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JOSÉ A. CABRANES, Circuit Judge: This case—the first criminal appeal related to the London Interbank Offered Rate (“LIBOR”) to reach this (or any) Court of Appeals—presents the question, among others, whether testimony given by an individual involuntarily under the legal compulsion of a foreign power may be used against that individual in a criminal case in an American court. As employees in the London office of Coóperatieve Céntrale Raiffeisen-Boerenleenbank B.A. (“Rabo-bank”) in the 2000s, defendants-appellants Anthony Allen and Anthony Conti (“Defendants”) played roles in that bank’s LIBOR submission process during the now-well-documented heyday of the rate’s manipulation. Allen and Conti were, for unrelated reasons, no longer employed at Rabobank by 2008 and 2009, respectively. By 2013, they were among the persons being investigated by enforcement agencies in the United Kingdom (“U.K.”) and the United States for their roles in setting LIBOR. The U.K. enforcement agency, the Financial Conduct Authority (“FCA”), interviewed Allen and Conti (each a U.K. citizen and resident) that year, along with several of their coworkers. At these interviews, Allen and Conti were compelled to testify and given “direct use”—but not “derivative use”—immunity. In accordance with U.K. law, refusal to testify could result in imprisonment. The FCA subsequently decided to initiate an enforcement action against one of Defendants’ coworkers, Paul Robson, and, following its normal procedures, the FCA disclosed to Robson the relevant evidence against him, including the compelled testimony of Allen and Conti. Robson closely reviewed that testimony, annotating it and taking several pages of handwritten notes. For reasons not apparent in the record, the FCA shortly thereafter dropped its case against Robson, and the Fraud Section of the United States Department of Justice (the “DOJ”) promptly took it up. Robson soon pleaded guilty and became an important cooperator, substantially assisting the DOJ with developing its case. Ultimately, Robson was the sole source of certain material information supplied to the grand jury that indicted Allen and Conti and, after being called as a trial witness by the Government, Robson provided significant testimony to the petit jury that convicted Defendants. In October 2014, a grand jury returned an indictment charging Defendants with one count of conspiracy to commit wire fraud and bank fraud, in violation of 18 U.S.C. § 1349, as well as several counts of wire fraud, in violation 18 U.S.C. § 1343. Following a trial held in October 2015 in the United States District Court for the Southern District of New York (Jed S. Rakoff, Judge), a jury convicted on all counts. The District Court sentenced Allen principally to two years’ imprisonment and Conti to a year-and-a-da/s imprisonment. Agreeing that Defendants had raised a “substantial issue” for appeal, the District Court granted bail pending appeal. In their appeal, Allen and Conti challenge their convictions on several grounds. We address only their Fifth Amendment challenge, however, and conclude as follows. First, the Fifth Amendment’s prohibition on the use of compelled testimony in American criminal proceedings applies even when a foreign sovereign has compelled the testimony. Second, when the government makes use of a witness who has had substantial exposure to defendant’s compelled testimony, it is required under Kastigar v. United States, 406 U.S. 441, 92 S.Ct. 1653, 32 L.Ed.2d 212 (1972), to prove, at a minimum, that the witness’s review of the compelled testimony did not shape, alter, or affect the evidence used by the government. Third, a bare, generalized denial of taint from a witness who has materially altered his or her testimony after being substantially exposed to a defendant’s compelled testimony is insufficient as a matter of law to sustain the prosecution’s burden of proof. Fourth, in this prosecution, Defendants’ compelled testimony was “used” against them, and this impermissible use before the petit and grand juries was not harmless beyond a reasonable doubt. Accordingly, We REVERSE: the judgments of conviction and hereby DISMISS the indictment. I. BACKGROUND A. LIBOR Some journalists and bankers have called LIBOR the world’s most important number. It is a “benchmark” and “reference” interest rate meant to reflect the available borrowing rates on any given day in the “interbank market”—-in which banks borrow money from other banks. The so-called LIBOR fixed rates, as published daily, are regularly incorporated into the terms of financial transactions entered into across the globe, and the overall value of these LIBOR-tied transactions reaches (measured in U.S. dollars) into thé hundreds of trillions. Throughout the time period relevant to this case, LIBOR rates were administered by a private trade group, the British Bankers’ Association (“BBA”). As summarized by a New York Federal Reserve staff report: LIBOR’s origination has been credited to a Greek banker by the name of Minos Zombanakis, who in 1969 arranged an $80 million syndicated loan from Manufacturer’s Hanover to the Shah of Iran based on the reported funding costs of a set of reference banks. In addition to providing loans at rates tied to LIBOR, banks whose submissions determined the fixing had also begun to borrow heavily using LIBOR-based contracts by the mid-1980s, creating an incentive to underreport funding costs. As a result, the [BBA] took control of the rate in 1986 to formalize the data collection and governance process. InHhat year, LIBOR fixings were calculated for the U.S. dollar, the British pound, and the Japanese yen. Over time, the inclusion of additional currencies and integration of existing ones into the euro left the BBA with oversight of fixings over ten currencies as of 2012. During that period of time, there was no direct governmental regulation of LIBOR submissions. For each of the world’s major currencies, the BBA assembled a panel of banks—typically established institutions that were active in the interbank market in that currency and had a large presence in London. The LIBOR panels for the U.S. Dollar (“USD”) and Japanese Yen (“JPY”) consisted of 16 banks, including Rabobank, a Dutch bank. As explained below, these panel banks submitted the figures that the BBA used to calculate a currency’s official LIBOR rates. According to the LIBOR “definition” on the BBA’s website during the relevant time period, each panel bank, every day at around 11 a.m. London time, was to “contribute the rate at which it could borrow funds, were it to do so by asking for and then accepting inter-bank offers in reasonable market size just prior to 1100.” Each panel bank typically designated a particular employee to be principally responsible for submitting that bank’s LIBOR contributions generally or for a particular currency or set of currencies. That employee, a so-called LIBOR submitter, would submit multiple rates within each currency that varied based on the hypothetical loan’s “tenor,” or duration (pursuant to the basic proposition that the interest rate of a loan will vary based, among other things, on the loan’s duration). There were fifteen tenors ranging from overnight to one year—e.g., one month (or “1M”), three months (or “3M”), and so forth. After receiving submissions from each panel bank, the BBA would, within each tenor of each currency, sort the submissions from