BACKGROUND
McLAUGHLIN, Circuit Judge:
Zolton Williams is a Jamaican-born, former law student at Columbia Law School in New York City. In August 1998, he was indicted in the United States District Court for the Eastern District of New York (Dearie, /.), on one count of conspiracy to import cocaine and one count of importation of cocaine. The alleged conspiracy, which lasted from November 1995 to June 1997, involved Williams and his friends, Anthony Fleurancois and Keith Carmichael, all of whom engaged in an ongoing scheme to smuggle cocaine into the United States from Jamaica. The completed importation occurred on June 14, 1997, when Williams and Fleurancois succeeded in smuggling one kilogram of cocaine into this country.
Williams’s first trial took place in October 1998. The government’s case consisted of essentially two witnesses, Fleuran-cois and Carmichael, both of whom had agreed to cooperate. After deliberating for over two days, the jury announced that it could not reach a verdict. Finding the jury deadlocked, the district court declared a mistrial.
Although the government introduced some additional evidence at the second trial, the bedrock evidence against Williams remained the testimony of the government’s cooperating witnesses, Fleu-rancois and Carmichael. The government’s proof at trial revealed the following details of the charged offenses.
Williams had dealt with Fleurancois and Carmichael well before the trio hatched the cocaine importation conspiracy. He had obtained several pounds of marijuana from them in 1994; and in 1995, he had engaged in credit card fraud with Fleuran-cois.
In 1995, Williams, then a law student at Columbia, persuaded Fleurancois and Carmichael to join him in a scheme to import cocaine from Jamaica. According to Williams’s plan, they would hire strippers to act as couriers. The trio would go to Jamaica where Williams would buy cocaine, and have the strippers smuggle the cocaine back into the United States inside their bodies. Williams told his cohorts that he had successfully used this method to import cocaine several times in the past. Carmichael, who knew several strippers, was placed in charge of finding a suitable woman to act as a courier.
Their first two attempts to carry out the conspiracy failed when they had trouble
making arrangements for suitable couriers. Williams scheduled the first trip to Jamaica for December 1995 during a scheduled break at Columbia Law School. The trip had to be postponed, however, when the woman Carmichael had recruited to act as a courier got cold feet. The second target date was in March 1996, when Williams would have another scheduled recess from law school. This attempt also failed, when the woman Carmichael had recruited showed up at the airport without proper travel documents.
Williams and Fleurancois were angry about the aborted plans and blamed Carmichael. A dispute arose among Carmichael and his two co-conspirators, who had by now lost faith in him. On Williams’s initiative, Williams and Fleurancois ultimately filed fraudulent charges of assault and robbery against Carmichael in order to discredit him if he ever talked to the police.
In April 1997, Williams and Fleurancois revised the plan. This time, Williams offered Fleurancois $10,000 to become the courier himself by carrying the cocaine in his stomach. Williams assured Fleuran-cois that he could safely swallow the cocaine encased in several small plastic packages and expel them after he arrived in the United States. Williams told Fleuran-cois that he usually imported cocaine in this manner with a courier named Steve, but that Steve was unavailable. Fleuran-cois, who was then saddled with approximately $45,000 in student loan and credit card debt, agreed to the plan.
In order to learn what law enforcement authorities looked for in identifying drug smugglers, the pair researched drug profiles on Westlaw, a computerized legal database. Notes from the research session, in Williams’s and Fleurancois’s handwriting, were introduced into evidence, as were computer printouts of some of the research materials bearing Williams’s name and student Westlaw password.
The pair set a target date for the Spring of 1997. In May, the conspirators traveled to Jamaica to execute their plans. However, they returned home empty-handed after they began to suspect that their potential suppliers were planning to rob them.
They tried again in early June, traveling on separate flights. Fleurancois arrived in Kingston, Jamaica on June 8, 1997, a few days after Williams. Fleurancois financed the trip with $3700 that Williams had transferred to Fleurancois’s credit card. This transfer was corroborated by documents introduced into evidence. When they found no reasonably priced cocaine in Kingston, they decided to get the drugs in Negril, a town five or six hours away where Williams had located a supplier. They drove to Negril on or about June 11, 1997, and checked into the Negril Beach Club Hotel.
To corroborate Fleurancois’s testimony that Williams was in Negril with Fleuran-cois at the time, and that he had stayed at the Negril Beach Club, the government introduced, over Williams’s objection, a receipt dated June 12 from the Negril branch of the Bank of Nova Scotia. The receipt reflected a cash advance of $900 on Williams’s credit card. It bore Williams’s signature and the handwritten local address of the Negril Beach Club. An official from the Bank of Nova Scotia, Cyril Woung, testified that he was familiar with the bank’s practice for processing a cash advance on a credit card and with the documents generated during such a transaction. He identified the receipt as memorializing a cash advance. Woung also testified that the bank maintained such records as a regular part of its business.
