McKEAGUE, Circuit Judge.

ARGUED: Hilary Holt LoCicero, BENNETT DOYLE LLP, Washington, D.C., for Appellant. David Lieberman, UNITED STATES DEPARTMENT OF JUSTICE, Washington, D.C., for Appellee. ON BRIEF: Hilary Holt LoCicero, Robert S. Bennett, Lisa Hertzer Schertler, SCHERTLER & ONORATO, LLP Washington, D.C., for Appellant. David Lieberman, UNITED STATES DEPARTMENT OF JUSTICE, Washington, D.C., Charles P. Wisdom, Jr., Kate K. Smith, UNITED STATES ATTORNEY’S OFFICE, Lexington, Kentucky, for Appellee.

Before: BATCHELDER, McKEAGUE, and GRIFFIN, Circuit Judges.

McKEAGUE, Circuit Judge.

Richard Paulus was convicted of healthcare fraud and making false statements relating to healthcare matters. Before sentencing, Paulus learned that the government withheld evidence from him on the district court’s orders. On appeal he argues that this withholding violated his due process rights under Brady v. Maryland , 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963). We agree. Therefore, we VACATE Paulus’s conviction and REMAND for further proceedings.

I

A.

For years Paulus was a successful cardiologist at King’s Daughters Medical Center (KDMC). He performed an incredible number of angiograms and was "first in the nation for the total amount billed to Medicare for these procedures." United States v. Paulus , 894 F.3d 267, 272 (6th Cir. 2018) ( Paulus I ). But not all was well. Complaints emerged that Paulus was performing medically unnecessary procedures. And several audits indicated that in multiple cases Paulus had reported a higher degree of blockage in his patients’ arteries than their angiograms reflected. Id. at 272–73. Meaning, in some cases, the patient’s angiogram showed a low degree of blockage and thus that the patient didn’t need a stent inserted. Yet Paulus reported a much more severe blockage, inserted a stent, and then billed patients and their insurance companies for the stent procedure. See id. at 273.

Eventually, these allegations reached the federal government. At first, the government considered entering into a civil settlement with Paulus. In a letter setting forth its demands, the government stated that its consultants had reviewed 496 of Paulus’s procedures and concluded that 146 of them (or about 30%) were unnecessary because the patients’ angiograms showed minimal arterial blockage. The government further noted that its experts weren’t the only ones who found Paulus’s procedures to be problematic: the letter explained that KDMC’s "consultants [had] also reviewed a random selection of Dr. Paulus’ procedures, and found 75 angiographic films with [minimal blockage] in the artery he stented." But after some back-and-forth, the attempts at a civil settlement fell through, and the government obtained an indictment.

B.

At trial the government called three expert witnesses, Drs. Ragosta, Morrison, and Moliterno, who showed angiograms from 72 different patient files to the jury. Id. at 273–74. While displaying each angiogram, the doctors diagnosed the amount of blockage in the patient’s artery and contrasted their diagnosis with that stated in Paulus’s report. Based on the differences between what the government’s experts saw in the angiograms and what Paulus reported, the experts concluded that Paulus overstated his patients’ arterial blockage and inserted medically unnecessary stents. They also emphasized that this was not "an isolated case[.]" Instead, Ragosta presented evidence of overstatements in 62 out of the 250–300 cases he reviewed, and he called the 62 cases a "representative sample"; Morrison noted that over half of the 11 randomly selected procedures he reviewed were unnecessary; and Moliterno asserted that all of the stent procedures he reviewed were unnecessary. Based on this testimony, the government argued that Paulus "saw one thing on the angiogram and consciously wrote down another." Id. at 276. And he didn’t just do it occasionally. According to the government’s closing argument, Paulus did it "frequently, repetitive[ly], daily."

After 23 days of trial, four days of jury deliberations, one judicial pep talk, and one Allen charge, the jury convicted Paulus of one count of healthcare fraud and ten counts of making false statements relating to healthcare. But the case didn’t proceed to sentencing. The district court vacated the convictions, finding that there was insufficient evidence both that Paulus made false statements and that he had fraudulent intent. But that didn’t stand. We disagreed with the district court’s reasoning and reversed its order. Paulus I , 894 F.3d at 280.

