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JOHN M. WALKER, JR., Chief Judge. TABLE OF CONTENTS THE FIRST TRIAL.81 I. Factual Background.81 A. Pre-trial Proceedings.81 B. Trial Proceedings.84 C. Post-trial Proceedings.88 D. Prior Proceedings on Appeal.89 II. Schwarz’s Challenges to the First Trial. .90 A. The Conflict of Interest Issue.90 1. The Conflict of Interest.90 a. The Actual Conflict.91 b. The Lapse in Representation.92 2. The Waiver.95 B. The Jury Contamination Issue .97 THE SECOND TRIAL .100 I. Factual Background O O T — 1 II. The Challenge to the Sufficiency of the Evidence in the Second Trial O T — ! A. The Agreement. O T — 1 B. Knowledge of the Pending Federal Grand Jury O T — I C. Intent to Obstruct the Federal Grand Jury_ O T — ( REMAINING CLAIMS. o T-ri 1 1 CONCLUSION.110 Defendants-Appellants Charles Schwarz, Thomas Bruder, and Thomas Wiese appeal from their convictions, after two jury trials, on charges brought related to the events surrounding the brutal assault on Abner Louima in the early hours 0f August 9; 1997, while he was in custody at the 70th Police Precinct in Brooklyn, New York, and its aftermath. The three appellants and defendant Justin Volpe were ultimately charged, in a twelve-count superseding indictment handed down on March 3, 1999, with conspiracy to deprive and with depriving Louima of his civil rights, in violation of 18 U.S.C. §§ 241 and 242, by assaulting him in a police ear (“the car assaults”); Schwarz and Volpe were charged with conspiracy to deprive and with depriving Louima of his civil rights by sexually assaulting him in the bathroom of the 70th Precinct; and Schwarz, Bruder, and Wiese were charged with conspiracy to obstruct justice, in violation of 18 U.S.C. §§ 371 and 1503, by lying to state and federal prosecutors in an effort to exculpate Schwarz with respect to the bathroom assault. See United States v. Volpe, 42 F.Supp.2d 204, 208 (E.D.N.Y.1999). In addition, Volpe and defendant Michael Bellomo were charged with various offenses in connection with an arrest unrelated to the assaults on Louima. Id. Neither Volpe nor Bellomo are appellants in this appeal. The district court severed the charge of conspiracy to obstruct justice (Count Twelve) from the remaining counts, which were tried first. Prior to the close of the first trial, before the government rested and out of the jury’s presence, Volpe entered a guilty plea to six of the seven counts with which he was charged, including assaulting Loui-ma in the patrol car and in the bathroom. See United States v. Volpe, 78 F.Supp.2d 76, 81 (E.D.N.Y.1999). At the end of that trial, the jury found Schwarz guilty of both conspiring to violate and violating Loui-ma’s civil rights based on the bathroom assault, but acquitted Schwarz, Wiese, and Bruder of all charges related to the car assaults. At the second trial, the jury found Wiese, Bruder, and Schwarz guilty on the single charge at issue: conspiracy to obstruct a federal grand jury proceeding based on their statements to various investigators to the effect that Schwarz did not participate in the bathroom assault. On June 27, 2000, the United States District Court for the Eastern District of New York (Eugene H. Nickerson, District Judge) sentenced Schwarz to 188 months of imprisonment, five years of supervised release with a special prohibition on possession of a firearm, and a special assessment of $300, and ordered restitution to Louima in the amount of $277,495. See United States v. Bruder, 103 F.Supp.2d 155, 185 (E.D.N.Y.2000). Bruder and Wiese were each sentenced to 60 month prison terms, three years of supervised release with a special prohibition on possession of a firearm, and a $100 special assessment. See id. at 190. Appellants raise a host of challenges to their convictions. We discuss only those claims that are dispositive of this case and intimate no view on other issues on appeal that we have found unnecessary to address. The first part of our discussion will review the facts and proceedings relevant to the first trial, and will then consider Schwarz’s challenges to that trial, specifically addressing: (A) whether Schwarz’s attorney labored under an unwaivable conflict of interest that required his disqualification; and (B) whether the district court erred in denying without a hearing Schwarz’s motion for a new trial based on the jury’s exposure during jury deliberations to extrinsic information that Volpe’s guilty plea referred to another police officer in the bathroom. The second part of our discussion will review the facts and proceedings relevant to the second trial and will consider the challenge made by all three appellants with respect to their convictions at the second trial: that there was insufficient evidence that appellants conspired to obstruct a federal grand jury investigation, as required by 18 U.S.C. § 1503. For the reasons that follow, we hold that Schwarz’s convictions for the civil rights violations must be vacated and remanded for a new trial because his attorney’s un-waivable conflict of interest denied him effective assistance of counsel and because the jury was improperly exposed to prejudicial extrinsic information during jury deliberations. We also hold that all three appellants’ convictions at the second trial for conspiracy to obstruct justice must be reversed for insufficient evidence. THE FIRST TRIAL I. Factual Background. A. Pre-trial Proceedings Shortly after the assault on Louima in August 1997, the law firm that represented the Policeman’s Benevolent Association (“PBA”), the police officers’ union, hired Stephen Worth and Stuart London as trial counsel to represent Schwarz and Bruder respectively. Both attorneys were hired as outside conflict counsel to avoid any conflicts of interest that might arise if the PBA’s regular retained law firm were to represent multiple defendants. Worth’s and London’s fees were to be paid by the PBA. In February 1998, after Schwarz had been indicted by the federal grand jury, Worth, London, and some other attorneys formed a law firm, Worth, Longworth & Bamundo, LLP (the “Worth firm”). In May 1998, the Worth firm entered into a two-year $10 million retainer agreement with the PBA (the “PBA retainer”) to represent all police officers in administrative, disciplinary, and criminal matters as well as to provide them with civil legal representation. After entering into the PBA retainer, Worth and London agreed to continue their representation of Schwarz and Bruder without charging further fees beyond the PBA retainer. Shortly after learning of the formation of the Worth firm and its agreement with the PBA, the government wrote a letter to the district court dated May 28, 1998, to advise it of potential conflicts of interest arising from the joint representation of Schwarz and Bruder by partners in the same law firm and from the Worth firm’s PBA retainer. The government urged the district court to conduct a hearing pursuant to United States v. Curcio, 680 F.2d 881 (2d Cir.1982). Worth, on behalf of himself and London, wrote a letter to the district court dated June 17, 1998, to provide details concerning these issues. The letter asserted that no substitution of counsel was needed, in part because the Worth firm had not represented any PBA officials or delegates that had been called to testify before the grand jury, and in part because “[tjhere is no de facto conflict between the respective defenses of Officer Schwarz and Officer Bruder. In