Glenn Lewellen, a dirty cop with the Chicago Police Department (CPD), arrested Refugio Ruiz-Cortez for possessing cocaine. Lewellen served as the key witness at the trial, where Ruiz-Cortez was convicted. Ruiz-Cortez then spent a decade in prison before the federal government discovered Lewellen's crimes, which included drug conspiracy, racketeering, and, according to the government, perjury at Ruiz-Cortez's trial. The government prosecuted Lewellen and moved to vacate Ruiz-Cortez's conviction, recognizing that without Lewellen's testimony there was no evidence to prosecute Ruiz-Cortez.

Ruiz-Cortez sued the City of Chicago and Lewellen for violating his constitutional rights. See 42 U.S.C. § 1983 . He complained that the City and Lewellen withheld material impeachment evidence-namely, evidence of Lewellen's drug and racketeering crimes. See Giglio v. United States , 405 U.S. 150 , 92 S.Ct. 763 , 31 L.Ed.2d 104 (1972) ; Brady v. Maryland , 373 U.S. 83 , 83 S.Ct. 1194 , 10 L.Ed.2d 215 (1963). The district court dismissed the claim against the City at summary judgment, concluding that there was no evidence of municipal liability. See Monell v. Dep't of Social Servs. , 436 U.S. 658 , 98 S.Ct. 2018 , 56 L.Ed.2d 611 (1978). A jury later found for Lewellen, despite his refusal to testify based on the Fifth Amendment right against self-incrimination.

*595 We affirm the dismissal of the City. Ruiz-Cortez failed to marshal the evidence needed to meet Monell 's high standard. But we vacate the judgment for Lewellen and remand for a new trial against him. The district court allowed Lewellen to offer innocent explanations for his Fifth Amendment invocation, ones that fly in the face of Fifth Amendment law, and it then failed to instruct the jury about when a Fifth Amendment invocation is proper. Those errors, taken together, made for a fundamentally unfair trial.

I. Background

The background to this appeal concerns two drug-dealing schemes, one involving Ruiz-Cortez and the other involving Lewellen and his go-to informant Saul Rodriguez. It also concerns three trials: the prosecution of Ruiz-Cortez, the prosecution of Lewellen, and the civil dispute that gives rise to this appeal.

In June 1999, the CPD and Drug Enforcement Administration (DEA) started surveilling Ruiz-Cortez's suburban home, suspecting it was a part of a drug-dealing operation. They arrested two people for picking up drugs from the home on June 23, 1999, and a few weeks later, on July 8, 1999, they arrested Ruiz-Cortez. Lewellen claimed to have recovered a bag filled with cocaine bricks just outside of Ruiz-Cortez's home. A search of the home turned up $1,800 in hundred-dollar bills stored in a broken vacuum cleaner.

A grand jury indicted Ruiz-Cortez for cocaine possession with intent to distribute in December 1999. At trial, the government relied primarily on Lewellen as a witness; he was the only member of law enforcement who claimed to have seen Ruiz-Cortez with the drugs. Lewellen testified that he and others had been observing Ruiz-Cortez's home on the day of the arrest, when Lewellen saw Ruiz-Cortez stick his head out the door a few times, as if he was expecting company. Lewellen said that Ruiz-Cortez later walked onto his back porch with a plastic bag. Lewellen and another officer pulled up to the home, and, according to Lewellen, Ruiz-Cortez dropped the bag and returned inside. Ruiz-Cortez, for his part, took the stand and maintained that the drugs had been planted. The jury found Ruiz-Cortez guilty, and the district court sentenced him to 17 and a half years in prison.

Several years later, the DEA began investigating Lewellen and Rodriguez for their crimes. In 2009, a grand jury indicted the two for, among other things, conspiracy and racketeering. The predicate acts in the racketeering count included murder, kidnapping, and-most relevant here-obstruction of justice, stemming from Lewellen's testimony in Ruiz-Cortez's trial. Rodriguez pleaded guilty and began cooperating with the government, including by testifying at Lewellen's eventual criminal trial.