C.

The plot twisted once more. After remand and before sentencing, the government disclosed to Paulus for the first time the "Shields Letter." According to the letter, when KDMC was facing its own legal trouble, it hired a team of independent experts to review Paulus’s work ("KDMC Review"). KDMC’s consultants reviewed 1,049 of Paulus’s cases and flagged 75 of his procedures as unnecessary. In the Shields Letter, KDMC’s attorneys explained to the government their consultants’ findings and offered to refund Medicare for the payments the hospital had collected for the 75 flagged procedures.

While Paulus already knew that KDMC had identified 75 of his procedures as problematic, he did not know that KDMC consultants had reviewed 974 other procedures that they apparently found non-problematic. The defense viewed this evidence as exculpatory because it meant that the KDMC Review found that the rate of unnecessary surgeries, 75 out of 1,049, or about 7%, was far lower than what the government experts had testified at trial; this lower percentage was less consistent with systemic and purposeful fraud and more consistent with occasional mistakes or diagnostic differences of opinion between cardiologists. Seeking more information, Paulus moved to compel the government to produce all information related to the letter.

It was only then that the defense got the full picture. The government disclosed to Paulus a series of events that had taken place before his trial. Long before Paulus was indicted, KDMC sent the government the Shields Letter. And when the government later elected to charge Paulus, it planned to use the Shields Letter in its case-in-chief and to disclose the letter to Paulus. But KDMC objected, arguing that the letter was both privileged and inadmissible. So, about a month before trial, the government brought the dispute to the district court, and the court scheduled an ex parte hearing, so as to protect KDMC’s asserted privilege.

But even though privilege was ostensibly the reason for holding the hearing ex parte, the district court made no decision regarding the privilege issue. The court opened the hearing by saying it would put privilege aside and decide instead whether the information was inadmissible under Federal Rule of Evidence 408. The government argued that the letter was admissible. And to its credit, the government also argued that even if the letter wasn’t admissible, the government was obligated to disclose it to Paulus under Brady . Although the government wished to introduce evidence of the KDMC Review at trial for its inculpatory value, it also recognized that the review had exculpatory value to Paulus. But the district court was unconvinced. It held that the information was inadmissible—a ruling that both parties now agree was wrong—and that the government wasn’t obligated to turn it over to Paulus. And even though it made no ruling on privilege, the district court concluded the hearing by inexplicably ordering that the parties "[we]re not to disclose" any more information about the KDMC Review to Paulus.

Having discovered this information after his trial, conviction, and remand from this court, Paulus moved for a new trial. The district court rejected Paulus’s arguments and proceeded to sentencing. It sentenced Paulus to five years’ imprisonment and ordered him to pay $1,156,102.23 in restitution.

On appeal, Paulus challenges the ex parte hearing as violating his Sixth Amendment right to counsel, the ruling on the admissibility of the Shields Letter as a reversible evidentiary error, and the failure of the government to disclose the letter as a violation of his due process rights under Brady . He also challenges the district court’s Allen charge and restitution order. We start and end by addressing his constitutional claims.

II

Paulus argues that the ex parte hearing in the district court violated his Sixth Amendment rights. Under the Sixth Amendment, criminal defendants have the right to the assistance of counsel for their defense. U.S. Const. amend. VI. Thus, when defense counsel is excluded from a critical stage of a criminal proceeding, it is a per se Sixth Amendment violation. United States v. Cronic , 466 U.S. 648, 659 n.25, 104 S.Ct. 2039, 80 L.Ed.2d 657 (1984). In Van v. Jones , we explained that a stage is critical when "there [is] a reasonable probability that [the defendant’s] case could suffer significant consequences from his total denial of counsel at that stage." 475 F.3d 292, 313 (6th Cir. 2007). Paulus contends that the ex parte hearing in the district court was just such a critical stage. The government doesn’t disagree; rather, the government argues that ex parte hearings are generally permissible to resolve privilege disputes.