lowest to highest, disregard the lower and upper quartiles, and average the remaining submissions. The resulting number became the LIBOR fixed rate and was released to the public daily (through Thomson Reuters, acting as the BBA’s agent). Accordingly, for sixteen-bank panels like the USD and the JPY panels, each day, and with respect to each tenor, the BBA would disregard the highest four and lowest four submissions from the panel, and then average the remaining eight submissions to produce that day’s LIBOR fixed rate in each tenor of USD and JPY— e.g., the 1M USD LIBOR rate. As noted, LIBOR fixed rates, as published every day shortly after 11 a.m. London time, are incorporated into the terms of financial transactions—such as so-called “interest rate swaps”—throughout the world. An interest rate swap, to take one example of a LIBOR-based financial instrument, is an agreement between two parties in which one agrees to pay a fixed interest rate on some agreed-upon notional amount, while the other party agrees to pay a floating rate (usually tied to the LIBOR) on that same amount. The two sides agree to exchange payments on agreed-upon dates over the course of an agreed-upon time period. The date on which the floating rate is set (or reset) is often called the “fixing” or “fixing date.” If the floating rate references LIBOR, the relevant LIBOR rate on a fixing date determines how much or how little that party pays. Put simply, one party bets that interest rates (using LIBOR as the reference) will increase, and the other bets that interests rates (again, based on LIBOR) will decrease. In effect, and in short, money changes hands as LIBOR rates change. And the panel banks, the joint controllers of LI-BOR rates, themselves entered and were parties to large-volume LIBOR-tied transactions as a matter of course. B. LIBOR Submissions, and Their Manipulation, at Rabobank As relevant here, Rabobank was a contributor panel bank for USD LIBOR and JPY LIBOR. Allen joined Rabobank in 1998 as a cash trader and was the bank’s USD LIBOR submitter until 2005, when he became Rabobank’s Global Head of Liquidity and Finance. In that new role, which he held until being laid off when Rabobank closed its London branch in late 2008, he was responsible for supervising other cash traders. One of those cash traders was Conti, who assumed primary responsibility for USD LIBOR submissions starting in 2005 and continuing through 2009, when he quit shortly after his job was moved to Utrecht. Another cash trader, Paul Robson (whose testimony is central to the issue before us), was primarily responsible for Rabobank’s JPY LI-BOR submissions during the relevant time period. Others, including Allen himself, would sometimes submit USD LIBOR rates or JPY LIBOR rates when Conti or Robson were unavailable. According to the “Final Notice” issued to Rabobank by the FCA. for its LIBOR-related misconduct, “Rabobank did not explicitly have a policy in place to. address LIBOR submissions procedures until 30 March 2011, and certain LIBOR-related compliance risks were not addressed until August 2012.” In addition to LIBOR submitters, Rabo-bank also, employed derivatives traders who would regularly enter into interest rate swap. agreements. It was a routine practice of these derivatives traders to submit requests to Conti and Robson (or, at times, their stand-ins) for higher or lower LIBOR submissions. The Govemment’s theory of the case was that these trader requests were dictated by the traders’ (and thus Rabobank’s) interest in having LIBOR be higher or lower on particular dates based on the transactions that the trader had entered or positions they held. Allen and Conti, the Government alleged, honored those requests in lieu of making good-faith estimates of Rabo-bank’s projected borrowing rates. One USD derivatives trader, Lee Stewart (nicknamed the “Ambassador”), sat in the same line of desks at Rabobank’s London office as did Allen and the cash traders—including Conti, the principal USD LIBOR submitter. Stewart testified at trial that he offered LIBOR requests, “out loud,” “in front of everyone,” and never used “code” or “tr[ied] to hide what [he] was talking about.” Robson testified that every morning before 11 a.m,, Conti led, and Allen participated in, a “gather[ing]” and “discussion]” of the best way to influence LIBOR, prefaced by the shout, “right, LIBOR times[!]” By contrast, those derivatives traders located in other offices, like USD derivatives trader Christian Schluep (located in New York) or JPY derivatives trader Ta-kayuki Yagami (located in Tokyo), would more often submit their LIBOR requests in writing. Thus there are numerous arguably incriminating written exchanges between the latter traders and the LIBOR submitters. Schluep and Conti had several exchanges regarding the setting of USD LIBOR—for example: • On July 17, 2006, Schluep asked Conti, “IF ANY CHANCE, A HIGH 3MTH TODAY PL!” Conti replied, “[o]k matey ... high one today.” • On October 31, 2006, Schluep sent Conti a message discussing market activity and then stated, “SMALL FAVOUR AS USUAL, LOW 2S HIGH 3S IF POSSIBLE MATEY,” meaning he wanted a low two-month LIBOR and a high three-month LI-BOR. Conti responded to the earlier parts of Schluep’s message and added, “[w]ill do matey on the libors.” • On August 13, 2007, Schluep sent a message to Conti, requesting “HIGH 3S AND 6S PLS TODAY MATE (ESP 6MNTHSÜ) IF U WOULD BE .SO KIND .. [sic] GOTTA MAKE '.MONEY SOMEHOW!” Conti responded simply, “cool,” to which Schluep replied, “CHEERS TC.. [sic] EVERY LITTLE HELPS!” Schluep also had exchanges with Allen— for example: • Op October 6, 2006, Schluep sent a message to Allen .stating, “HELLO SKIPPER, CAN U PUT 3S AT 37 FOR ME TOMORROW PLS... MANY THANKS.” Allen replied, “NEVER IN DOUBT!” • On November 29, 20Ó6, Schluep sent a message to Allen asking for a “LOW IS HIGH 3S tlBOR PLS!!!” Allen replied “OK MATE, WILL DO MY BEST ... SPEAK LATER.” Schluep later thanked Allen, because the submissions were “BANG ON THE MONEY!” Allen replied, “NO WORRIES” and joked that he “HAD TO WORK MY WAY OUT OF AN AM-BASS HEADLOCK TO GET THOSE IN!” • On December 1, 2006, Schluep sent a message to Allen stating, “APPRECIATE 3S GO DOWN, BUT A HIGH 3S TODAY WOULD BE NICE.” Allen responded, “I AM FAST TURNING INTO YOUR LIBOR BITCH!!!!” Schluep replied, “JUST FRIENDLY ENCOURAGEMENT THAT’S ALL, APPRECIATE THE HELP” Allen replied, “NO WORRIES MATE, GLAD TO HELP[.]” There were similar, if perhaps more explicit and thus arguably more incriminating, exchanges between Yagami and Robson regarding the setting of JPY LIBOR—for example: • On September 21, 2007, Robson told Yagami that market information supported a submission of 0.85 for the one-month JPY LIBOR. Yagami asked for a higher rate, specifically 0.90. Robson agreed, even though he would “probably get a few phone calls,” telling Yagami that there were “bigger crooks in the market than us guys!” • On March 19, 2008, Yagami told Robson “[w]e have loads of 6mth fixings today” and—conveying a request from another trader—asked Robson to submit 1.10 for the six-month yen LI-BOR. Robson responded that market information supported a 1.03 submission for the six-month LIBOR but that he would submit 1.10 as asked, even though it would likely prompt “a phone call.” Robson added that it “will be quite funny to see the reaction” to his submission at Yagami’s requested rate. Whether Allen and Conti did, in fact, accommodate trader requests by adjusting their LIBOR submissions was an issue that Defendants contested at trial. Although Allen and Conti claim they ignored the trader requests, the Government presented evidence at trial purporting to show that these trader requests were accommodated. For instance, on August 13, 2007, Schleup e-mailed Conti and said: GONNA NEED A FRICKIN HIGH 6 MTH FIX TOMORROW IF OK WITH U ... 