■ On June 13, Williams left the hotel. When he came back he had a kilogram of cocaine. Williams prepared the cocaine in several small plastic packages which Fleu-rancois began swallowing shortly thereafter. Fleurancois continued to swallow these packages throughout the night and into the next day as the pair drove back to the airport to catch a June 14 flight to
New York. Upon arrival at JFK Airport, the conspirators left the airport separately.
Fleurancois went to his apartment. He was nauseated and began hallucinating because the cocaine packages in his stomach had started to dissolve. He managed to expel some of the cocaine packages at his apartment, but his hallucinations became so bad that he asked neighbors to take him to the hospital. Williams’s telephone records show that he- called Fleurancois’s number 18 times between the time when the pair split up in New York and when Williams later learned that Fleurancois was in the hospital. He also called Fleu-rancois’s parents’ house twice and several local hospitals.
Eventually, Fleurancois was visited at the hospital by his sister and Williams. Fleurancois’s sister witnessed the pair whispering between themselves. She testified that she heard Williams tell Fleuran-cois that he should not worry because he had gotten into Fleurancois’s apartment and had flushed the “stuff’ down the toilet. Fleurancois was later arrested when packages of cocaine were found in his hospital bed. Ultimately, 104 packages of cocaine were recovered from Fleurancois’s stomach.
The government also introduced evidence of Williams’s unexplained wealth to support the conspiracy charge. It introduced evidence that, despite Williams’s apparent lack of financial resources, he purchased a $27,000 cooperative apartment for cash in 1996. Williams’s mother, Pauline Bygrave, later testifying in Williams’s defense, asserted that she had provided the money for the apartment from funds she had received as part of an insurance settlement. On cross-examination, the government asked Bygrave if she had any documents proving the source of the funds for the apartment. Bygrave answered that she did not have the documents with her but that she could get them. In summation, the government reminded the jury of Bygrave’s inability to produce these documents, stating that if the documents had indeed existed, she would have produced them at trial.
In his defense, Williams introduced alibi testimony. Williams’s father, a resident of Jamaica, testified that Williams had stayed at the home of a relative in Kingston and that he had seen his son there on June 12, 13, and 14, and thus defendant had never gone to Negril from June 11 to June 14.
A friend of Williams, Michael Cummings, also testified. He stated that he had met Williams on the subway in the Spring of 1997, in the weeks before Williams went to Jamaica. When the pair realized that they would be in Jamaica at the same time, Cummings stated, they agreed to meet after Cummings’s scheduled arrival on June 12. Cummings stated that he traveled to Jamaica on June 12, and that on June 13 and 14, he called Williams at a number Williams had given him. He testified that when he called these two times, he reached Williams directly, rather than through a hotel receptionist, as would have most likely been the case if Williams had been staying at the Negril Beach Club Hotel.
In its rebuttal case, the government recalled Cummings to the stand. Cummings recanted his earlier defense testimony. He admitted that his testimony had been a tissue of lies, that he had
not
met Williams on the subway in the Spring of 1997, that he had
not
called Williams in Jamaica, and that Williams had contacted him before the first trial and told him what to say. He further testified that after he had left the witness stand, for the defense, he was approached by agents of the government, that the agents had discussed his defense testimony and whether that testimony was consistent or inconsistent with certain records, and that they told him if he took the stand and was candid, he would not be charged with perjury.
The jury convicted Williams on both counts of the indictment. After the verdict, Williams’s defense counsel resigned on the ground that Cummings’s recanta
tion testimony “potentially calls into question [counsel’s] conduct and therefore creates a conflict of interest that makes it impossible for [him] to .represent Mr. Williams’ interest effectively.”
Williams’s replacement counsel moved for a new trial and dismissal of the indictment. He argued that the government had violated Williams’s right to present a defense by intimidating the defense witness Cummings. Williams alleged that the government had approached Cummings without notifying defense counsel or advising Cummings of his right against self-incrimination, and intimidated him into recanting by falsely telling him that his testimony was “inconsistent” with (non-existent) airline records. In support of this claim, Williams’s new counsel submitted his own affidavit recounting a conversation that had occurred between himself and Cummings. According to new counsel, Cummings said that the agents had approached him outside the courtroom after he had given his defense testimony and asked if he would accompany them to a room in the courthouse. There, they told him that they did not believe his testimony, that it was inconsistent with certain records, including airline records, and that if he retook the stand and testified truthfully, he would not be prosecuted for perjury. Williams’s counsel accused the agents of lying to Cummings, stating that there were no airline.records that refuted Cummings’s testimony.