fact, it was and is our intention to move for separate trials ... because Officer Bruder can offer testimony which is exculpatory in nature.” Worth’s letter informed the court that Schwarz and Bruder had been advised about the potential conflicts and were prepared to waive their right to conflict-free counsel, but it made no mention of Wiese or whether Wiese’s defenses might conflict with Schwarz’s. Wiese, like Schwarz and Bru-der, was a member of the PBA; he was also one of its elected delegates. Schwarz and Bruder submitted identical affidavits stating that they understood the potential conflicts raised by being represented by attorneys from the same law firm and that they agreed “that our separate and joint defenses to these charges are such that one defendant’s defense will have no impact on the other defendant’s defense, since there is no inconsistency in our defenses. In fact the defenses dovetail with each other.” Both defendants asserted that they wanted to keep Worth and London as their counsel. The affidavits made no mention of any potential conflicts that might arise in connection with the PBA retainer. The government, Worth, and London filed additional letters with the district court fleshing out the areas of potential conflict. These letters focused primarily on the dangers of two defendants being represented by the same law firm and on potential conflicts that might arise if PBA officials and delegates were called as witnesses at the trial. With respect to the latter, the Government expressed the view that “the Worth firm’s representation of both the instant defendants and the PBA represents an actual conflict [that] cannot be waived.” Worth and London argued that disqualification of the attorneys without a Curdo hearing would violate Schwarz’s and Bruder’s Sixth Amendment right to counsel of their choice. They also urged that there was no unwaivable conflict, stating that “if this Court’s concern focuses on the relationship of the PBA with the various defendants and witnesses, that concern is illusory” because there was no showing that the government would call any PBA witnesses and, in any event, the law firm had not and would not represent any other PBA witnesses or parties. Thus, the only conflict presented, they argued, arose from the joint representation of Schwarz and Bruder by the Worth firm- — a conflict that could be waived by the defendants. On September 11, 1998, with the first trial still several months away, the district judge held a hearing in which he advised Schwarz and Bruder regarding the risks presented by the potential conflicts. The district judge told Schwarz and Bruder that while he could not foresee all of the potential conflicts that might arise, some of the potential conflicts with respect to the joint representation of Schwarz and Bru-der by the same law firm included that (1) defense counsel might not offer independent advice concerning the benefits of taking a plea bargain or testifying in court because it would be detrimental to “the other one of you”; (2) “[t]here may be some defense that could be made or evidence offered that helps one of you but hurts the other one”; (3) the attorney may not be able to independently judge whether to cross-examine or impeach a witness that “helps one of you but hurts the other one” or whether to offer reputation evidence or argue “that one of you is less [culpable] than the other one”; and (4) defense counsel might inadvertently or deliberately reveal confidences covered by the attorney-client privilege to his partner representing the other defendant. Hr’g Tr. dated Sept. 11,1998, at 9-11. In describing conflicts that might arise in connection with the PBA retainer, the district judge noted that the PBA and its president, Lou Matarazzo, who had signed the PBA retainer, were defendants in a civil suit that had been filed by Louima. Id. at 12. Louima’s suit alleged a conspiracy among the PBA (through its agents), Matarazzo, and the criminal defendants to injure Louima and to cover up the conspiracy, and raised claims of negligent supervision and monitoring. The district judge informed Schwarz and Bruder that what occurred in the criminal case could have a significant effect on the civil case and that the testimony in the criminal case would be relevant to the civil ease. Id. at 12-13. The district judge also told the two defendants that the PBA’s and Matarazzo’s interests might differ from those of Schwarz and Bruder in, for example, pleading guilty, testifying, or cross-examining witnesses, and that these different interests might affect counsel’s ability to offer advice that was in the defendants’ best interests. Id. The district judge concluded his advice by observing that “it would be unrealistic to suppose that the beneficiaries of a ten-million-dollar contract, which evidently the firm hopes will be renewed in the year 2000, would be indifferent to the welfare of the PBA.” Id. at 13. Following the hearing, the district court issued an order scheduling a Curdo hearing, appointing independent counsel to advise Schwarz and Bruder, and prohibiting the Worth firm from representing the PBA or any of its members other than Schwarz and Bruder in the Louima civil suit. At the Curdo hearing, the government once again took the position that the conflict resulting from the PBA retainer was so serious that it could not be waived. Hr’g Tr. dated Sept. 16, 1998, at 4. The district court then addressed each defendant individually, including the following colloquy with Schwarz: THE COURT: Mr. Schwarz, tell me what you see here as inconsistencies between your case and Mr. Bruder’s case. DEFENDANT SCHWARZ: I understand that with this case, there may be some potential conflicts of interest, one being that my attorney and Mr. Bruder’s attorney are now with the same firm. This is a conflict in that one defendant may receive a better defense at the expense of the other defendant. I’m also aware of the contract that my attorney has with the PBA. I know that there’s another conflict with that, in that the government may call other police officers who are a member of the PBA or even PBA officials. There’s a concern that possibly my attorney may have another agenda and may not be vigorous in his cross-examination of these witnesses. I’m also aware of in the calling of witnesses with this potential conflict, with the two lawyers in the same firm. If they call a witness who — my lawyer may be reluctant to call a witness who may be able to help me but who in his testimony may be harmful to the other defendant. I understand that there could be a conflict in that. Other conflict issues were if the government were to offer some type of plea to one defendant, that would probably be harmful to the other defendant. Aso, if there were a guilty conviction, another conflict may be that my attorney may be reluctant, if he was trying to plead for some type of leniency, he may be reluctant to try to shift blame on to the other defendant in this case. THE COURT: Do you want to keep your lawyer? DEFENDANT SCHWARZ: Yes, sir. Id. at 12-13. Ater the independent counsel appointed by the district court on behalf of Schwarz told the court that he had advised Schwarz of all of these conflicts and believed Schwarz understood them, the court accepted Schwarz’s waiver of the right to conflict-free counsel and permitted Worth to continue representing Schwarz, while Worth’s partner London was permitted to continue representing Bruder. Id. at 