At Lewellen's trial, in 2012, Rodriguez testified that he met Lewellen in 1996. He quickly began providing Lewellen confidential information about local drug sales. Rodriguez also continued selling drugs himself, and in 1997, federal agents arrested him after discovering more than 150 pounds of marijuana in his vehicle. Lewellen, however, convinced federal law enforcement not to press charges against Rodriguez, citing his substantial cooperation with the CPD. And substantial it was-records, according to Ruiz-Cortez, show the CPD paid Rodriguez more than $800,000 for his information over the course of several years.

Rodriguez's testimony highlighted the various crimes he committed with Lewellen. Rodriguez explained, for example, that in 1998 Lewellen gave him multiple kilograms of cocaine, which he resold. The *596 same year, Rodriguez and Lewellen plotted to rob another drug dealer of $500,000 under the guise of a legitimate police stop. The two planned to repeat that crime against another dealer some months later, this time for $800,000. Rodriguez also testified that he had planted drugs on at least one unwitting person at Lewellen's behest.

Rodriguez further touched on the events that led to Ruiz-Cortez's arrest. Rodriguez testified that he knew two suppliers, Carlos Rodriguez (no relation; we will refer to him as Carlos to avoid confusion) and Lisette Venegas. In July 1999, Venegas told Rodriguez that she planned to pick up drugs from the suburbs at what turned out to be Ruiz-Cortez's home. Rodriguez shared the information with Lewellen, and he told Lewellen what kind of car Venegas would be driving to ensure that she was not arrested during the bust. This testimony formed the basis of the obstruction-of-justice charge: the government submitted that Lewellen perjured himself at Ruiz-Cortez's trial by lying about the circumstances of the arrest in order to protect Rodriguez and Venegas. Rodriguez, however, faced serious impeachment at trial; he admitted he was cooperating to avoid the death penalty or a life sentence and he had previously lied to law enforcement and the grand jury.

The jury ultimately found Lewellen guilty of conspiring to possess cocaine with intent to distribute. But it hung on the racketeering count. The government did not retry Lewellen on that count, and the district court later sentenced Lewellen to 18 years in prison.

The revelation of Lewellen's wrongdoing led the government in 2010 to move the district court to vacate Ruiz-Cortez's conviction. Recognizing that the case against Ruiz-Cortez rested almost solely on Lewellen's testimony and reports, the government noted that "there is virtually no admissible evidence of defendant's guilt." The district court granted the motion and Ruiz-Cortez was released from custody.

Ruiz-Cortez then filed this suit against Lewellen, other CPD officers, and the City. He brought a slew of claims, but the only ones relevant to this appeal sound in due process. Ruiz-Cortez asserted that the defendants deprived him of due process in two ways: by withholding exculpatory information-namely, Lewellen's crimes and his conspiracy with Rodriguez-in violation of Brady v. Maryland , 373 U.S. 83 , 83 S.Ct. 1194 , 10 L.Ed.2d 215 (1963), and by fabricating evidence against him. And, Ruiz-Cortez claimed, the City was liable under Monell v. Dep't of Social Servs. , 436 U.S. 658 , 98 S.Ct. 2018 , 56 L.Ed.2d 611 (1978), which permits liability when a municipality is directly responsible for the constitutional deprivation.

After discovery, the parties cross moved for summary judgment. The City argued that there was no issue of fact regarding its liability. Ruiz-Cortez, in response, relied heavily on the 1997 Report of the Commission for Police Integrity-or the "Webb Report," named for the Commission's Chairman, Dan Webb. The Webb Report, Ruiz-Cortez argued, highlighted for the City the dangers of police corruption, and thus, there was reason to hold the City liable for failing to act adequately in its wake. The district court, however, disagreed; it concluded that there was no issue of fact regarding the City's liability, the Webb Report notwithstanding, and so it dismissed the City from the case.

As to Lewellen's liability, the district court decided that there was an outstanding issue of fact. Lewellen had invoked his Fifth Amendment right against self-incrimination when Ruiz-Cortez sought to depose him. But the court concluded it would not draw from that invocation a conclusively adverse inference against *597 Lewellen. So the due process claims against Lewellen went to trial.