Defense counsel also claimed,
inter alia,
that the prosecution had violated due process by falsely arguing that Williams’s apartment had been purchased with drug money. In support, he produced records (not introduced at trial) that corroborated his mother’s assertion that the money for the apartment had indeed come from an insurance settlement.'
At sentencing in May 1999, the district court denied Williams’s motions. The court specifically rejected Williams’s claim that the government had violated Williams’s right to present a defense by inducing Cummings to recant. The court found that the government’s conduct had not deprived Williams of a defense witness because Cummings had in fact taken the stand and testified on Williams’s behalf. That Cummings later recanted after his discussion with government agents did not result in a constitutional violation. The court explained that Cummings was not easily intimidated, that his recantation was credible, and that the government was justified in accusing Cummings of lying. He then sentenced Williams to 84 months in prison.
Williams now appeals.
DISCUSSION
The linchpin of Williams’s appeal is his argument that the government violated his due process right to present a defense by intimidating his defense witness into recanting favorable alibi testimony. Secondarily, Williams maintains that: (1) the proof at trial disclosed multiple conspiracies, creating an improper and prejudicial variance with the single conspiracy alleged in the indictment; (2) the district court committed various evidentiary errors; (3) the prosecutor falsely argued at summation that Williams’s apartment was purchased with drug money; (4) trial counsel rendered ineffective assistance; and (5) his second trial subjected him to double jeopardy.
I.
Right to Present a Defense
Williams alleges that the government improperly intimidated his witness when it approached Cummings and accused him of perjury. He argues that the government violated his due process right to present a defense and his Sixth Amendment right to compulsory process by approaching Cummings without notifying defense counsel or warning Cummings of his self-incrimination rights, and by lying to Cummings about the strength of its evidence of perjury. Although we are profoundly disturbed
by the government’s conduct in this ease, we find no basis for reversal.
It is elementary that criminal defendants have a right to establish a defense by presenting witnesses.
See Webb v. Texas,
409 U.S. 95, 98, 93 S.Ct. 351, 34 L.Ed.2d 330 (1972). The Supreme Court has described this right as follows:
The right to offer the testimony of witnesses, and to compel their attendance, if necessary, is in plain terms the right to present a defense, the right to present the defendant’s version of the facts as well as the prosecution’s to the jury so it may decide where the truth lies.
Taylor v. Illinois,
484 U.S. 400, 409, 108 S.Ct. 646, 98 L.Ed.2d 798 (1988) (quoting
Washington v. Texas,
388 U.S. 14, 19, 87 S.Ct. 1920, 18 L.Ed.2d 1019 (1967)). The right to establish a defense by presenting witnesses serves the truth-seeking function of the trial process by protecting against the dangers of judgments “founded on a partial or speculative presentation of the facts.”
See Taylor,
484 U.S. at 411, 108 S.Ct. 646 (internal quotation marks and citation omitted).
Relying on this principle, courts have held that judicial or prosecutorial intimidation that dissuades a potential defense witness from testifying for the defense can, under certain circumstances, violate the defendant’s right to present a defense.
See, e.g., United States v. Golding,
168 F.3d 700, 705 (4th Cir.1999) (government intimidation dissuaded witness from testifying and prosecutor further abused her power by commenting on witness’s failure to testify);
United States v. Vavages,
151 F.3d 1185, 1190-92 (9th Cir.1998) (prosecutor dissuaded witness from testifying and commented on defendant’s failure to present corroborating witnesses, and trial judge failed to scrutinize basis for witness’s invocation of Fifth Amendment right against self-incrimination);
United States v. Heller,
830 F.2d 150, 153-54 (11th Cir.1987) (government intimidation deprived defendant of an important defense witness and induced witness to provide false testimony against defendant).
Of course, “[t]he right to present a defense, and its concomitant right to compulsory process, are not unqualified; they are subject to ‘countervailing public interests,’”
Buie v. Sullivan,
923 F.2d 10, 11 (2d Cir.1990) (quoting
Taylor,
484 U.S. at 414, 108 S.Ct. 646). Such countervailing interests include preventing perjury and investigating past criminal conduct.
See United States v. Whittington,
783 F.2d 1210, 1218-19 (5th Cir.1986). Accordingly, courts have held that a due process violation does not arise merely because the prosecutor interviews a potential defense witness in hopes of obtaining his testimony,
see United States v. Simmons,
670 F.2d 365, 371 (D.C.Cir.1982), or because the government warns a defense witness of the consequences of committing perjury, see
United States v. Thompson,
130 F.3d 676, 687 (5th Cir.1997). As the Seventh Circuit has stated: “[T]he government told the witnesses that they had to testify truthfully and, if not, they would go to jail. That procedure however, even if carried out in a caustic manner, is no cause to dismiss the indictment against the defendants.”