5.42?” The next day, Schluep sent a reminder and Allen informed another trader that the six-month LIBOR submission would be 5.42 because “i think thats [sic] what [C]hristian [Schluep] needs.” The Rabobank submission for six-month USD LIBOR that day was 5.42. To be clear, Defendants did not argue at trial that it was permissible to accommodate such requests. Allen and Conti agreed with the Government that making submissions based on the interests of Rabobank’s traders was not permitted. And Defendants and the Government further agreed—putting aside whether, in the end, Allen and Conti honored or ignored trader requests—that the process for submitting LIBOR involved collecting “market information” in the morning, typically from brokers who would canvass the rates that might be on offer in the market. There was further agreement that, as “estimates,” LIBOR submissions were necessarily imprecise even when there was decent market information, such that, at any given time, there existed a “range” of reasonable LIBOR submissions. This imprecision was exacerbated during periods of illiquidity in the interbank market, such as the financial crisis in 2007-2008. In a September 26, 2008 phone call, for example, the BBA’s LIBOR Manager, John Ewan, told Allen that LIBOR is “just a line in the sand. What’s it based on? Nothing.” At the same time, however, the Government presented evidence that Defendants understood that it was improper to take Rabo-bank’s traders’ interests into account in determining their submissions, and that their proper role was to give an honest estimate of Rabobank’s borrowing costs. Where Defendants and the Government parted ways on the facts was whether the traders’ requests were honored. While Conti did not take the stand at trial, Allen testified that he never actually accommodated such requests. On direct examination by the Government, by contrast, Robson—Rabobank’s JPY LIBOR submitter— explained that LIBOR’s lack of precision allowed him to accommodate trader requests without raising eyebrows: [Robson]. I would ask the broker where he felt the LIBORs would be. They would then give us—for example, three months they would give us a number of submissions or possible rates where the three months could be depending on credit rates and stuff like that. So there would be kind of a range of two or three numbers where LIBOR could possibly be. Q. Before I ask about trader positions, let’s say no trader request was made. What would you do with that information? [Robson]. I would go straight down the middle as much as I could. So, for example, if the broker came on and said, three months I think I’m hearing might be 80, might be 85, might be 90, but probably 75, I would go down the middle. Q. Now, let’s say you, in fact, had a trader request where a trader wanted you to submit a LIBOR to favor their position. What would you do? [Robson]. So given those circumstances, if one of the traders had contacted and said three months, if I needed a higher three months, I would have moved it higher at his request. I would have moved it towards the 90 level or set 90. Q. Was that permissible? [Robson]. No, it wasn’t. Moreover, Robson proffered to the Government that Conti likewise accommodated trading positions when making LIBOR submissions. And Robson was the sole source of trial and grand jury testimony that Allen specifically directed and instructed others in this scheme. The scheme was established by May 2006 and continued through early 2011; as noted previously, however, Allen and Conti left Rabobank in 2008 and 2009, respectively. C. Investigation and Indictment By 2013, the British and American authorities had commenced LIBOR-related investigations into Rabobank and other institutions. As part of their investigations, the U.K FCA and the U.S. DOJ began conducting interviews. The FCA’s interviews were compulsory; they were conducted under a grant of direct (but not derivative) use immunity, and a witness’s failure to testify under such terms could result in imprisonment. In order to avoid potential problems under Kastigar, the DOJ took care to conduct their interviews wholly independently of the FCA’s interviews and their fruits. Specifically, the FCA agreed to procedures to maintain a “wall” between its investigation and the DOJ’s investigation, including a “day one/day two” interview procedure in which the DOJ interviewed witnesses prior to the FCA. In accordance with that protocol, the FCA interviewed Robson (on January 17, 2013), Conti (on January 25, 2013), and Allen (on June 20 and 21, 2013), among others. Robson, in his compelled testimony to the FCA, denied any improper conduct at Rabobank. In November 2013, the FCA initiated an enforcement action against Robson and, following its normal procedure, disclosed to Robson the relevant evidence against him, including the compelled testimony of Allen and Conti. Robson’s attorney instructed him to review the materials sent by the FCA in preparation for a meeting between Robson and his attorney. Robson “reviewed the materials over the course' of two to three successive or nearly successive days sometime in or about November and/or December of 2013.” During this review, Robson underlined, annotated, and circled certain passages of both Allen’s and Conti’s compelled testimony. Robson also took roughly five pages of handwritten notes. Before Robson had the chance to discuss this material with his attorney, however, the FCA stayed its regulatory proceeding in favor of a criminal prosecution of Robson by the DOJ. On instruction from his lawyer, Robson placed the FCA materials in a box, put them in his attic, and did not review them further. On April 28, 2014, a grand jury in the United States District Court for the Southern District of New York returned an indictment charging Robson (Rabobank’s JPY submitter)' and two JPY derivatives traders, Paul Thompson and Tetsuya Mo-tomura, -with, inter alia, wire fraud. The Government had not requested that the grand .jury indict Conti or Allen. In mid-July 2014, the DOJ first interviewed Robson at a so-called proffer session. On August 5, 2014, Robson signed a cooperation agreement and shortly thereafter pleaded guilty. At Robson’s plea hearing, the prosecutor informed the District Court that “there is ... a chance that we would seek a superseding indictment in light of information that has come to light from our two cooperators” and that there was “a distinct possibility” the new indictment would “involve[ ] other individuals.” So it did. On October 16,2014, the grand jury returned a superseding indictment charging two new individuals—Allen and Conti—with one count of conspiracy to commit wire fraud and bank fraud as well as several counts of wire fraud. It is not disputed that the Government’s presentation of evidence to the grand jury that indicted Defendants relied on evidence that Robson had provided. While Robson did not himself testify, the new information he gave was relayed to the grand jury through FBI Special Agent Jeffrey Weeks, who did testify. And Weeks’s testimony to the grand jury