At trial, Ruiz-Cortez testified that he had been coerced by a man named Carlos into holding the cocaine and giving it to Venegas. He admitted, however, that this narrative was inconsistent with the one he advanced during his criminal trial, when he testified that he had never held the drugs and that they were planted by law enforcement.

Lewellen also took the stand, so to speak, testifying by video from prison. When asked if he lied in a police report and at trial, Lewellen stated: "as I'm currently in the process of challenging my federal case, I have been advised by my criminal lawyers to decline to answer any questions under my Fifth Amendment. Mr. Smith, I would love to testify in this ... ." Ruiz-Cortez's lawyer cut him off with an objection and the court instructed Lewellen to simply answer the question, though it did not instruct the jury to disregard Lewellen's comment about how he would "love to testify." After a few more Fifth Amendment invocations, the parties stipulated that Lewellen would assert the Fifth Amendment to all additional questions. Lewellen's testimony from Ruiz-Cortez's criminal case was also read to the jury.

Other witnesses testified, including Ruiz-Cortez's girlfriend, his sister, Venegas, and DEA agents. Ruiz-Cortez's criminal lawyer also testified, stating that federal prosecutors never shared Rodriguez's relationship with Lewellen during Ruiz-Cortez's criminal case. Rodriguez's testimony from Lewellen's prosecution was read to the jury as well (he had asserted the Fifth Amendment during his deposition). The parties then entered stipulations relating to Lewellen's criminal case: (1) Lewellen had been "indicted on charges of obstruction of justice as part of the" racketeering count, which related to his testimony in Ruiz-Cortez's prosecution; (2) the jury had hung on the racketeering count; and (3) the jury had, however, convicted Lewellen "of felony conspiracy to possess with intent to distribute cocaine."

After the presentation of the evidence, the district court held a conference to discuss jury instructions. It was off the record, for reasons unknown. But we can gather that during the conference the parties disputed how to properly instruct the jury regarding the consequences of Lewellen's Fifth Amendment invocation. Ruiz-Cortez says that he offered an instruction which stated that the jury could infer from that invocation that truthful answers would have incriminated Lewellen-that is, the jury could make an "adverse inference" against Lewellen for his invocation. Ruiz-Cortez's proposed instruction also made clear that the Fifth Amendment could only be invoked "when honest answers would tend to subject the answerer to criminal liability."

The district court rejected that instruction. It is not clear why-again, the conference was held off the record-but the parties seem to agree that the district court's decision stemmed from a belief that incrimination is not the sole basis for a Fifth Amendment invocation. The district court had, in fact, made this belief express in its motion-in-limine rulings. There, in deciding that Lewellen and his lawyers could explain Lewellen's invocation of the Fifth Amendment, the district court asserted that "potential liability" is not "the only reason a defendant may have to invoke the Fifth." So at trial the district court opted to give another instruction, as it briefly noted during a subsequent, on-the-record conference. This instruction told the jury that it could, but did not have to, draw an adverse inference from a Fifth Amendment invocation. It did not, as Ruiz-Cortez *598 wanted, instruct the jury about when a Fifth Amendment invocation is proper.

After receiving this and other instructions, and after deliberation, the jury found for Lewellen. Ruiz-Cortez then filed a motion for judgment as a matter law, Fed. R. Civ. P. 50, or alternatively a new trial, Fed. R. Civ. P. 59. The district court granted the first motion and overturned the jury's verdict, concluding that the stipulation to Lewellen's conviction required a finding that he had withheld Brady material, namely, his criminal activity. But on the City's motion for reconsideration, the district court reversed course. It decided that the stipulation did not indicate when that criminal activity had occurred-it was possible that it occurred after Ruiz-Cortez's arrest and prosecution and therefore had not been withheld-and the jury did not have to accept the other testimonial evidence. Ruiz-Cortez appealed.

II. Discussion

On appeal, Ruiz-Cortez contends that the judge erred both at summary judgment, in dismissing his Monell claim against the City, and after trial, reversing course and letting the jury's judgment for Lewellen stand. We address both contentions in turn.