United States v. Hayward,
6 F.3d 1241, 1257 (7th Cir.1993).
Our own circuit has shaped the contours of the right to present a defense.
See United States v. Pinto,
850 F.2d 927, 933-34 (2d Cir.1988);
Buie,
923 F.2d at 11-12. To establish a violation of the right, a criminal defendant must generally show that he was deprived of material and exculpatory evidence that could not be reasonably obtained by other means.
See id.
at 11. In addition, we have held that a defendant pressing such a claim must show bad faith on the part of the government.
See id.
at 11-12. Finally, in order to elevate this misconduct to a due process violation, the defendant “must demonstrate that the absence of fundamental fairness infected the trial; the acts complained of must be of such quality as necessarily
prevents a fair trial.” See id. (internal quotation marks omitted).
Applying these standards, we find no violation of Williams’s right to present a defense. A number of considerations compel this conclusion. First, the government’s encounter with Cummings did not deprive Williams of any material or exculpatory evidence. The right to present a defense is designed to serve the truth-seeking function of the trial process. It does not grant criminal defendants license to knowingly present perjured testimony. See
United States v. Simmons,
670 F.2d at 371. The district court—which had the opportunity to observe Cummings at both trials—found that Cummings’s recantation testimony was “patently credible.” In other words, the district court found that Cummings was testifying truthfully when he recanted, and by necessary implication, that he was lying when he testified in Williams’s defense. While Williams now claims that the government’s coercive tactics render Cummings’s recantation “inherently untrustworthy,” he does not contend that the recantation was actually false, much less that the district court’s credibility findings were clearly erroneous. We cannot hold that Williams’s right to present a defense required the district court to allow false testimony to go unchallenged.
Additionally, we find no evidence that the agents acted in bad faith when they approached Cummings and told him they thought he was lying. Indeed, the district court—which, we emphasize, had the opportunity to evaluate Cummings’s testimony first-hand—found that the government had good reason to accuse Cummings of perjury:
[I]n light of what the government’s level of knowledge was, and you have to put it in context how, I hate to say silly, but his testimony was for a number of reasons far-fetched to begin with...-. The government ... had very good reason to approach [Cummings] and say we think you lied.
(Sentencing Transcript at 11-12). We cannot conclude that this finding was clearly erroneous.
See Buie,
923 F.2d at 12-13 (holding that the district court’s good faith finding is reviewed for clear error).
The testimony of the government witness, Fleurancois, contradicted Cummings’s alibi testimony and was corroborated by a great deal of other testimonial and documentary evidence in the record. Moreover, Cummings’s testimony was also “far-fetched” in other respects. Cummings initially testified, for example, that he called Williams on June 14 to try to arrange a meeting despite the fact that, according to his own testimony, Williams had told him the day before, that he (Williams) would be leaving Jamaica that very day. Asked about this apparent discrepancy, Cummings stated lamely that he had simply forgotten what Williams had told him the day before. This is not like
Webb v. Texas,
409 U.S. at 95-98, 93 S.Ct. 351, where the trial judge, without any basis in the record to conclude that the witness might lie, delivered a lengthy and unnecessary harangue to the defense witness about the possibility of a perjury prosecution. Here, there was “a particular basis” in the record for believing that Cummings’s testimony was untruthful.
United States v. Smith,
997 F.2d 674, 680 (10th Cir.1993).
Williams asserts that the government acted in bad faith because the agents lied to Cummings about the evidence of perjury, intimidating him into recanting his initial testimony. This argument is based on Cummings’s assertion that the agents told him that his testimony was “inconsistent” with certain records, including airline records. However, given that Fleurancois’s testimony flatly contradicted that of Cummings, and given that overwhelming evidence-including airline records—corroborated Fleurancois’s testimony, we conclude that the agents’ statement that Cummings’s testimony was “inconsistent” with records, was at most ambiguous. Moreover, even if the government overstated
the probative value of the evidence of perjury, there is no indication that the agents affirmatively attempted to deceive Cummings. To the contrary, the record suggests that any overstatement more likely resulted from the government’s confusing the airline records of Fleurancois’s flight with those of Williams’s flight. Absent some evidence that the government affirmatively attempted to mislead Cummings, we are not persuaded that the agents acted in bad faith, or that their tactics were unduly coercive.