There is something to the government’s argument. According to our precedent, the government can sometimes justify ex parte proceedings that would otherwise violate the Sixth Amendment. Relevant to this case, the government can justify ex parte proceedings by showing that there was a compelling state interest for holding the proceedings ex parte, United States v. Barnwell , 477 F.3d 844, 850 (6th Cir. 2007) ; United States v. Minsky , 963 F.2d 870, 874 (6th Cir. 1992) ; the proceedings were narrowly tailored to that compelling state interest, Barnwell , 477 F.3d at 851 ; and the defendant was not prejudiced by the ex parte proceedings, id ; Minsky , 963 F.2d at 874. The government contends that the court had to hold the hearing ex parte, because there is a compelling state interest in protecting attorney-client privilege.

We are not convinced that the ex parte hearing in this case was permissible for at least three reasons.

First , even if we assume that attorney-client privilege is a compelling state interest that can justify ex parte communications, the district court said from the outset that it would not decide the privilege issue. It put privilege to the side and decided issues of admissibility and discoverability instead. And "[i]f ex parte communications are to be allowed at all, they must continue no further than the extent to which they are absolutely necessary to protect the state’s compelling interest." Barnwell , 477 F.3d at 851. This hearing continued much further than necessary. The district court put aside the issue that would have determined whether a state interest existed at all. And as it turns out, the parties agree that the letter was neither privileged nor inadmissible.

Second , the district court made no attempt to involve the defense. The court could have ordered the government to give Paulus a broad outline of the privilege and admissibility issues, without disclosing the Shields Letter. With limited information, the defense could have mounted arguments that the letter was both non-privileged and admissible. See United States v. Lloyd , 400 F.2d 414, 416 (6th Cir. 1968) ; see also Moeller v. Harris , 428 F. App'x 771, 773–74 (9th Cir. 2011). Privilege logs aren’t unheard of in criminal proceedings, and one could have been used here. Cf. In re Grand Jury Subpoenas , 454 F.3d 511, 524 (6th Cir. 2006). Further, without telling the defense any details at all, the court could have asked the defense to explain its trial strategy, which would have provided helpful context for the court’s Brady analysis. See United States v. Amawi , 695 F.3d 457, 472 (6th Cir. 2012) ("We should stress that the district court also held ex parte hearings with defense counsel in order to learn about their theories and prepare for ex parte hearings with the government."). Thus, without vitiating KDMC’s asserted privilege, the district court could have sought the defense’s input in multiple ways. The court didn’t do that. Instead, it kept Paulus in the dark about the issues and considered only the arguments made by the government and KDMC, which had interests divergent from Paulus’s.

Third , the risks of proceeding ex parte were realized in this case. Ex parte hearings are problematic because "the Court does not have available the fundamental instrument for judicial judgment: an adversary proceeding in which both parties may participate." Carroll v. President & Comm’rs of Princess Anne , 393 U.S. 175, 183, 89 S.Ct. 347, 21 L.Ed.2d 325 (1968) ; see also United States v. Carmichael , 232 F.3d 510, 517 (6th Cir. 2000) (calling ex parte hearings with the government a "dangerous procedure" (quoting Minsky, 963 F.2d at 874 )). Thus, when a court rules on important issues without hearing from the defense, it takes the risk of making erroneous decisions that will unfairly disadvantage the defendant. That’s exactly what happened here. First, the district court ruled that the Shields Letter was inadmissible. The parties agree that was wrong. Second, the district court determined that because the letter was inadmissible, it couldn’t be Brady material. That is flatly wrong. Barton v. Warden, S. Ohio Corr. Facility , 786 F.3d 450, 465–66 (6th Cir. 2015). Third, the district court ordered the government and KDMC not to disclose the Shields Letter to Paulus. That was wrong too: neither the erroneous admissibility ruling nor the erroneous discoverability ruling could justify that instruction.

Thus, even if there are cases where attorney-client privilege claims can justify ex parte hearings, we are not convinced that this was one of those cases. Nevertheless, we need not decide whether the ex parte hearing was permissible, because we find that the evidence withheld from Paulus, based on the district court’s erroneous order, violated his Fifth Amendment rights under Brady .

