-rious in part. I don't think his stipulation of any — that he had, knows nothing else is sufficient to meet the fifth element of the safety valve, where there is contrary evidence in the, produced at trial as to his involvement. In other words, I cannot find that he candidly explained to the Court his role in the offense.
      Hrg. Tr. 38-39 (2/5/96).
     
      
      . It is clear that Zambrano did not meet the requirement of full and candid disclosure at trial, so we need not reach the issue of whether "trial testimony alone may satisfy the fifth requirement of the [safety valve provision]” in cases where that testimony is complete and truthful. Brief for Appellant Zambrano, at 13 (arguing that ”[t]he recent case law clearly indicates that as long as the defendant provides truthful information — be it in the form of a letter, a guilty plea or other testimony — he has met the fifth requirement of the statute”).
     
      
      . As the Government rightly points out in its brief, see Brief for Appellee, at 131-32, we need not reach the issue of whether the November 7 sale was a reasonably foreseeable act in furtherance of the conspiracy because Zambrano’s liability for that sale was based on his personal participation, not on a co-conspirator liability theory.
     
      
      . This subsection of the Guidelines provides that relevant conduct includes "(1)(A) all acts and omissions committed, aided, abetted, counseled, commanded, induced, procured, or willfully caused by the defendant....” U.S.S.G. § lB1.3(a)(l)(A) (1995).
     