Cf. United States v. Mast,
735 F.2d 745, 750 (2d Cir.1984) (holding that government conduct during noncustodial interrogation did not violate defendant’s right against compelled self-incrimination where agents had not affirmatively attempted to mislead the defendant).
Finally, even if we were inclined to disagree with the district court’s good faith finding, we would find no basis for reversal because any error did not so “infect” the proceedings as to “necessarily prevent[ ] a fair trial.”
United States v. Valenzuela-Bernal,
458 U.S. 858, 872, 102 S.Ct. 3440, 73 L.Ed.2d 1193 (1982). The evidence against Williams — the sufficiency of which he does not challenge on appeal — included direct testimony of his two co-conspirators, a plethora of corroborating documentary and testimonial evidence, and the testimony of Fleurancois’s sister concerning incriminating statements made by Williams. Williams has “offered nothing, beyond [his] conclusory assertions ... that evinces a reasonable possibility that the [alleged government intimidation] affected the ... verdict.”
Pinto,
850 F.2d at 933 (internal quotation marks and citation omitted). Cummings’s recantation did nothing more than provide the jury with additional evidence of what was already obvious to the district court: that Cummings’s original exculpatory testimony was “far-fetched” and false.
Nothing impaired the opportunity of the jury to assess the credibility of Cummings’s favorable alibi testimony during its deliberations. The agents’ mid-trial discussion with Cummings led him to give
additional,
albeit unfavorable, testimony in the government’s rebuttal case. But “the Constitution protects a defendant’s right to call witnesses. It does not guarantee favorable testimony.”
Soares v. United States,
66 F.Supp.2d 391, 407 (E.D.N.Y.1999). And the jury — which was fully aware that Cummings’s recantation was delivered under threat of perjury prosecution — was not deprived of any significant evidence bearing on Cummings’s credibility. Under these circumstances, it cannot be said that Williams was deprived of his right “to present [his] version of the facts as well as the prosecution’s to the jury so it may decide where the truth lies.”
Washington,
388 U.S. at 19, 87 S.Ct. 1920. Nor can it be said that the jury verdict was “founded on a partial or speculative presentation of the facts.”
See Taylor,
484 U.S. at 411, 108 S.Ct. 646 (internal quotation marks and citation omitted).
Although we find no basis to reverse Williams’s conviction, we are nonetheless troubled by the conduct of the government in this ease. Here, as in
United States v. Pinto,
the government tactics undoubtedly created “an appearance of impropriety.” 850 F.2d at 934. In
Pinto,
we declined to reverse several convictions despite the defendants’ allegations that prosecutorial intimidation of a counseled defense witness dissuaded him from offering important defense testimony.
See id.
at 932-33. We found that the district court had not clearly erred on the witness intimidation question and that, in any event, any error was harmless.
See id.
At the same time, however, we noted that we were “dismayed by the prosecutorial tactics involved.”
Id.
Specifically, we disapproved of the prosecutor’s failure to notify the witness’s attorney or defense counsel of the intended interview with the witness, the decision to proceed with the interview without warning the witness of his right against self-incrimination, and, most importantly, the
conscious choice to exclude the witness's counsel from the interview.
Some of the same professional lapses we criticized in
Pinto
reared their heads here. For example, the government failed to notify Williams’s defense counsel of its intention to approach Cummings, a defense witness, to interview
him
about the content of his testimony. See
Pinto,
850 F.2d at 933-34. This omission leaves the distinct impression that the government was engaging in ambush tactics. That Williams’s counsel felt compelled to resign (whether or not justifiably) as a result of Cummings’s unexpected recantation, did nothing to improve the appearance of impropriety.
In addition, the agents failed to advise Cummings of the possible need for counsel and of his right against self-incrimination before proceeding with the interview — an omission we described in
Pinto
as “inconsistent with established standards of prosecutorial conduct.”
See id.
at 934 (noting that “before interviewing [a] prospective witness, [a] prosecutor or prosecutor’s agent 'should advise the witness concerning possible self-incrimination and the possible need for counsel’ ”) (quoting STANDARDS RELATING TO THE ADMINISTRATION OF CRIMINAL JUSTICE, Standard 3-3.2(b) (1979)). Such a warning would have dispelled the clouds of suspicion that the government agents intended to intimidate Cummings.
Unlike the witness in
Pinto,
Cummings was not represented by counsel when the agents approached him. Therefore, we obviously cannot fault the government for excluding the witness’s counsel from the meeting, a tactic which gave us “the greatest pause” in
Pinto. Id.
at 934. Nonetheless, the gravity of the professional laxity in this case should not be understated. Here, as in
Pinto,
the Assistant United States Attorney and her ■ agents created “an appearance of impropriety” and “exposed [the prosecutor’s] office to accusations of taking unfair advantage.”