12, 14. B. Trial Proceedings The first trial began on May 4, 1999. See Bruder, 103 F.Supp.2d at 174. It concerned all of the charges against the defendants except for the single charge of conspiracy to obstruct justice, which had been severed by the district court, on consent of the government and without objection by the defendants, and would be the subject of the second trial. See id.; Volpe, 42 F.Supp.2d at 209. The evidence presented to the jury at the first trial can be summarized as follows: In the early morning hours of Saturday, August 9, 1997, several New York City police officers were summoned from the 70th Precinct to the Club Rendez-Vous in Brooklyn, New York to disperse a crowd gathered around a street fight between two of the club’s patrons. See Bruder, 103 F.Supp.2d at 159. Appellants Schwarz, Bruder, and Wiese and defendant Volpe were among the officers who arrived at the scene at approximately 4:00 a.m. See id. The crowd, which had spilled out into the street to watch the fight, was noisy and boisterous. See id. At one point, Louima had a verbal altercation with Volpe and, while this was going on, another individual struck Volpe and knocked him to the ground. See id. Volpe thought — mistakenly, as it turned out — that Louima was the person who struck him. See id. Loui-ma was then arrested and handcuffed by Schwarz and other officers, including Wiese, who was Schwarz’s regular patrol partner, and Officer Eric Turetzky. See id. at 159-60. Schwarz and Wiese put Louima in the back of their patrol car to be transported to the 70th Precinct. See id. at 160. It was undisputed that Schwarz drove the patrol car, Wiese sat in the passenger seat, and Louima sat alone in the back seat. See id. at 159-60, 162. Louima testified that the patrol car made three stops en route to the station-house and that during two of these stops he was assaulted by Volpe, Schwarz, Wiese, and Bruder. See id. at 160. Because Volpe pled guilty and the other defendants were acquitted on these charges, none of these alleged assaults are at issue in this appeal. When the patrol car arrived at the sta-tionhouse, Louima was taken to the front desk. See id. Schwarz searched him and removed his wallet and cash from his pockets. See id. Turetzky testified that when Schwarz searched Louima, Louima’s pants fell down, and that Schwarz “left the pants down by Mr. Louima’s knees.” See id. at 161. Similarly, Louima testified that “the driver” pulled his pants and underwear down to his knees. See id. Schwarz and Sergeant Jeffrey Fallon, the desk officer on duty, counted Louima’s money, and Schwarz filled out a “pedigree card” containing basic information about Louima. See id. at 160-61. Officer Mark Schofield testified that when he returned to the precinct following the events at the Club Rendez Vous, he saw Volpe standing at the rear of the stationhouse holding a stick-like object two to three feet in length. Tr.l at 1575. Volpe later approached Schofield when he was standing near the front desk and borrowed a pair of leather gloves from him. See id. at 1578. The events that followed the processing of Louima at the front desk were central to the government’s case and were hotly contested at both trials; however, evidence and testimony that strongly contradicted the government’s version of events was not introduced until the second trial. At the first trial, two government witnesses, Officers Turetzky and Schofield, testified that they saw Schwarz lead Louima away from the front desk and toward the back area of the stationhouse. See Bruder, 108 F.Supp.2d at 161-62. The back area contained a room of holding cells and, after a right-hand turn, a bathroom. Turetzky stated that he saw Schwarz walk Louima to within a few feet of the bathroom. See id. at 162. Both witnesses stated that Louima’s pants were down around his ankles, although Schofield testified that he did not see Louima’s bare buttocks. See id. at 161-62. Sergeant Fallon testified that Louima was not led away from the front desk until after the pedigree card was filled out and the cash was counted and returned to Louima. See id. at 161. Similarly, Tu-retzky told state investigators that he saw Schwarz “put the [pedigree] card on the top of the [front] desk” before Louima was led away. See id. Fallon testified that, after receiving the completed pedigree card, he ordered that Louima be taken to a cell in the back of the stationhouse and that when he gave that order, Schwarz was “right up next to [Louima]” and “just pretty much [had] control of [him].” See id. Schofield stated that a few minutes after he saw Schwarz leading Louima to the back of the precinct, he, Wiese, and other officers, but not Schwarz, waited together by the front desk to go to the hospital, and that a few minutes later, Volpe “walked out from the back area” and “gave back the gloves that he borrowed” from Scho-field. See id. at 164; Tr.l at 1583-85. Louima consistently testified that two officers led him toward and into the bathroom and that both took part in the assault that took place there. See Bruder, 103 F.Supp.2d at 162-63. However, he could identify only one of them. Louima was able to identify Volpe, both in court and previously from a photo array, as one of the men who led him to the bathroom and attacked him there. See id. at 162, 163; Tr.l at 558-61; 628-29. The most he could offer about the second officer was that he was “the driver.” Bruder, 103 F.Supp.2d at 162-63. However, Louima was unable to identify Charles Schwarz, either from a photo array or in court, as the driver. See id. at 162; Tr.l at 557-60, 661-62. Louima was never shown a photo array containing Wiese’s photo. Tr.l at 557-59. Louima testified that the “face ... and hair style” of the driver and passenger were similar. See Bruder, 103 F.Supp.2d at 162; Tr.1 at 661. The government offered evidence to support a finding that Louima’s testimony about “the driver” referred to Schwarz. See Bruder, 103 F.Supp.2d at 162. In addition to the undisputed fact that Schwarz was the driver of the patrol car and Wiese was the passenger, see id. at 160, Louima’s statement that “the driver” handcuffed him was consistent with Tu-retzky’s testimony that Schwarz was one of the officers that arrested Louima and put handcuffs on him, see id. at 160, 162, although according to Turetzky, he and Wiese also participated in handcuffing Louima. See id. at 160; Tr.l at 1226, 1229-31. Louima also stated that it was “the driver” who searched him at the front desk. See Bruder, 103 F.Supp.2d at 162. Fallon. and Turetzky both testified that Schwarz searched Louima. See id. And, as we have described, Turetzky and Scho-field corroborated Louima’s testimony that it was the driver who led him away from the front desk toward the bathroom. See id. Once in the bathroom, according to Louima, the driver participated in the assault with Volpe by hitting him, putting his foot on Louima’s mouth when he cried out, and pulling him up by the handcuffs while Volpe brutally forced a broken broomstick into Louima’s rectum. See id. at 163. Turetzky testified that sometime after seeing Schwarz lead Louima toward the bathroom, he saw Volpe walking from the bathroom carrying a stick and leading Louima toward the arrest room and holding cells. Tr.l at 1173-75. On cross-examination, Volpe’s defense counsel introduced several portions of an interview of Turetzky that had been conducted and tape-recorded by investigators of the New York Police Department