III

Paulus alleges that the prosecution’s failure to disclose the Shields Letter violated his Fifth Amendment due process rights under Brady . We agree. We review Brady claims de novo. United States v. Tavera , 719 F.3d 705, 710 (6th Cir. 2013).

The Brady inquiry has three prongs: "The evidence at issue must be favorable to the accused, either because it is exculpatory, or because it is impeaching; that evidence must have been suppressed by the State, either willfully or inadvertently; and prejudice must have ensued." Strickler v. Greene , 527 U.S. 263, 281–82, 119 S.Ct. 1936, 144 L.Ed.2d 286 (1999). But there is "no Brady violation where a defendant ‘knew or should have known the essential facts permitting him to take advantage of any exculpatory information.’ " United States v. Castano , 906 F.3d 458, 466 (6th Cir. 2018) (quoting United States v. Clark , 928 F.2d 733, 738 (6th Cir. 1991) ). The government concedes that the Shields Letter had "potential exculpatory value," and that "[n]o dispute exists on the threshold prong." It also admits that it failed to disclose "one specific fact: ‘the sample size of stent procedures reviewed’ by KDMC." Thus, there are two issues for us to resolve on appeal: (1) whether Paulus knew or should have known the essential facts about the KDMC Review and (2) whether the prosecution’s omission caused prejudice.

A.

The prosecution is not obligated under Brady to disclose information to the defense that the defense already "knew or should have known." Castano , 906 F.3d at 466 (quoting Clark , 928 F.2d at 738 ). The government argues that Paulus knew the essential facts described in the Shields Letter and that he could have gathered the missing detail (the sample size) with "minimal investigation." Jalowiec v. Bradshaw , 657 F.3d 293, 311 (6th Cir. 2011) (quoting Coleman v. Mitchell , 268 F.3d 417, 438 (6th Cir. 2001) ). The prosecution had informed Paulus in a letter that KDMC consultants reviewed a random sample of Paulus’s procedures and flagged 75 as unnecessary. According to the government, based on this information, Paulus could and should have gathered the missing detail—the sample size—by simply asking KDMC.

We would have to completely ignore the record to accept the government’s argument here. After all, it was KDMC that opposed the government’s disclosing the Shields Letter to Paulus in the first place. And it was KDMC that argued that the Shields Letter was privileged and inadmissible. Thus, it is not reasonable to assume that Paulus would only have had to ask KDMC in order to get the missing details. The government points out that KDMC was wrong and the Shields Letter wasn’t privileged; so presumably, even if the hospital initially refused to give Paulus the missing details, Paulus could have sought a subpoena. But even if the government is right about that, the question is not whether Paulus could have eventually obtained the omitted information. Brady "does not [allow] the State simply to turn over some evidence, on the assumption that defense counsel will find the cookie from a trail of crumbs." Barton , 786 F.3d at 468. Thus, the question is whether Paulus would have had to follow a long trail of crumbs to get the missing details or whether he could have gotten the same information with minimal investigation.

Our prior cases give helpful examples of what constitutes minimal investigation. The government cites two in particular. In United States v. Castano , we held that a defendant who knew about a witness’s indictments should have searched the public record to find the witness’s convictions. 906 F.3d at 466. In Stojetz v. Ishee , we held that a capital defendant who knew he had been stabbed in prison and that the prison had medical records should have acquired his own prison medical records. 892 F.3d 175, 205–06 (6th Cir. 2018). These are examples of minimal investigation, because a simple search or request, without more, would provide the information sought. Seeking a subpoena and fighting KDMC’s privilege assertions rises to a level beyond minimal investigation.

Moreover, it seems unreasonable to expect much investigation at all, given that Paulus had no reason to think that the KDMC Review held exculpatory value. While Paulus knew that KDMC had hired independent consultants to review his procedures, he had no idea that any relevant information would be exculpatory. The information as given to him and used by the government seemed facially inculpatory. All he knew was that the hospital had flagged 75 procedures as problematic and that the government was using that information to its advantage. Paulus had no reason to follow the trail of crumbs in search of a cookie, unlike the defendants in Castano and Stojetz to whom the potential for favorable evidence should have been obvious.