Id.
at 933-34.
The government conduct at this trial left much to be desired. But while “[w]e cannot ‘wholeheartedly accept the government’s assertions of the pristine nature of its motivations,’ ... such misgivings, standing alone, are insufficient to warrant reversal.”
Id.
at 933 (internal quotation marks and citation omitted). The questionable conduct that occurred, while indecorous, did not deprive Williams of due process.
II.
Single/Multiple Conspiracies
Williams contends that the proof at trial created an improper variance from the single conspiracy charged in the indictment. Instead of the single conspiracy charged, he asserts that the proof at trial disclosed multiple conspiracies and resulted in prejudicial spillover evidence. Williams contends that the evidence disclosed three or more conspiracies: á planned but abandoned conspiracy to import cocaine by Williams, Fleurancois, and Carmichael in March 1996; a conspiracy which led to the completed importation of cocaine by Williams and Fleurancois in June 1997; and conspiracies to import cocaine between Williams and people other than Fleurancois and Carmichael. It is not without significance that at trial Williams never asked for a charge on the metaphysics of multiple conspiracies.
Whether the government has proved a single conspiracy or multiple conspiracies is a question of fact for a properly instructed jury.
See United States v. Aracri,
968 F.2d 1512, 1519 (2d Cir.1992). Here, although Williams asserts (without elaboration) that his counsel was ineffective for failing to request an instruction that the jury should acquit if they found multiple conspiracies, he does not allege that the district court committed plain error in charging the jury.
See United States v. Desimone,
119 F.3d 217, 226 (2d Cir.1997). Accordingly, the issue is whether the evidence supported the jury’s finding that a single conspiracy- — rather than
multiple conspiracies—existed, and if not, whether that variance resulted in prejudice to Williams.
See id.
“A single conspiracy may be found where there is mutual dependence among the participants, a common aim or purpose or a permissible inference from the nature and scope of the operation, that each actor was aware of his part in a larger organization where others performed similar roles equally important to the success of the venture.”
United States v. Vanwort,
887 F.2d 375, 383 (2d Cir.1989). “[A] single conspiracy is not transposed into a multiple one simply by lapse of time, change in membership, or a shifting emphasis in its locale of operations.”
United States v. Cambindo Valencia,
609 F.2d 603, 625 (2d Cir.1979).
The jury’s finding of a single conspiracy is supported by the record. Williams told Fleurancois and Carmichael that he had successfully smuggled cocaine into the United States from Jamaica using female couriers. He later told Fleurancois that he had also smuggled cocaine with the assistance of a male courier named Steve. Evidence of Williams’s unexplained wealth tended to corroborate the extent of the conspiracy. In addition, Fleurancois and Carmichael testified extensively about their own efforts in furtherance of the ongoing importation scheme. Although the details of the plan and the members of the conspiracy changed somewhat as time passed, the “common aim or purpose” remained the same. A jury could reasonably conclude that the evidence established a single, ongoing conspiracy, orchestrated by Williams, to use couriers to import cocaine into the United States from Jamaica.
Even if the evidence at trial disclosed multiple conspiracies, rather than the single one alleged in the indictment, Williams has failed to show any prejudice resulting from the variance. Williams’s only attempt to show prejudice is a Delphic reference to certain unspecified “spillover” evidence. However, because Williams was himself involved in all the conspiratorial conduct proved at trial, there was no prejudicial spillover evidence likely to confuse the jury, and Williams is not entitled to reversal.
See United States v. Cunningham,
723 F.2d 217, 229 (2d Cir.1983).
III.
Evidentiary Rulings
Williams also challenges several of the district court’s evidentiary rulings. Specifically, he claims that the district court improperly: (1) admitted evidence of crimes not charged in the indictment; (2) excluded evidence that he had made innocent trips to Jamaica; (3) violated the law of the case by modifying at the second trial certain evidentiary rulings it had made at the first; and (4) admitted a cash advance receipt under the business records exception to the hearsay rule. None of these arguments have merit.
We review the district court’s evidentia-ry rulings for abuse of discretion.
See United States v. Arena,
180 F.3d 380, 400 (2d Cir.1999).
We reject Williams’s contention that the district court abused its discretion when it admitted evidence of Williams’s uncharged criminal conduct. Specifically, Williams objects to evidence that in 1994 Williams participated in a marijuana deal with Fleurancois and Carmichael, that in 1995 Williams and Fleurancois had committed credit card fraud, and that in 1996 Williams and Fleurancois caused Carmichael to be arrested on false charges of assault. “Evidence of prior criminal conduct is admissible under Federal Rules of Evidence 404(b) and 403 if it is relevant to an issue at trial other than the defendant’s character, and if its probative value is not substantially outweighed by the risk of unfair prejudice.”