Internal Affairs Bureau (“IAB”) on August 15, 1997 — six days after the assault on Louima — including the following colloquy between IAB Captain Barry Fried (“BF”) and Turetzky (“ET”): BF: Okay. At some point, I believe when we discussed this informally a little bit earlier, you indicated to me that you did see the prisoner being removed? [ET]: Yes. BF: From the bathroom? ET: From the bathroom. BF: Tell us about that. ET: He was rear cuffed still with his pants still below his ankles. When I originally spoke to you I — I didn’t know who was doing it, but if Officer Volpe was standing by the opening, the word openings with the stick, it couldn’t be, it had to be either Officer Schwarz or officer Wiese, but, again, in my mind I’m not clear who was transporting him. [] BF: And that’s fine, and I appreciate your candor. So as you told me earlier you’re reiterating— ET: Right. BF: You don’t know which officer actually walked out of the bathroom? ET: Correct, with— BF: With that individual. [....] [BF:] Officer Schwartz or Schwarz, is that the individual you saw take the defendant into the bathroom? [ET]: Yes. BF: You are positive of that? [ET]: Yes. BF: And you saw no other officer accompany them in? ET: No, cause I was walking up the steps. BF: I understand. You came downstairs; you saw Officer Volpe holding a broken piece of wood. ET: Piece of wood. BF: And then you saw a police officer who you can’t identify. ET: Right. BF: Removing that same defendant from the bathroom? ET: Correct. BF: Was the officer — think now, was he white or black? [] [ET]: White. BF: Big or small, tall or short? ET: Big, big, tall. BF: As tall as you? ET: Broader. Ah, tall, but broader. BF: Right. So big, bigger than you? ET: I’m — I may be confused with, with a, ah, turn off, I don’t know if— what I had told you before was I saw somebody take the prisoner out of the bathroom and bring him to the cell room. BF: Right. ET: Then I saw Officer Volpe standing with a stick. BF: Right. ET: I think I’m getting confused with the times. It’s very — it very well may be Officer Volpe that exited the bathroom and then was standing there with a stick, but it only— BF: Was, was— ET: It only took me a minute to walk down the stairs. BF: I know it’s difficult, Eric. We’ll go slow. ET: Sorry. BF: The scenario that you just presented would have Officer Volpe in the corridor area with a stick in his hand and now you’re suggesting that he may be the one who removed— ET: Like I said before, I wasn’t sure who removed the defendant from the bathroom, but I distinctly remember Officer Volpe standing there with a stick. [....] BF: Why don’t you take a moment and try to fix in your mind — there is no rush, just close your eyes, if you want and get a picture of who is walking this defendant out of the bathroom. Try and fix that in your mind. [] ET: Looking back ... I think — looking ... Back I think it’s Officer Volpe ... Officer Volpe holding the stick in his right hand ... BF: Yes. ET: ... Carrying, not carrying, marching the defendant along with his left hand. Tr.l at 1243-53 (quoting Ex. 3500 ET1) (alterations other than brackets in original). After he was placed in the holding cell, Louima asked for and received assistance from a police officer whom he could not identify. Bruder, 103 F.Supp.2d at 164. Other evidence indicated that it was Bru-der. See id. Later, Louima was taken to Coney Island Hospital, where he was treated for head injuries and underwent surgery for internal injuries to his bladder and rectum. See id. at 165. Meanwhile, several officers involved in the events outside the nightclub, including Volpe, Schwarz, Wiese, and Schofield, drove to New York Community Hospital to be treated for minor injuries. See id. at 164-65. Volpe shared a patrol car with Schofield and Police Officer Christopher Barr. See id. at 165. Wiese and Schwarz were in a separate car. See id. Schofield testified that when he, Barr, and Volpe arrived at the hospital, Volpe remained outside for a few moments, and then came in with Wiese and Schwarz. See id. Schofield testified that as he entered the hospital’s waiting room, he overheard Volpe say, “I broke a man down.” See id.; Tr.l at 1588-89. As Volpe said this, he was sitting across from Wiese and about six feet away from where Schwarz was standing. See Bruder, 103 F.Supp.2d at 165; Tr.1 at 1588-89. On May 25, 1999, shortly before the scheduled close of the government’s casein-chief, the first trial was interrupted so that Volpe could plead guilty, out of the jury’s presence, to six counts of the superseding indictment. See id.; Tr.l at 2645, 2687. During the plea allocution, Volpe stated under oath, While I was in the bathroom, there was another • police officer in the bathroom with me. That police officer saw what was going on, did nothing to stop it. It was understood from the circumstances that that police officer would do nothing to stop me or to report it to anyone. Tr.l at 2659. The jury, which would continue to hear evidence on all assault charges against Schwarz, Bruder, and Wiese, was informed by the district court that Volpe had pleaded guilty. See id. at 2687. The jury was not presented with any of the details of Volpe’s allocution and neither side called Volpe to testify. The district court instructed the jury that “[t]he fact that defendant Volpe has pleaded guilty can’t be used by you as evidence in determining whether the other defendants ... are guilty of any of the offenses with which they are charged.” See id. Schwarz’s principal defense at the first trial was that Volpe acted alone. In opening and closing arguments, Schwarz’s attorney, Stephen Worth, argued that Loui-ma had fabricated the presence of a second officer in the bathroom to support his claim that the bathroom assault was the result of “systemic” police brutality and not the actions of one aberrant cop. See Tr.l at 73-75, 3486-88. During closing arguments, Schwarz’s attorney also suggested that an additional motive for Loui-ma to fabricate the presence of a second officer in the bathroom was to preserve his “manhood” or “dignity.” See id. at 3491-92. On June 2,1999, the jury found Schwarz guilty of participating in and conspiring with Volpe to participate in the sexual assault of Louima in the bathroom, and acquitted Schwarz, Wiese, and Bruder of the patrol car assaults. See Bruder, 103 F.Supp.2d at 174. C. Post-trial Proceedings Following his conviction, Schwarz moved for a new trial on the ground, among others, that the jury’s verdict was tainted because the jury was exposed to facts that were not in evidence. In support of his motion, Schwarz submitted three nearly identical affidavits from members of the anonymous jury that had convicted him. See Volpe, 62 F.Supp.2d at 891. Two of them, executed the same day Schwarz filed his motion, were signed “Juror # 2” and “Juror # 6.” The third affidavit was unsigned, but appeared to have been prepared for “Juror No. 3.” Each affidavit stated that the juror contacted Schwarz’s attorney after the verdict and .