on certain matters derived exclusively from Robson. In particular, Robson was the only source for Weeks’s testimony that Allen “instructed, specifically instructed, LIBOR submitters in London to consider the positions and the requests of Rabobank traders and adjust their submissions for LIBOR and various currencies based on the means of those traders,” and that “Mr. Robson said that sitting near Mr. Conti he was aware that Mr. Conti set U.S. dollar LI-BOR rates in which he considered his own positions as appropriate reason or justification for setting the rates.” D. Trial and Post-Trial Kastigar Hearing Allen and Conti each waived his right to contest extradition from the U.K. and appeared voluntarily. Prior to trial, they moved under Kastigar to dismiss the indictment or suppress Robson’s testimony, but the District Court opted to address any Kastigar issues after trial “in accordance with prevailing practice in the Second Circuit.” Trial thus commenced on October 14,2015, and lasted approximately three weeks. At trial, the Government’s case-in-chief consisted of documentary evidence (e.g., emails, “instant chats,” and phone calls involving Allen, Conti, or their alleged co-conspirators) and testimony from eight witnesses, including three eooperators: Stewart, Yagami, and Robson. In addition to cross-examination of the Government’s witnesses, Allen and Conti each offered an expert witness, and Allen testified in his own defense. On November 5, 2015, the jury returned a verdict of guilty on all counts (nineteen counts, in total, for Allen and nine for Conti). Defendants’ Kastigar challenge remained pending, however. Beginning on December 16, 2015, the District Court held a two-day hearing on Kastigar issues at which Robson and Agent Weeks testified. During this hearing it came to light that Robson had not only read but also marked up, and drafted notes regarding, Defendants’ compelled testimony, and that material parts of Agent Weeks’s testimony to the grand jury derived solely from Robson. Following subsequent Kastigar briefing from the parties, the District Court denied Defendants’ motion by written opinion. The District Court held that, assuming Kastigar applies to testimony compelled by a .foreign power, there had been no Kastigar violation. In its ruling, the District Court explicitly declined to apply case law of the United States Court of Appeals for the District of Columbia Circuit (“D.C. Circuit”) on the legal standards applicable when a government witness has previously reviewed a defendant’s compelled testimony. Looking to Second Circuit precedent, the District Court concluded that Robson’s review of Defendants’ compelled testimony did not taint the evidence he later provided, because the Government had shown an independent source for such evidence, “to wit, [Robson’s] personal experience and observations.” II. DISCUSSION Although Defendants raise a number of substantial issues on appeal, we reach only their Kastigar challenge. Defendants contend that the Government violated their Fifth Amendment rights when it used—in the form of tainted evidence from Robson—their own compelled testimony against them. Specifically, they argue that the District Court applied the wrong legal standard in assessing whether the evidence provided by Robson was tainted by his review of their compelled testimony. They also assert that, properly assessed, the Government cannot meet its burden of showing that' Robson’s evidence was not tainted, and that the prosecution’s use of tainted evidence from Robson was not harmless beyond a reasonable doubt. The Government takes a different view. It submits, as a threshold argument, that testimony compelled by a foreign sovereign and used in a U.S. criminal prosecution “do[es] not implicate the Fifth Amendment.” In -the - event that the Fifth Amendment does apply, the Government argues that the District Court employed the correct legal standard to determine, properly, that evidence provided by Robson was untainted. In the alternative; the Government argues that any use of tainted evidence was harmless. For the reasons that follow, we conclude that Defendants prevail on each point., A. Applicability of the Fifth Amendment In arguing that Fifth Amendment protections apply in this case, Defendants rely on our cases pertaining to foreign and cross-border law enforcement, which have consistently held that “in order to be admitted in our courts, inculpatory statements obtained overseas by foreign officials must have been made voluntarily.” In so holding, we joined our sister circuits that have considered the issue. Defendants contend that these cases are sufficient to resolve the present dispute regarding whether compulsion by a foreign power implicates the Fifth Amendment. We agree. 1. The Requirement of Voluntariness The Supreme Court has “recognized two constitutional bases for the requirement that a confession be voluntary to be admitted into evidence: the Fifth Amendment right ‘ against self-incrimination and the Dúe Process Clause of the Fourteenth Amendment.” Of these two potential “constitutional bases,” our precedents applying such a requirement to confessions procured by foreign law enforcement have been grounded in the Self-Incrimination Clause and Bram v. United States, 168 U.S. 532, 18 S.Ct. 183, 42 L.Ed. 568 (1897). This constitutional footing is significant. The freedom from self-incrimination guaranteed by ,the Fifth Amendment is a personal trial right of the accused in any American “criminal case.” To that end, “a violation of the Fifth Amendment’s right against self-incrimination occurs only when a compelled statement is offered at trial against the defendant.” Whatever may occur prior to trial, the right not to testify against oneself at trial is “absolute.” Even a negative comment by a judge or prosecutor on a defendant’s silence violates that defendant’s constitutional right. These features of the Self-Incrimination Clause distinguish it from the exclusionary rules attached to unreasonable searches and seizures and to otherwise-valid confessions given without Miranda warnings. As the Supreme Court has explained, the Fourth Amendment’s exclusionary rule “is a judicially created remedy designed to safeguard Fourth Amendment rights generally through its deterrent effect, rather than a personal constitutional right of the party aggrieved.” So too with the exclusionary rule buttressing Miranda warnings, which “were primarily designed to prevent United States police officers from relying upon improper interrogation techniques.” Such exclusionary rules “have little, if any, deterrent effect upon foreign police officers.” Accordingly, we do not apply the strictures of our Fourth Amendment and Miranda jurisprudence to foreign authorities. The Supreme Court has taken care, however, to.distinguish extraterritorial applications of the Fourth Amendment from those of the Self-Incrimination Clause of the Fifth Amendment. The Fourth Amendment “prohibits unreasonable searches and seizures whether or not the evidence is sought to be used in a criminal trial,” such that “a violation of the Amendment is fully accomplished at the time of an unreasonable governmental intrusion.” By contrast, in the case of the Fifth Amendment’s Self-Incrimination Clause, “a constitutional violation occurs only at trial,” even if “conduct by law enforcement officials prior to trial may ultimately impair that right.” In light of that distinction, “it naturally follows that, regardless of the origin—ie., domestic or foreign—of a statement, it cannot be admitted at trial in the United States if the statement was ‘compelled.’ ” Thus, the Self-Incrimination Clause’s prohibition of the use of compelled testimony arises from the text of the Constitution itself, and directly addresses what happens in American courtrooms, in contrast to the exclusionary rules that are crafted as remedies to deter unconstitutional actions by officers in the field. Its protections therefore apply in American courtrooms even when the defendant’s testimony was compelled by foreign officials. Moreover, for much the same reasons, the Clause applies in American courtrooms even where, as here, the defendant’s testimony was compelled by foreign officials lawfully—that is, pursuant to foreign legal process—in a manner that does not shock the conscience or violate fundamental fairness. The Clause flatly prohibits the use of compelled testimony and is not based on any matter of misconduct or illegality on the part of the agency applying the compulsion.. In short, compelled testimony cannot be used to secure a conviction in an American court. This is so even when the testimony was compelled by a foreign government in full accordance with its own law. It is true that, with respect to statements taken abroad by foreign agents, we have often referred to the Fifth Amendment’s prohibition against illicit use as encompassing “involuntary,” rather than “compelled,” statements. But this semantic distinction does not bear significant, much less dispositive, weight. Accordingly,'we agree with Defendants that our cases applying a voluntariness test in the context of physical coercion extend to the present context of lawful compulsion. 2. The Government’s Counterarguments The Government’s three principal counterarguments are unpersuasive. The Government first questions the validity of our precedents on the basis of Colorado v. Connelly and subsequent cases involving foreign and cross-border law enforcement that have relied on Connelly, That case concerned a mentally ill defendant who sought out police and confessed to a murder. Despite the absence of any law enforcement misconduct, the Colorado Supreme Court affirmed the suppression from evidence of Connelly’s statements because they were “ ‘involuntary’ ”—that is, not “ ‘the product of a rational intellect and a free will.’ ” In reversing, the Supreme Court held “that coercive police activity is a necessary predicate to the finding that a confession is not ‘voluntary1 within the meaning of the Due Process Clause of the Fourteenth Amendment.” We are not persuaded that Connelly requires reconsideration of our precedents. For one thing, Connelly is explicitly a Due Process Clause case, whereas the precedents we rely on today were grounded in the Self-Incrimination Clause—which, by its terms, is an exclusionary rule grounded in the very text of the Constitution and designed to protect a defendant at trial. For another, Connelly did not concern cross-border investigations or foreign government conduct (and accordingly, the majority did not even mention Bram). And the final reason we do not believe Connelly renders our precedents invalid stems from an important acknowledgment the Government makes on appeal. ■ . Specifically, the' Government submits— in a footnote pregnant with meaning—that “there may be some other constitutional doctrine apart from the Fifth Amendment right against self-incrimination that would require exclusion of a confession coerced by foreign officials, such as a due process violation based on conduct that ‘shocks the judicial conscience,’ ” That could only be so, however, if the Due Process Clause applied in some degree to the conduct of foreign officials—the very proposition that the Government otherwise contends Con-nelly rejected. By dangling a “shocks the conscience” test in this footnote, the Government implies that it takes issue not with whether confessions procured by foreign-officials can be excluded from American trials based on our Constitution, but with the standard our courts should apply in evaluating admissibility. The Government’s second counterargument extends from the premise that foreign governments are on the same footing as private employers when it comes to compelled testimony. In particular, the Government points to the fact that private employers may question an employee under threat of discharge without Fifth Amendment consequence, whereas in certain circumstances courts have found that the same threat by an American government employer rendered an employee’s testimony “compelled” and excludable under the Fifth Amendment. “For purposes of the Fifth Amendment,” the Government submits, “the .British government is on the same footing as- a private entity such as the New York Stock Exchange.” We disagree. Only sovereign power exposes “ ‘those suspected of crime to the cruel trilemma of self-accusation, perjury or contempt.’” Only the U.K. government could have immunized Defendants (neither of whom were employed by Rabobank at the time), compelling them to testify or go to jail. To the extent there may be an “official/private action spectrum,” when foreign authorities compel testimony they are acting in the quintessence of their sovereign authority, not in their capacity ás a mere employer, and thus their compulsion is cognizable by the Fifth Amendment (when testimony so compelled is used in a U.S. trial), The Supreme Court’s decision in Garrity v. New Jersey—like Con-nelly—does not foreclose constitutional review of a foreign sovereign’s threats to deprive, an individual of his liberty. If our Constitution is to prohibit the- use. in American trials of confessions coerced or compelled by a foreign sovereign under some circumstances, as the Government suggests “may be” the case, it cannot be the case that compulsion by a foreign authority ipso facto ends the constitutional inquiry. • ■ Finally, the Government’s third counterargument is that testimony is only “compelled” for purposes of the Self-Incrimination Clause if the compelling sovereign is bound by the Fifth Amendment. Here, too, we disagree. The Government’s argument relies on the so-called “same-sovereign” principle, under which Fifth Amendment protections apply only if the same sovereign (or, at least, a Fifth— Amendmentr-bound sovereign) both compelled and used testimony. This “same-sovereign” principle has never been fully abandoned; it still applies, for example, where the- prosecuting sovereign is not bound by the Fifth Amendment (i.e., where the prosecuting authority is a foreign government). But where, as here, the prosecuting sovereign is bound by the Fifth Amendment, the “same-sovereign” principle no longer has force. As already explained, it is now clear that the Fifth Amendment is a personal trial right—one violated only at the time of “use” rather than at the time of “compulsion.” Accordingly, the Government’s reliance on the “same-sovereign” principle in the circumstances of this case is unavailing. 