The government also argues that Paulus could have gotten his own expert to perform a review of his procedures, but that is even further from minimal investigation. If its other argument suggested that Paulus should have followed a trail of crumbs in search of a cookie, this argument suggests that Paulus should have just made his own cookie, because he had the same ingredients. And even if we agreed that Paulus should have made his own cookie, that misses a larger point: his own expert wouldn’t necessarily have provided Paulus the same information the Shields Letter offered. The government’s argument is akin to saying that the prosecution doesn’t have to disclose an exculpatory statement by one eyewitness because the defense could have just asked another eyewitness. It’s not a given that two witnesses saw the same thing or that their testimony would be equally exculpatory. So it is with experts. That experts can review samples drawn from the same pool and reach different conclusions is clearly evidenced by the dramatically different conclusions reached by the government’s experts compared to the hospital’s experts.

Because Paulus had no reason to think the KDMC Review held any exculpatory value and because he lacked a readily available means to get the missing details, we find that he didn’t have the essential facts.

B.

The other issue is prejudice. In order to prove that prejudice ensued from the government’s withholding of the Shields Letter, Paulus must prove that the evidence was material. Meaning, Paulus must prove that "there is a reasonable probability that, had the evidence been disclosed to the defense, the result of the proceeding would have been different." Strickler , 527 U.S. at 280, 119 S.Ct. 1936 (quoting United States v. Bagley , 473 U.S. 667, 682, 105 S.Ct. 3375, 87 L.Ed.2d 481 (1985) ). "The question is not whether the defendant would more likely than not have received a different verdict with the evidence, but whether in its absence he received a fair trial, understood as a trial resulting in a verdict worthy of confidence." Id. at 289–90, 119 S.Ct. 1936 (quoting Kyles v. Whitley , 514 U.S. 419, 434, 115 S.Ct. 1555, 131 L.Ed.2d 490 (1995) ). The revelation of the Shields Letter and the missing details from the KDMC Review undermines our confidence in the verdict, and thus we find that withholding them prejudiced Paulus.

The argument that the omitted details from the Shields Letter were material is fairly simple. Because the KDMC Review found misdiagnoses in a much smaller percentage of cases than the government experts found (around 7% compared to nearly 50%), the study tends to refute the government’s evidence that Paulus systematically misdiagnosed the amount of blockage in his patients’ arteries. Instead, he may have made occasional mistakes or had occasional differences of opinion. And if Paulus didn’t systematically overstate his patients’ arterial blockages, then that weakens the government’s evidence that Paulus intentionally defrauded his patients, their health insurance companies, and the government. Paulus also could have used the Shields Letter to impeach the government’s witnesses by calling into question how representative their samples were. The government experts testified that Paulus repeatedly and systematically overstated the degree of blockage in his patients’ arteries. Paulus I , 894 F.3d at 274. But Morrison and Moliterno each evaluated fewer than 20 procedures. Id. Given the Shields letter, Paulus could have pointed out that KDMC’s much more extensive review found that Paulus misdiagnosed his patients less than 8% of the time. And while Ragosta reviewed 250–300 of Paulus’s procedures, that is still far fewer than the 1,049 reviewed by KDMC. Id. Furthermore, Ragosta’s sample was not random; 75 of the 250–300 files reviewed by Ragosta were selected for review because KDMC flagged them as problematic. Armed with the fact that KDMC pulled those 75 from a sample of 1,049, Paulus may have argued that Ragosta’s sample was cherry-picked.