“discussed certain aspects of the jury’s deliberations with him.” See id. The jurors asserted that despite their “best efforts to avoid publicity,” they had learned from one juror during jury deliberations that Volpe had pleaded guilty to assaulting Louima in the bathroom and “had indicated that he had done this assault ‘with’ another police officer.” See id. The affidavits also stated that, after the verdict was returned and their service was completed, the jurors learned through press accounts that “Volpe’s attorney had told the prosecutors that a second police officer was in the bathroom, but that the second officer was not Mr. Schwarz.” See id. The jurors asserted that had they known about the attorney’s statements before reaching a verdict, they would have had reasonable doubt as to Schwarz’s guilt. See id. The district judge refused to hold an evidentiary hearing and denied the motion for a new trial. He reasoned that (1) none of the jurors indicated in their affidavits that the first statement — the assertion that Volpe had admitted the presence of another officer — affected their deliberations; (2) there was ample evidence at trial that another officer had been present, thus it “could hardly have been news to the jury” — notwithstanding Schwarz’s “fanciful” assertion that Volpe acted alone; (3) jurors are presumed to follow instructions and the jury had been repeatedly admonished by the district court to ignore extrinsic information and, in particular, had been told that Volpe’s guilty plea had no bearing on the trial; and (4) there are strong policy reasons for not engaging in a post-verdict inquiry of the jury, including the presumption that jury deliberations were proper and the impropriety in defense counsel’s communicating with the jurors without the district court’s permission or supervision. Id. at 891-93. D. Prior Proceedings on Appeal One of appellants’ claims on appeal was that the government had violated its disclosure obligations under Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963), by not disclosing compelled statements taken from appellants’ co-workers and other witnesses by the IAB during the course of their investigation into the Louima assault (the “GO-15 statements”). In order to fully evaluate these claims, we ordered the government to provide to appellants and this court, under seal and pursuant to a protective order, all of the GO-15 statements as well as any summaries of those statements or FBI reports of interviews of the GO-15 witnesses, and invited the parties to submit supplemental briefing. See United States v. Volpe, No. 00-1479 (2d Cir. June 28, 2001) (order requiring filing with the Court); United States v. Volpe, No. 00-1479 (2d Cir. July 6, 2001) (protective order requiring disclosure to defendants). In their supplemental briefing, appellants argued that several of the newly disclosed statements contained exculpatory and impeachment material that was improperly suppressed by the government in violation of Brady. In addition, appellants produced an affidavit that had been obtained by defense counsel and was executed in April 2001 by retired police sergeant and IAB investigator Patrick Walsh stating that he was the first officer to interview Turetzky (before the recorded interview by IAB Captain Barry Fried, described above) and that during that unrecorded interview, [i]n response to my inquiries concerning how Louima came to be in the bathroom, Turetzky said that he saw either ... Wiese or ... Schwarz walking Loui-ma toward the bathroom, but that Tu-retzky could not say which officer it was because he only saw them from the rear and Wiese and Schwarz look alike from that position. I went over Turetzky’s observations with him numerous times, and he repeated each time that he could not tell whether the officer he saw walking Louima toward the bathroom was Wiese or Schwarz. Ex. C ofWhite Aff., ¶ 3 at 2. Because none of the foregoing materials had been reviewed by the district court in deciding various Brady challenges raised there, and because the Walsh affidavit was likely to be the subject of a fresh motion for a new trial based on newly discovered evidence pursuant to Federal Rule of Criminal Procedure 33, we remanded this case to the district court using the procedure we enunciated in United States v. Jacobson, 15 F.3d 19, 21-22 (2d Cir.1994), for the limited purpose of determining whether the Walsh affidavit, either alone or in combination with the other statements identified by the appellants, provided a basis to order a new trial either on the ground that the government failed to comply with Brady and Giglio v. United States, 405 U.S. 150, 154, 92 S.Ct. 763, 31 L.Ed.2d 104 (1972), or on the ground of newly discovered evidence. See United States v. Schwarz, 259 F.3d 59, 65 (2d Cir.2001) (per curiam). On remand, the district court held a hearing at which Turetzky, Walsh, and other investigators involved in the August 15, 1997 interviews of Turetzky testified. See United States v. Bruder, No. 98 CR 196, 2001 WL 1328461, at *1, *3-*10 (E.D.N.Y. Sept.5, 2001). After reviewing all of the evidence, the district court found that Walsh’s affidavit and his testimony at the hearing — to the effect that Turetzky told him that Louima’s escort to the bathroom could have been either Wiese or Schwarz — were not credible. See id. at *3-*7. With respect to the other evidence identified by the appellants from the GO-15 statements and related materials produced pursuant to this court’s order, the district court concluded that they “are not Brady material because they are either inculpatory or immaterial. They would not have undermined any critical element of the prosecution’s case, and were in fact consistent with that case.” Id. at *12. Based on the foregoing factual findings and credibility determinations, the district court held that appellants were not entitled to a new trial based either on the government’s alleged Brady violations or on newly discovered evidence because the evidence produced at the hearing was not “material,” and, therefore, “[t]here is no reasonable probability that [the new evidence] would have put the whole case in such a different light as to undermine confidence in the verdict.” Id. at *12. II. Schwarz’s Challenges to the First Trial A. The Conflict of Interest Issue On appeal, Schwarz, represented by new counsel, argues that the loyalties owed by his trial attorney, Worth, to the PBA and Worth’s pecuniary interest in the PBA retainer created an actual conflict of interest that adversely affected Worth’s representation of him and deprived him of his Sixth Amendment right to effective assistance of counsel. Schwarz further contends (1) that Worth’s conflict was so serious as to be unwaivable and (2) that, in any event, the waiver he made during the district court’s Curdo hearing was ineffective because he was not specifically apprised and had no reason to believe that Worth’s interests in the PBA retainer would conflict with his defenses in the particular way that they did. 1. The Conflict of Interest “A defendant’s Sixth Amendment right to effective assistance of counsel includes the right to representation by conflict-free counsel.” United States v. Blau, 159 F.3d 68, 74 (2d Cir.1998); see also Wood v. Georgia, 450 U.S. 261, 271, 101 S.Ct. 1097, 67 L.Ed.2d 220 (1981) (“Where a constitutional right to counsel exists, our Sixth Amendment cases hold that there is a correlative right to representation that is free from conflicts of interest.”); Armienti v. United States, 234 F.3d 820, 823 (2d Cir.2000); United States v. Rogers, 209 F.3d 139, 143 (2d Cir.2000); United States v. Levy, 25 F.3d 146, 152 (2d Cir.1994). Whether a defendant’s representation violates the Sixth Amendment right to effective assistance of counsel is a mixed question of law and fact that is reviewed de novo. See Blau, 159 F.3d at 74; United States v. Kliti, 156 F.3d 150, 152-53 (2d Cir.1998); United States v. Stantini, 85 F.3d 9, 16 (2d Cir.1996). While a defendant is generally required to demonstrate prejudice to prevail on a claim of ineffective assistance of counsel, see Strickland v. Washington, 466 U.S. 668, 687, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984), this is not so when counsel is burdened by an actual conflict of interest. Id. at 692, 104 S.Ct. 2052. Prejudice is presumed under such circumstances. See id.; United States v. Malpiedi, 62 F.3d 465, 469 (2d Cir.1995); United States v. Iorizzo, 786 F.2d 52, 58 (2d Cir.1986). Thus, a defendant claiming he was denied his right to conflict-free counsel based on an actual conflict need not establish a reasonable probability that, but for the conflict or a deficiency in counsel’s performance caused by the conflict, the outcome of the trial would have been different. Rather, he need only establish (1) an actual conflict of interest that (2) adversely affected his counsel’s performance. See Cuyler v. Sullivan, 446 U.S. 335, 348, 100 S.Ct. 1708, 64 L.Ed.2d 333 (1980); see also Levy, 25 F.3d at 152. a. The Actual Conflict “An attorney has an actual, as opposed to a potential, conflict of interest when, during the course of the representation, the attorney’s and defendant’s interests diverge with respect to a material factual or legal issue or to a course of action.” Winkler v. Keane, 7 F.3d 304, 307 (2d Cir.1993) (internal quotation marks omitted). Schwarz argues that an actual conflict of interest was created when the Worth firm entered into the PBA retainer. We need not decide whether the PBA retainer itself created an actual conflict of interest with respect to Worth’s representation of Schwarz at trial because we find that even if the conflict at the time the PBA retainer was signed could be categorized as only a potential conflict, it became an actual conflict after the Louima civil suit was filed. As we will explain more fully, the PBA’s interests in defending against the civil lawsuit, which alleged that the PBA, through its agents, and the PBA’s president, Matarazzo, participated in a conspiracy to injure Louima and cover it up, diverged from Schwarz’s interests in putting on a defense that would implicate anyone other than Volpe as participating in the assault in the bathroom. While the Worth firm had been barred by the district court from formally representing the PBA or any of its members in the Louima civil suit, Worth nevertheless had an unalloyed duty to the PBA as his client to refrain from any conduct injurious to its interests. Moreover, because the Worth firm’s retainer agreement with the PBA provided that (a) a portion of the $10 million retainer (which was otherwise payable in equal monthly installments) would be held back and paid quarterly to ensure the PBA’s satisfaction with the Worth firm’s performance and (b) the PBA could unilaterally cancel the contract upon thirty days’ notice, and because Worth could expect that satisfaction with the firm’s performance would result in a renewal of the retainer upon its expiration, Worth had -a strong personal interest in refraining from any conduct to which the PBA might object. Because Louima had consistently maintained that he was assaulted in the bathroom by at least two officers, Schwarz had an obvious strategic interest in implicating another officer in the bathroom assault from the moment he was charged with that crime. As further discussed below, that interest became stronger during the course of his trial. Such a defense, however, could have hampered the PBA in its defense of the Louima civil suit. As a result, Worth faced an actual conflict between his representation of Schwarz, on the one hand, and both his professional obligation to the PBA and his self interest, on the other. b. The Lapse in Representation The finding of an actual conflict, however, is only the first step in determining whether Schwarz has established his claim of ineffective assistance of counsel. He must also show that the actual conflict adversely affected Worth’s performance by demonstrating that “a ‘lapse in representation’ resulted from the conflict.” Iorizzo, 786 F.2d at 58 (quoting Cuyler, 446 U.S. at 349, 100 S.Ct. 1708). To prove a lapse in representation, a defendant must “demonstrate that some ‘plausible alternative defense strategy or tactic might have been pursued,’ and that the ‘alternative defense was inherently in conflict with or not undertaken due to the attorney’s other loyalties or interests.’ ” Levy, 25 F.3d at 157 (quoting Winkler, 7 F.3d at 309); see also Triana v. United States, 205 F.3d 36, 41 (2d Cir.), cert. denied, 531 U.S. 956, 121 S.Ct. 378, 148 L.Ed.2d 292 (2000). A defendant is not required to show that the lapse in representation affected the outcome of the trial or that, but for the conflict, counsel’s conduct of the trial would have been different. Malpiedi, 62 F.3d at 469. The forgone strategy or tactic is not even subject to a requirement of reasonableness. Id. As we have previously recognized, [t]he test is a strict one because a defendant has a right to an attorney who can make strategic and tactical choices free from any conflict of interest. An attorney who is prevented from pursuing a strategy or tactic because of the canons of ethics is hardly an objective judge of whether that strategy or tactic is sound trial practice. Id. (i) The “plausible alternative defense strategy” Schwarz argues that Worth’s loyalties to the PBA caused him to forgo the “plausible alternative defense strategy” of implicating Wiese as the police officer who escorted Louima to the bathroom with Volpe. Worth would have known that such a theory was viable in light of proffer statements that Wiese and Bruder had made during the initial investigation into the assault and that were disclosed to the defendants by the government before trial. In these proffer statements, Wiese stated that he had escorted Louima towards the bathroom with Volpe and had later entered the bathroom during Volpe’s assault on Loui-ma, while Bruder stated that he had observed Wiese and Volpe escorting Louima to the bathroom. Rather than pursue this strategy, Schwarz contends, Worth advanced the implausible and factually unsupported theory that Volpe acted alone and that Louima fabricated the presence of a second officer to demonstrate systemic police brutality and to salvage his “manhood,” all in an effort to obtain an acquittal for Schwarz without having to implicate another member of the PBA. We agree that impheating Wiese as the second officer in the bathroom was a plausible alternative strategy that Worth did not pursue. In fact, this strategy became a compelling one after Volpe entered a guilty plea before the defense had begun to put on its case, thereby becoming available to Schwarz as a witness. On May 24, 1999, the day before Volpe’s guilty plea, Volpe’s attorney told Worth that “my guy [Volpe] can take your guy [Schwarz] out of the bathroom.” Thus, by the time Volpe pled guilty and alloeuted to the fact that there was a second officer in the bathroom, Worth had the following information: (1) Volpe, the only witness indisputably in the bathroom with Louima, was willing to testify that Schwarz was not the second officer in the bathroom; (2) Louima had been unable to identify Schwarz and had acknowledged that Schwarz and Wiese look similar; (3) both Wiese and Bruder had indicated in their proffer statements that it was Wiese, not Schwarz, who