3. The Consequences of Our Holding The Government also asserts that a prohibition on its use in U.S. courts of testimony compelled by a foreign authority “could seriously hamper the prosecution of criminal conduct that crosses international borders.” In particular, the Government submits: A foreign government could inadvertently scuttle prosecutions in the U.S. by compelling testimony and then making the testimony available to potential witnesses or the public. Worse yet, a hostile government bent on frustrating prosecution of a defendant would have to do no more than compel [that defendant] to testify and then publicize the substance of that testimony, unilaterally putting the United States to its heavy Kastigar burden. The Government’s first concern—that foreign powers could inadvertently or negligently obstruct federal prosecutions— fails to account for the fact that this risk already exists within our own constitutional structure. In our system—composed of “State and National Governments,” with the latter government further divided into separate co-equal branches—the DOJ does not control the granting or handling of witness immunity by the States or by the U.S. Congress. Similarly, and “[f]or better or for worse, we live in a world of nation-states in which our Government must be able to ‘function effectively in the company of sovereign nations.’ ” We are confident the Government is able to do so. Indeed, in a March 2016 address that specifically discussed the immunity issue in this case, Leslie Caldwell, then-Assistant Attorney General for the Criminal Division, observed that as we and our [foreign] counterparts work together more frequently and better understand our respective systems, we are having ... conversations [about double jeopardy and Fifth Amendment protections] earlier, so that individuals are much less likely to be caught in the middle of last minute turf battles over where and by whom a prosecution should be brought. In the present case, the Government was plainly aware from the outset—well before the FCA transmitted the Defendants’ compelled testimony to Robson—of the need for close coordination of its efforts with those of the U.K. authorities. The practical outcome of our holding today is that the risk of error in coordination falls on the U.S. Government (should it seek to prosecute foreign individuals), rather than on the subjects and targets of cross-border investigations. As to the Government’s concerns that a hostile foreign government. might hypothetically endeavor to sabotage U.S. prosecutions by immunizing a suspect and publicizing his or her testimony—that, of course, is not this case. This case raises no questions regarding the legitimacy or regularity of the procedures employed by the U.K. government or the U.K, government’s investigation more generally. We thus need only say, here that should U.S. prosecutors or judges face the situation suggested by the Government, our holding today would not necessarily prevent prosecution in the United States. That is true not only if the U.S. prosecution navigated any resulting Kastigar issues by meeting its burden or by not using exposed witnesses. It is true for another reason as well. Specifically, should the circumstances in a particular case indicate that .a foreign defendant had faced no real threat of sanctions by his foreign government for not testifying, then that defendant’s testimony might well not be considered involuntary. In short, the situation hypothesized by the Government ⅛ not before us today, and our resolution of this- case on the facts that are before u's leaves open the issue of foreign efforts to sabotage a U.S. prosecution. On the other hand, the Government nowhere responds to the troubling consequences of accepting its argument. As conceded' at oral argument, the Government's rule would remove any bar to introducing compelled testimony directly in U.S. prosecutions similar to this one—as in, “Your honor, we offer Government Exhibit 1, the defendant’s compelled testimony.” To be sure, the Government did not introduce Defendants’ compelled testimony directly and appears to have generally sought in good faith to respect the principles underlying the- Fifth Amendment. But it is well established .that a defendant’s "preserva-: tion of his rights” does not turn “upon the integrity and good faith of the prosecuting authorities.” We cannot entertain a rule that discards the most basic Fifth Amendment right simply because prosecutors can be expected to respect its objectives generally. The concerns that we express here are not idle. However unusual this particular prosecution may prove to be, so-called cross-border prosecutions have become more common. Such prosecutions, necessarily entail intimate coordination between the United States and foreign authorities. As then-Assistant Attorney General Caldwell put it in the address to which we referred earlier, “[cjollaboration and coordination among multiple regulators in cross-border matters is the future of major white collar criminal enforcement.’.’ Perhaps the most striking development in cooperative conduct is the embedding of U.S. prosecutors in foreign law enforcement. According to Caldwell,, the DOJ “recently placed Criminal Division prosecutors'with Eurojust in-The Hague and INTERPOL in France” and was “exploring the possibility .of- embedding prosecutors with other foreign law enforcement as well.” In a more recent address, Acting Principal Deputy Assistant Attorney General Trevor N. McFadden announced that DOJ will be detailing one of its anti-corruption prosecutors to work at the U.K. FCA—“the first time the Criminal Division .,, will detail -a -prosecutor to work in a foreign regulatory agency on white collar crime issues.” One area in particular where intimate cooperation and coordination will be needed between U.S. prosecutors and foreign authorities (or, perhaps, between U.S. prosecutors and U.S. prosecutors on detail to foreign authorities) is the securing of witness testimony. As the Government explained in a letter to the District Court in this case, “large scale economic crime conspiracies that harm U.S. markets, such as LIBOR rigging and the manipulation of the foreign exchange spot; often occur, in large part, overseas and successful prosecutions of these matters frequently rely on evidence provided by witnesses who live in foreign countries.” And as this case illustrates, foreign authorities may conduct compulsory witness interviews, including interviews of those who end up being—or are already—the targets of U.S. prosecution. We do not presume to know exactly what this brave new world of international criminal enforcement will entail. Yet we are certain that these developments abroad need not affect the fairness of our trials at home. If as a consequence of joint investigations with foreign nations we are to hale foreign men and women into the courts of the United States to fend for their liberty we should not do so while denying them the full protection of a “trial right” we regard as “fundamental” and “absolute.” Accordingly, we adhere to our precedent in assessing the voluntariness of inculpato-ry testimony compelled abroad by foreign governments. In the instant appeal, there is no question that the Defendants’ testimony was compelled and, thus, involuntary. We therefore conclude in this case that the Fifth Amendment prohibited the Government from using Defendants’ compelled testimony against them. B. Whether Defendants’ Rights Were Violated We thus turn to the parties’ arguments under the doctrines of the Fifth Amendment and the seminal case of Kastigar. The Fifth Amendment provides that “[n]o person ... shall be compelled in any criminal case to be a witness against himself .... ” Like the privilege itself, the lawful compulsion of testimony under a grant of immunity has “historical roots deep in Anglo-American