United States v. Livoti,
196 F.3d 322, 326 (2d Cir.1999). In our view, evidence of Williams’s prior criminal conduct with his co-conspirators was relevant “to inform the jury of the background of the conspiracy charged, to complete the story of the crimes charged, and to help
explain to the jury how the illegal relationship between the participants in the crime developed.”
United States v. Pitre,
960 F.2d 1112, 1119 (2d Cir.1992). Moreover, we find no undue prejudice under Rule 403; the evidence did
not
involve conduct more serious than the charged crime and the district court gave a proper limiting instruction.
See Livoti,
196 F.3d at 326.
We similarly reject Williams’s assertion that the district court improperly excluded, on relevancy grounds, evidence that during two trips to Jamaica in March 1996 and March 1997, Williams had apparently not engaged in drug activity. “A defendant" may not seek to establish his innocence ... through proof of the absence of criminal acts on specific occasions.”
See United States v. Scarpa,
897 F.2d 63, 70 (2d Cir.1990). We reject Williams’s assertion that the evidence of innocent travel was necessary to rebut the government’s allegation that Williams had been involved in other cocaine importations from Jamaica. Although the govern.ment did argue that Williams had been involved in other importations, it did not allege that Williams had engaged in drug activity during these particular trips. Nor did the government even assert that Williams’s other cocaine importations, allegedly achieved using couriers, required him to travel to Jamaica himself. Because the district court’s relevancy determination was not “arbitrary or irrational,” we find no abuse of discretion.
See United States v. Amuso,
21 F.3d 1251, 1263 (2d Cir.1994).
Also unavailing is Williams’s assertion that the district court violated the law of the case by reconsidering, at the second trial several of the evidentiary rulings it had made at the first. Specifically, Williams challenges certain modifications by the district court of its prior rulings on evidence of other crimes and innocent trips to Jamaica. Assuming, without deciding, that the law of the case doctrine even applies to mere evidentiary rulings in a second trial of the same case,
but see United States v. Akers,
702 F.2d 1145, 1147-48 (D.C.Cir.1983) (holding that the doctrine does not apply in such circum-stancesi), we find no abuse of discretion in the district court’s modification of its earlier rulings. The law of the case doctrine is, “at best, a discretionary doctrine which does not constitute a limitation on the court’s power but merely expresses the general practice of refusing to reopen what has been decided.”
United States v. Martinez,
987 F.2d 920, 923 (2d Cir.1993). As discussed above, the district court’s evi-dentiary rulings were sound as modified. Moreover, because Williams does not suggest that he was prejudiced by insufficient notice of the changed rulings, we find no abuse of discretion in the court’s decision to reconsider some of its prior rulings at the first trial.
See United States v. Uccio,
940 F.2d 753, 758 (2d Cir.1991).
Finally, the district court did not abuse its discretion when it admitted the cash advance receipt from a Negril bank as a business record. We have stated that Rule 803(6) “favor[s] the admission of evidence rather than its exclusion if it has any probative value at all.”
In re Ollag Constr. Equip. Corp.,
665 F.2d 43, 46 (2d Cir.1981) (internal quotation marks omitted). The “principal precondition” to admissibility is that the record have “sufficient indicia of trustworthiness to be considered reliable.”
Saks Int’l v. M/V “EXPORT CHAMPION”,
817 F.2d 1011, 1013 (2d Cir.1987). To lay a proper foundation for such a record, a “custodian or other qualified witness” must testify that the document was “kept in the course of a regularly conducted business activity and also that it was the regular practice of that business activity to make the [record].”
United States v. Freidin,
849 F.2d 716, 719-20 (2d Cir.1988) (internal quotation marks and citation omitted). Contrary to Williams’s argument, “[t]he custodian need not have personal knowledge of the actual creation of the document” to lay a proper foundation for the receipt.
Phoenix Assocs. III v. Stone,
60 F.3d 95, 101 (2d Cir.1995). Here, the government
laid a proper foundation for the cash advance receipt because Cyril Woung, the bank official who testified, was sufficiently familiar with the bank’s practice and testified that such receipts were made as part of that practice.
See id.
Williams also challenges the handwritten notation on the receipt giving the address of the Negril Beach Club Hotel. He argues that this information was not admissible as a business record because it was supplied to the bank teller by someone who had no duty to report it accurately. However, because Williams himself supplied the address to the bank teller, the information was admissible as a party admission contained within a business record.