escorted Louima to the bathroom and that Wiese had actually been in the bathroom with Volpe and Louima; and (4) as had already been introduced by the defense on cross-examination, the interview tape of Turetz-ky indicated some confusion about whether Schwarz or Wiese escorted Louima from the bathroom. With all of this ammunition, Worth was positioned to try to create a reasonable doubt in the jurors’ minds by arguing that Louima and Turetzky had both mistaken Schwarz for Wiese because they look similar, that the second officer in the bathroom was Wiese, and that Schwarz was innocent. Indeed, shortly after the trial and after Volpe’s attorney stated publicly that had Volpe been called to testify, he would have said that Schwarz was not in the bathroom, Worth filed a post-verdict motion for a new trial in which he himself acknowledged the potential importance of Volpe’s testimony. In that motion, which was based on the allegation that the government violated its Brady obligations by failing to disclose Volpe’s exculpatory statements made during plea negotiations conducted during the trial, Worth argued to the district court that “[t]he exculpatory value of the disclosure that Mr. Volpe would state that Mr. Schwarz was not in the bathroom and that the defendant Wiese was the other officer referred to in his plea colloquy is too plain to require extended explication.” Nevertheless, at trial Worth had doggedly pursued the theory that Volpe acted alone, a theory the district court later characterized as “fanciful,” Volpe, 62 F.Supp.2d at 892, despite his knowledge that both Wiese and Bruder had made statements implicating Wiese as the person who escorted Louima. And he continued to pursue this theory, and eschewed the opportunity to call Volpe to the stand, despite being told by Volpe’s attorney that “my guy can take your guy out of the bathroom.” The government argues that Worth’s decision not to implicate Wiese was made for sound tactical reasons and that he did not call Volpe to testify because Volpe was not a credible witness. For the reasons we have stated above, we are unpersuaded. In any event, this argument is beside the point because Schwarz does not need to prove that the forgone strategy was reasonable or that it would have affected the outcome of the trial, only that it was a plausible one and that it was forgone. We also reject the government’s claim that Worth actually took steps to implicate Wiese, but was foreclosed from doing so by evidentiary decisions of the district court. While it is true that Worth sought to sever the trial and to disqualify Wiese’s attorney in order to introduce statements made by Wiese to his attorney, a close examination of those efforts shows that Worth did so in a manner that sought to avoid implicating Wiese, which was consistent with the conflict faced by Worth. See Volpe, 42 F.Supp.2d at 211, 213-16. Worth’s basis for seeking to sever Schwarz’s trial from Wiese and Bruder’s was not that it would allow him to present the defense that Wiese was the second officer in the bathroom or that Schwarz’s defense was otherwise antagonistic to Wiese’s. Rather, he requested a severance to allow Wiese and Bruder to testify only that they did not see Schwarz escort Louima to the bathroom — and only on the condition that Wiese and Bruder be tried first. Compare id. at 210-11 (Volpe’s motion based on antagonistic claims) with id. at 211 (Schwarz’s motion). In addition, Schwarz’s motion to disqualify Wiese’s counsel did not seek to introduce Wiese’s statement, made pursuant to his proffer agreement, that it was Wiese who had escorted Louima to the bathroom. See id. at 213-14. Rather, Schwarz sought to introduce different statements, ones to which Wiese’s attorney stipulated Wiese had told Louima’s attorneys in connection with Louima’s civil action. See id. In an affidavit filed in support of Schwarz’s motion, Worth told the district court that [Wiese’s counsel] agreed that he had told counsel for Abner Louima that Mr. Wiese had told him that “Wiese did not see Schwarz strike Louima,” that “Schwarz did not go with” Volpe and Louima to the men’s room, and that when he looked into the men’s room he saw that only Volpe and Louima were in there. Aff. of Stephen C. Worth in Support of Omnibus Mot. dated Dec. 1998, ¶ 5, at 5. The clear import of the stipulated statements was that Volpe acted alone. Presumably, they were made in response to Louima’s allegations in the civil action that his beatings and sexual victimization were the result of a conspiracy. Significantly, Wiese’s “admission” that he, not Schwarz, escorted Louima to the bathroom was not included among those statements. Volpe, 42 F.Supp.2d at 211, 213-16. In fact, the very reason the district court denied the disqualification motion was because none of the statements sought to be introduced were against Wiese’s interest, and therefore the statements were inadmissible hearsay. Id. at 211, 215-16. Similarly, the district court’s reason for denying the severance motion was that there was no indication that Wiese and Bruder would actually testify for Schwarz and because their good faith in seeking to do so was questionable. Id. at 211. It is unclear, moreover, whether the district court was even made aware of Wiese’s admission either for purposes of the Cur-do hearing or for the severance and disqualification motions. See id.; see also id. at 212 (discussing Wiese’s motion to sever on the ground, inter alia, that Bruder had previously stated that he — Bruder—saw Wiese escorting Louima with Volpe). (ii) Worth’s motivation We also agree that pursuit of this “plausible alternative strategy” implicating Wiese would have been “inherently in conflict” with Worth’s loyalty to the PBA (and, thus, with his self-interest) and that Worth’s failure to pursue this strategy was almost certainly the result of this conflict. See Levy, 25 F.3d at 157. Critically, implicating a second officer in the assault would have supported Louima’s claim in his civil case that he was assaulted both in the car and in the bathroom by multiple officers acting in furtherance of a conspiracy. Casting Volpe as an aberrant officer who acted alone, on the other hand, would likely have been consistent with any defense advanced in the civil case. Thus, the actual conflict created by the Louima civil suit sharply intensified at trial when Volpe— the only person who was indisputably in the bathroom with Louima — pleaded guilty and Volpe’s counsel informed Worth that Volpe could provide testimony from which Worth could argue that Schwarz was not the second officer in the bathroom, a course clearly in Schwarz’s interest. Indeed, to put Volpe on the stand to testify that there was in fact a second officer in the bathroom (who was not Schwarz) would plainly have been “inherently in conflict with ... the attorney’s other loyalties or interests,” Winkler, 7 F.3d at 309 (internal quotation marks omitted), because it would have provided support for Louima’s conspiracy claim in the civil suit against the PBA. This conflict would seem to be the only possible explanation for why Worth did not pursue the strategy of implicating Wiese. No evidence in the record up to then supported the theory that Volpe acted alone, while both Louima’s testimony and Volpe’s potential testimony (following his plea) supported a finding that a second officer participated in- the assault. Worth could have relied on Volpe’s potential testimony, Louima’s inability to