jurisprudence.” In Kastigar, the Supreme Court upheld the constitutionality of compelling testimony in exchange for “use and derivative use” immunity under 18 U.S.C. § 6002, because the scope of the protection afforded was “coextensive with the scope of the [Fifth Amendment] privilege.” Thus, the scope of the constitutional privilege and use and derivative use immunity are two sides of the same coin, and we therefore seek guidance from cases interpreting either. In its holding, the Kastigar Court emphasized the breadth of use and derivative use protection. Such protection bars “use of compelled testimony, as well as evidence derived directly and indirectly therefrom.” And it “prohibits the prose-cutorial authorities from using the compelled testimony in any respect, ... therefore insuring] that the testimony cannot lead to the infliction of criminal penalties on the witness.” As the Kastigar Court observed, “[t]his total prohibition on use provides a comprehensive safeguard, barring the use of compelled testimony as an investigatory lead, and also barring the use of any evidence obtained by focusing investigation on a witness as a result of his compelled disclosures.” Because this “very substantial protection[] [is] commensurate with that resulting from invoking the privilege itself,” it “leaves the witness and the prosecutorial authorities in substantially the same position as if the witness had claimed the Fifth Amendment privilege.” Kastigar also established a doctrine to enforce this protection. When a witness has been compelled to testify relating to matters for which he is later prosecuted, the government bears “the heavy burden of proving that all of the evidence it proposes to use was derived from legitimate independent sources.” This burden is “not limited to a negation of taint; rather, it imposes on the prosecution the affirmative duty to prove that the evidence it proposes to use is derived from a legitimate source wholly independent of the compelled testimony.” We interpreted the teaching of Kastigar a. mere four years after the Supreme Court’s decision, noting that [w]hile this formulation repeats rather than defines the word ‘derived,’ it places a significant gloss upon it by putting the burden firmly on the prosecution to demonstrate that an indictment [and/or conviction] is the product of legitimate rather than tainted evidence, and by insisting that legitimate evidence" be from a source wholly independent of the compelled testimony. ■ In United States v. Hubbell, the Supreme Court rejected the government’s attempt to shift this burden because doing so would “repudiat[e] the basis for ... Kastigar ” The Government must prove it has met this heavy, albeit not insurmountable, burden by a preponderance of the evidence. 1. Was Evidence from Robson Tainted? With the . foregoing principles in mind, we consider whether any evidence from Robson used, in Defendants’ prosecution was tainted. To be clear, there is no dispute that the Government “used” evidence from Robson: he was a key cooperator and a prominent trial witness. The less straightforward question is whether any evidence supplied by Robson-(to the government, to the grand jury, or at trial) was tainted by his earlier review of the testimony of Defendants compelled in the United Kingdom under U.K. law. Our Court apparently has never encountered the circumstance in which a government trial witness had, prior to testifying, reviewed a defendant’s compelled testimony. The D.C. Circuit, - however, has addressed the applicable legal standards in a pair of high-profile cases arising out of the Iran-Contra affair. In those cases, that Court held that “the use of immunized testimony by witnesses to refresh their memories, or otherwise to focus their thoughts, organize their testimony, or alter their prior or contemporaneous statements, constitutes” an impermissible use of the defendants’ compelled testimony. Despite briefing from both parties that cited the standards used by the D.C. Circuit, the 'District Court in this case relegated any mention of those precedents to a footnote that indicated that it would look only to Second Circuit precedent, of which there is none directly on point. As a result, it is unclear precisely what standards the District Court applied to determine whether the evidence supplied by Robson was tainted by his study of the Defendants’ compelled testimony. What is clear, however, is that the District Court impermissibly lowered the bar when' it determined that'the'Government had satisfied its heavy Kastigar burden based on the mere fact that Robson himself asserted that his testimony was not tainted by his review of Defendants’ compelled testimony and the fact that there was corroborating evidence .for Robson’s trial testimony. In apparent agreement with both parties on appeal, we! conclude that the legal standards set forth by the D.C. Circuit in North I are helpful here. Wé need not, in this case, decide whether the Government is required to demonstrate that Robson’s review of Defendants’ compelled testimony did not in any manner subtly “refresh his memory, focus or organize his thoughts,” or in some other traceless way influence his state of mind. At a minimum, however, we agree-with the D.C. Circuit that the Government is required to prove that his exposure to the compelled testimony did not shape, alter, or affect the information that he provided and that the Government used. The most effective way to demonstrate that a witness’s testimony was untainted by exposure to a defendant’s immunized testimony is by demonstrating that his or her testimony was unchanged from comparable testimony given before the exposure.. Thus, typically, the prosecution can meet its burden by memorializing (or “canning”) the witness’s testimony pri- or to his or her exposure. In the present case, Robson did testify to' the FCA regarding Rabobank’s submission and alleged manipulation of LI-BOR rates, as well as the roles of Allen and Conti, prior to Robson’s exposure to Defendants’ compelled testimony. But what Robson’s “canned” testimony preserved is toxic to the Government’s case; it omits or contradicts in material'parts the testimony Robson later provided indirectly to the grand jury and directly to the petit jury. At the Kastigar hearing held by the District Court, Robson agreed that “the testimony that [he] gave to the [FCA] and the testimony that [he] gave before the j,ury in this trial were very different.” For instance, Robson testified to the jury about an altercation between Stewart and Damon Robbins, an .alternate submitter for USD LIBOR, on Rabobank’s London desk. But Robson did not testify about this to the FCA, and the Kastigar hearing raised questions about whether he had even seen the incident at all or merely read about it in the compelled testimony. Far from rebutting the presumption that Robson’s trial testimony was tainted, his pre-exposure testimony actually evidences such taint through its material differences with Robson’s post-exposure trial testimony. As Robson’s FCA testimony hurts rather than helps its cause, the Government appears to contend on appeal that it satisfied its burden solely through Robson’s “‘persuasivet]’” testimony at the Kasti-gar hearing. We conclude, however, that Robson’s testimony at the hearing falls far short of satisfying the demands of Kasti-gar. As explained below, the Government adduced, at bottom, nothing more than bare, self-serving denials from Robson