See
Fed.R.Evid. 801(d)(2), 805.
See also United States v.
Basey, 613 F.2d 198, 201 n. 1 (9th Cir.1979).
IV.
Improper Argument
Williams asserts that the government violated due process by falsely arguing that he purchased an apartment in 1996 with drug proceeds. He relies on documents, not introduced at trial, corroborating his mother’s claim that the apartment was purchased with the proceeds of an insurance settlement. According to Williams, the government falsely argued that such documents did not exist when it knew or should have known otherwise. Again, we find no basis for reversal.
“The government has broad latitude in the inferences it may reasonably suggest to the jury during summation.”
United States v. Casamento,
887 F.2d 1141, 1189 (2d Cir.1989). We have stated that “we will not lightly overturn a conviction solely on the basis of a prosecutor’s misstatement in summation.”
United States v. Cruz,
797 F.2d 90, 93 n. 1 (2d Cir.1986).
The prosecutor’s argument in this case does not warrant reversal. Although given the opportunity to do so, Bygrave failed to produce documents supporting her claim that the apartment money came from an insurance settlement. Under these circumstances, it was reasonable for the prosecutor to question the veracity of Bygrave’s account of the source of the funds for the apartment. Williams’s law school financial aid records revealed that in the year prior to the purchase of the coop apartment, Bygrave, like Williams himself, had only a modest income. Although Williams asserts that the government knew or should have known about the records confirming that the apartment was purchased from Bygrave’s insurance settlement, he cites nothing in the record to support this assertion. We cannot find that Williams was deprived of a fair trial based on such speculative allegations of government misconduct.
V.
Ineffective Assistance of Counsel
Williams also argues that his trial counsel rendered ineffective assistance when he failed to: (1) obtain the records supporting his mother’s testimony about the legitimate source of the funds for the apartment; and (2) request a “multiple conspiracy” instruction. We decline to review this claim.
This Court may, in its discretion, entertain an ineffective assistance of trial counsel claim on direct appeal in a “narrow category of cases” where: (1) as here, the defendant has a new counsel on appeal; and (2) argues no ground of ineffectiveness that is not fully developed in the trial record.
See United States v. Salameh,
152 F.3d 88, 160 (2d Cir.1998) (citing
Billy-Eko v. United States,
8 F.3d 111, 115 (2d Cir.1993)). However, “[i]t must be remembered that the
Billy-Eko
doctrine is discretionary, and, given the baseline aversion to resolving ineffectiveness claims on direct review, it should not be invoked lightly.”
Salameh,
152 F.3d at 160-61 (internal citation omitted).
Under
Billy-Eko,
we decline to review Williams’s ineffective assistance claim because he argues grounds that are not fully developed in the record. To cite but one example, there is no statement in
the record from Williams s attorney indicating why documents corroborating Williams’s mother’s testimony were not produced at trial.
Cf. Sparman v. Edwards,
154 F.3d 51, 52 (2d Cir.1998)
(per curiam)
(stating that, “except in highly unusual circumstances,” the assertedly ineffective attorney should be offered an opportunity to be heard and to present evidence).
VI.
Double Jeopardy
Finally, Williams argues that his second trial violated double jeopardy because there was no “manifest necessity” for the termination of his first trial before the verdict. Although the government argues that Williams failed to preserve this claim, we need not reach the preservation issue because the district court did not abuse its discretion when it found that the jury was deadlocked.
When a defendant fails to consent to a trial court’s declaration of a mistrial, double jeopardy will bar a second prosecution unless there was a “manifest necessity” for the mistrial.
Maula v. Freckleton,
972 F.2d 27, 28-29 (2d Cir.1992). However, “[t]he trial judge may discharge a genuinely deadlocked jury and require the defendant to submit to a second trial.”
White v. Keane,
969 F.2d 1381, 1382-83 (2d Cir.1992) (quoting
Arizona v. Washington,
434 U.S. 497, 509-10, 98 S.Ct. 824, 54 L.Ed.2d 717 (1978)). The judge’s determination that the jury is deadlocked should be “accorded great deference by a reviewing court.”
Id.
We decline to disturb Judge Dearie’s determination that the jury was deadlocked. The jurors deliberated for over two days in this relatively simple conspiracy trial and declared on no fewer than four occasions that they could not reach a verdict. Under the circumstances, the district court’s determination was well within its discretion.
See id.; United States v. Beckerman,
516 F.2d 905, 910 (2d Cir.1975).
CONCLUSION
With the exception of Williams’s ineffective assistance claim, which we decline to review on direct appeal, we have considered all of Williams’s contentions and find them to be without merit. Accordingly, his conviction is affirmed.