identify Schwarz coupled with the fact that Wiese and Schwarz look similar, and Wiese’s own statement that he had been the officer who escorted Louima to the restroom to argue with considerable force that the second officer was Wiese. In contrast, he could rely only upon an attack on Louima’s credibility to support his argument that Volpe acted alone — a theory the district court deemed “fanciful”. Under these circumstances, we are convinced that no effective conflict-free defense attorney would have acted as Worth did, and, thus, only Worth’s conflict could explain his actions. Cf. Ciak v. United States, 59 F.3d 296, 305 (2d Cir.1995) (finding that only an attorney’s “personal interest” could explain a lengthy cross examination on an issue only marginally related to his client’s guilt or innocence). In short, we conclude that Worth’s actual conflict adversely affected his performance in representing Schwarz. See Cuyler, 446 U.S. at 348, 100 S.Ct. 1708. Accordingly, we find that Schwarz has established a violation of his Sixth Amendment right to effective assistance of counsel due to Worth’s conflict unless, as the government maintains, Schwarz effectively waived the conflict at the Curdo hearing. We now turn to that question. 2. The Waiver The waiver given by Schwarz at the Curdo hearing would defeat his claim of ineffective assistance of counsel unless it is determined that (1) the conflict with respect to the PBA retainer was so severe as to be unwaivable, or (2) the Curdo waiver by Schwarz was not knowing and intelligent with respect to the specific conflict that led to the lapse in Worth’s representation. We need not decide whether Schwarz’s waiver was knowing and intelligent because we conclude that the actual conflict that Schwarz’s attorney faced was unwaivable. In most eases when a defendant is faced with a situation in which his attorney has an actual or potential conflict of interest, it is possible for him to waive his right to conflict-free counsel in order to retain the attorney of his choice. See Kliti, 156 F.3d at 153; see also Blau, 159 F.3d at 74. Where an actual or potential conflict has been validly waived, the waiver cannot be defeated simply because the conflict subsequently affects counsel’s performance; such a result would eviscerate the very purpose of obtaining the waiver. Not all conflicts may be waived, however. An actual or potential conflict cannot be waived if, in the circumstances of the case, the conflict is of such a serious nature that no rational defendant would knowingly and intelligently desire that attorney’s representation. See Kliti, 156 F.3d at 153; Levy, 25 F.3d at 153. Under such circumstances, the attorney must be disqualified, regardless of whether the defendant is willing to waive his right to conflict-free counsel. See Levy, 25 F.3d at 153. We enunciated the distinction between waivable and unwaivable conflicts in United States v. Fulton, 5 F.3d 605 (2d Cir.1993). Fulton involved the representation of a defendant by an attorney who had been accused of participating in criminal activity related to the crimes for which the defendant was on trial. See id. at 607-10. The district court had advised the defendant ' of the conflict and had obtained a waiver. See id. at 608. On appeal, the defendant argued that the waiver was ineffective. See id. at 612. We agreed. We began by noting that, “[i]n such cases, we must assume that counsel’s fear of, and desire to avoid, criminal charges, or even the reputational damage from an unfounded but ostensibly plausible accusation, will affect virtually every aspect of his or her representation of the defendant.” M- at 613. We then distinguished between conflicts that implicate the attorney’s self-interest and those that implicate the attorney’s ethical obligation to someone other than the defendant, noting that the former are “of a different character” than the latter. Id. We concluded that because the conflict at issue there resulted in counsel’s “[ajdvice as well as advocacy [being] permeated by counsel’s self interest, and [because] no rational defendant would knowingly and intelligently be represented by a lawyer whose conduct was guided largely by a desire for self-preservation,” the conflict was not waivable. Id. Although the particular conflict at issue in Fulton belonged to that narrow category of conflicts that we have deemed to be per se violations of the Sixth Amendment right to counsel, see id. at 611-12; Solina v. United States, 709 F.2d 160, 168-69 (2d Cir.1983), Fulton’s rationale with respect to when an attorney’s self-interest renders a conflict unwaivable is equally applicable to the unusual facts of this case. As noted above, Worth’s representation of Schwarz was in conflict not only with his ethical obligation to the PBA as his client, but also with his own substantial self-interest in the two-year, $10 million retainer agreement his newly formed firm had entered into with the PBA. Like the conflict in Fulton, Worth’s conflict “so permeate[ed] the defense that no meaningful waiver could be obtained.” Fulton, 5 F.3d at 613. We must assume that, under such circumstances, the distinct possibility existed that, at each point the conflict was felt, Worth would sacrifice Schwarz’s interests for those of the PBA. Indeed, we think it likely that these very concerns motivated the government to argue to the district court at the Curcio hearing that the conflict created by the PBA retainer could not be waived. Thus, we conclude that the conflict between Worth’s representation of Schwarz, on the one hand, and his ethical obligation to the PBA as his client and his self interest in the PBA retainer, on the other, was so severe that no rational defendant in Schwarz’s position would have knowingly and intelligently desired Worth’s representation. Cf. id. (“[N]o rational defendant would knowingly and intelligently be represented by a lawyer whose conduct was guided largely by a desire for self-preservation.”); cf. also United States v. Arrington, 867 F.2d 122, 129 (2d Cir.1989) (upholding district court’s disqualification of attorney “saddled” with serious conflict where allowing waiver would have required defendant to “forego[ ] the presentation of ... evidence that would [have been] of great assistance”). In sum, we hold that Schwarz’s counsel suffered an actual conflict, that the conflict adversely affected his counsel’s representation, and that the conflict was unwaiva-ble. Accordingly, we are required to vacate Schwarz’s conviction in the first trial and remand for a new trial. B. The Jury Contamination Issue On appeal, Schwarz argues that the district court erred in denying him a new trial without holding a hearing on whether the exposure to extrinsic information affected the jury’s deliberations. As the district court observed in denying Schwarz’s post-trial motion on this issue, “[t]he sanctity of jury deliberations is a basic tenet of our system of criminal justice.” Volpe, 62 F.Supp.2d at 893 (internal quotation marks omitted); see also United States v. Thomas, 116 F.3d 606, 618 (2d Cir.1997) (“The secrecy of deliberations is the cornerstone of the modern Anglo-American jury system.”). See generally Thomas, 116 F.3d at 618-20 (discussing importance of maintaining the secrecy of jury deliberations). As a result, “[w]e are always reluctant to ‘haul jurors in after they have reached a verdict in order to probe for potential instances of bias, misconduct or extraneous influences.’