to meet its heavy burden. We hold that such conclusory denials are insufficient as a matter of law to sustain the prosecution’s burden of proof under Kastigar in the face of materially inconsistent pre-exposure testimony. By the Government’s own count, 27 of the 58 topics discussed by Robson during his trial testimony had an antecedent in Allen’s compelled testimony, and 18 of those 58 topics had an antecedent in Con-ti’s compelled testimony. Yet at no time during the Kastigar hearing did Robson claim that he could “segregate the effects of his exposure” with respect to each, or any, of those topics. Notably, the Government never asked Robson whether his memory was, or might have been, substantially refreshed by his review of Defendants’ compelled testimony—or, to put a finer point on the inquiry, whether Robson could testify under oath at the Kastigar hearing that his memory had not been refreshed. Robson was asked by the Government several times in various generalized, leading ways whether his review of the compelled testimony “inform[ed] ... in any way” his cooperation or testimony and he responded, without qualification, “no.” Despite Robson’s unqualified assertions in response to those leading questions, we are mindful that memory remains “a mysterious thing,” and its mysteries were on full display at the Kastigar hearing in the District Court. Perhaps most mysterious was what, exactly, Robson remembered of the compelled testimony of Allen and Conti that he had reviewed. For instance, Robson was asked if he had “any specific recollection of the materials that [he] had reviewed,” and he answered “[n]o, not specifically.” But sometimes Robson did have specific recollections: Q. But when you read Mr. Conti’s F[C]A transcript, you saw that he acknowledged that Lee Stewart made requests that were intended to benefit his derivative positions. Do you recall that? A. Yes, I do. Similarly, the Government asked Robson if he “learn[ed] any new facts from reviewing those materials,” to which he answered “[n]o, I didn’t.” But it later became apparent that he had learned, through reviewing the compelled testimony of Allen and Conti, of specific communications in which he had not been an original participant—and that Robson had discussed such communications with the DOJ when he began cooperating. This particular inconsistency eventually led to the following colloquy between Robson and the District Court: THE COURT: I just want to be sure I am clear on the chronology. You reviewed [Allen’s and Conti’s FCA testimony] when? THE WITNESS: Towards the end of November 2013. THE COURT: That was before you had begun cooperating with the government? THE WITNESS: Yes, it is. THE COURT: Some of the things you saw in this transcript were references to conversations that you had not been a party to yourself, yes? THE WITNESS: Yes, your Honor. THE COURT: And they were conversations that you did not know about until reading the transcripts, true? THE WITNESS: Yes, your Honor. THE COURT: So when you said, in answer to government counsel’s question, that you were already familiar with various things, you weren’t referring to these conversations, you were referring to some of the other things? THE WITNESS: Sorry, your Honor? THE COURT: A few minutes ago you said that you hadn’t underlined or circled things that you didn’t already know, or words to that effect, if I remember correctly. THE WITNESS: I underlined and circled things that I believe were things that I knew from my personal experiences at Rabobank. THE COURT: But not the specific conversations? THE WITNESS: No, your Honor. THE COURT: Is it your testimony that you did not bring any of those conversations to the attention of the government? THE WITNESS: No, I didn’t, your Honor. THE COURT: Now, you testified yesterday that in preparation for your testimony, the government, after you began cooperating, showed you some of the emails involving conversations between two third-parties that you were not a party to, yes? THE WITNESS: Yes. THE COURT: But you knew about them because you had seen references to them in the transcripts of Mr. Allen or Mr. Conti, yes? THE WITNESS: Some of them I had, yes. THE COURT: When they showed them to you, did you say to the government, I have seen that before? THE WITNESS: I don’t recall, sir, - THE COURT: Did you say, I haven’t seen them before? THE WITNESS: I think there were a couple I hadn’t seen, which I might have mentioned I hadn’t seen. Even Robson’s more generalized recollection of the transcripts appeared to wax and wane depending on the month (or even the day) in which he was asked. At one point during the Kastigar hearing, defense counsel directed Robson’s attention to an August 5, 2015 declaration—in which Robson had declared, “I recall that I did not agree with or believe everything reflected in transcripts of Messrs. Allen and Conti ”—ancj the following exchange ensued: Q. So did you recall when you signed this on August 5, 2015[,] not agreeing or believing with everything in Mr. Conti’s transcript? A. Yes. Q. Do you recall now [on December 16, 2015,] not agreeing at the time that you read ¡the transcript with everything Mr. Conti said?. A. I don’t recall." Sorry. Adding another wrinkle, Robson would, during the next day of testimony at the Kastigar hearing, explain his various purposes for annotating, underlining, or circling various passages of the compelled testimony of Allen and Conti, as including the “circl[ing of] anything that I felt was untrue.” Even putting aside such mnemonic curi-ositiés, Robson’s testimony at the Kastigar hearing with respect to his ability to “segregate the effects of his exposure” amounts to nothing more than simply replying “no” in a conclusory fashion to generalized leading questions from the Government. We have found the sorts of bare, self-serving denials given'by Robson, when given by a prosecutor (ie., an officer of the court), to be insufficient to satisfy the demands of Kastigar, and the Government supplies no convincing reason why the same rule should not apply here. In light of the foregoing discussion, moreover, it seems clear to us that the same rule should apply. Accordingly, we hold that a bare, generalized denial of taint from a witness who has materially altered his testimony'after being substantially exposed to a defendant’s compelled testimony is insufficient as a matter of law to sustain the prosecution’s burden of proof under Kastigar that that witness’s testimony was derived from a wholly independent source. - In view of our holdings, the District Court’s conclusion that the prosecution had met its heavy burden under Kast-igar to show that the evidence supplied'by Robson was untainted cannot stand. Moreover, a remand for a further factual hearing on the question of taint would be futile. For one thing, Robson was -again shown, and he again reviewed, critical portions of Defendants’ compelled testimony during the Kastigar-hearing, And what Robson did repeatedly claim at the hearing—an inability to recall clearly much of anything—establishes that he lacked the ability “to separate the wheat of [his] unspoiled memory from the chaff of [Defendants’] immunized testimony.” Notably, the Government does not even request a remand on this question or otherwise suggest it has some plausible alternative means of sustaining its burden of proof. In sum, the Government did not, and cannot, meet its burden under Kastigar, We therefore conclude that the Gov