This weakening of the government’s evidence regarding Paulus’s intent is especially important because there are several indications in the record that Paulus’s intent was a close issue. First, the jury deadlocked twice. Second, the district court vacated Paulus’s conviction, in part because it found that the government had failed to prove Paulus’s fraudulent intent. United States v. Paulus , No. CR 15-15-DLB-EBA, 2017 WL 908409, at *14 (E.D. Ky. Mar. 7, 2017). And although this panel reversed the district court’s order and reinstated the jury’s verdict, we still recognized that based on the evidence presented at trial—which did not include the Shields Letter or KDMC Review, of which we had no knowledge—a reasonable jury could conclude that Paulus didn’t have fraudulent intent. Paulus I , 894 F.3d at 276–77. We recognized that a reasonable jury could have gone either way, but that in such cases, we uphold the jury’s verdict. Id. Since Paulus’s intent was a close issue, and the Shields Letter would have given Paulus ammunition to rebut the government’s evidence of his intent, we find that its omission prejudiced him.

The government disagrees; it argues that "[o]n balance, the [Shields Letter] would have bolstered the government’s case and significantly damaged Paulus’s defense strategy." The government argues that the letter was inculpatory because it was another source confirming that Paulus performed medically unnecessary stent procedures. But the government "presented a phalanx of experts" at trial who testified to the same thing. Paulus I , 894 F.3d at 277. Thus, the Shields Letter would have added only marginal value to the government’s case: it would be one more voice chiming in to say that Paulus performed some medically unnecessary procedures. Furthermore, this does nothing to bolster the government’s evidence of Paulus’s intent, which is the close issue impacted by the exculpatory nature of the letter. The fact that the KDMC consultants reviewed Paulus’s procedures and, like the government’s experts, determined that he sometimes overstated his patient’s arterial blockage doesn’t add any additional proof that the overstatements were intentional.

The government also argues that the Shields Letter would have "shattered Paulus’s key storyline" that he was a brilliant doctor being treated unfairly by the government. But Paulus could have changed his defense strategy if he’d been given this evidence before trial. In fact, the government recognized this much at the ex parte hearing, as part of its argument that it was obligated under Brady to disclose the Shields Letter to Paulus. Furthermore, it doesn’t seem that the Shields Letter really is incompatible with the defense Paulus presented at trial. Paulus could have plausibly argued both that he was an excellent doctor and that excellent doctors still make mistakes sometimes or disagree with other excellent doctors. It’s hard to see why Paulus couldn’t have successfully incorporated the Shields Letter into his defense at trial, and so the government’s argument that the letter shattered his defense fails.

The government’s arguments that the Shields Letter was only minimally exculpatory are similarly unconvincing. The thrust of the government’s arguments is that the jury wouldn’t have credited the KDMC Review. First, the government argues that a jury wouldn’t have credited the KDMC Review because it was done by the hospital "in order to mitigate its own liability ." But that argument proves too much. After all, the government’s main expert, Dr. Ragosta, was retained by an interested party (the government) in preparation for litigation. If the jury should not have credited KDMC’s consultants, because they were retained by an interested party and therefore biased, then they also shouldn’t have credited Dr. Ragosta for the very same reason. Moreover, if the government is right, then juries shouldn’t believe most experts who testify at trial. The government also says a jury wouldn’t credit the KDMC Review because the KDMC consultants reviewed a sample from 2009–2010, while Paulus’s criminal conduct spanned between 2008–2013. But this isn’t persuasive, since a large majority of the procedures discussed by the prosecution’s experts also came from 2009–2010.

We do sympathize with the prosecution, because we recognize that the government believed it had an obligation to disclose the Shields Letter to Paulus and did not do so solely because of the district court’s order. But "[i]rrespective of the good faith or bad faith of the prosecution," the failure to disclose favorable, material evidence to the defense violates due process. United States v. Agurs , 427 U.S. 97, 110 n.17, 96 S.Ct. 2392, 49 L.Ed.2d 342 (1976) (quoting Brady , 373 U.S. at 87, 83 S.Ct. 1194 ). Because Brady is about the fairness of the trial and not about ferreting out the "misdeeds of a prosecutor," it doesn’t matter how blameless or blameworthy the prosecution might have been. Id.

IV

Because we find that the proceedings in the district court violated Paulus’s Fifth Amendment right to due process, we VACATE his conviction and REMAND for a new trial.