A. Monell Claim Against the City

The district court dismissed the Monell claim against the City at summary judgment, so we review that decision de novo. Mollet v. City of Greenfield , 926 F.3d 894 , 896 (7th Cir. 2019). Summary judgment is appropriate when there is no genuine issue of material fact regarding liability and the movant, here the City, is entitled to judgment as a matter of law. Fed. R. Civ. P. 56(a). We interpret the record in favor of Ruiz-Cortez, as the nonmovant. Valenti v. Lawson , 889 F.3d 427 , 429 (7th Cir. 2018).

There is no respondeat superior liability for municipalities under 42 U.S.C. § 1983 . Monell , however, holds that municipalities may be liable for § 1983 claims when they are directly responsible for the constitutional deprivation. 436 U.S. at 691-94 , 98 S.Ct. 2018 . To establish that responsibility, and thus liability under Monell , a plaintiff must ultimately prove three elements: (1) a municipal action, which can be an express policy, a widespread custom, or an act by an individual with policy-making authority; (2) culpability, meaning, at a minimum, deliberate conduct; and (3) causation, which means the municipal action was the "moving force" behind the constitutional injury. See Bd. of Cty. Comm'rs of Bryan Cty., Okl. v. Brown , 520 U.S. 397 , 404-07, 117 S.Ct. 1382 , 137 L.Ed.2d 626 (1997).

At summary judgment, Ruiz-Cortez complained of two City customs: the practice of using paid, active criminals as informants and the failure to supervise informants and their officer-handlers. We can generously assume, for analytical purposes only, that both customs were widespread and attributable to the City, thus meeting the first step of Monell . (And we can also assume, again for analytical purposes only, that Ruiz-Cortez in fact suffered a Brady injury by virtue of Lewellen's failure to disclose his criminal activity.) Ruiz-Cortez's claim against the City still falters at Monell 's other steps: there is no record evidence of culpability or causation.

Start with the first custom. Even assuming that there was a custom of using paid criminal informants, that practice is not "itself" violative of any federal right, including Brady . So Ruiz-Cortez must, as he concedes, show that the City engaged in that practice with deliberate indifference to the fact that it would lead officers to violate federal law.

*599 Bryan Cty. , 520 U.S. at 406-07 , 117 S.Ct. 1382 (a plaintiff challenging municipal action that is not "itself" violative of federal law must show that the action was taken with "deliberate indifference"); Lapre v. City of Chicago , 911 F.3d 424 , 430, 434 (7th Cir. 2018) (same). But no record evidence shows that degree of culpability. The Webb Report, on which Ruiz-Cortez relies most heavily, does not conclude that the use of informants poses a constitutional hazard to civilians. Nor does Ruiz-Cortez point to others who have suffered the Brady injuries he has as a result of the custom. Accord City of Oklahoma City v. Tuttle , 471 U.S. 808 , 824, 105 S.Ct. 2427 , 85 L.Ed.2d 791 (1985) (plurality) ("[W]here the policy relied upon is not itself unconstitutional, considerably more proof than the single incident will be necessary."). Without evidence that could have put the City on notice of the Brady risks in employing informants, there is no issue of fact regarding the City's lack of culpability.

Ruiz-Cortez's first custom suffers an even greater causation problem. Causation under Monell requires a "direct causal link" between the municipal action and the constitutional injury. Bryan Cty. , 520 U.S. at 404 , 117 S.Ct. 1382 . Ruiz-Cortez has not identified such causation-related evidence, which makes sense: there is a real gap between a custom of paying criminal informants, even handsomely paying prolific informants, and Ruiz-Cortez's alleged Brady injury, which resulted from an officer's corruption. Indeed, as far as the record shows, Lewellen's rogue decision to engage in a drug conspiracy entirely gave rise to the Brady injury. The City, therefore, cannot be liable; Monell does not subject municipalities to liability for the actions of misfit employees. See Glisson v. Indiana Dep't of Corr. , 849 F.3d 372 , 379 (7th Cir. 2017) (en banc); Thomas v. Cook Cty. Sheriff's Dept. , 604 F.3d 293 , 306 (7th Cir. 2010).

Ruiz-Cortez understands causation this way: Without the custom, there would have been no long-term relationship between Lewellen and Rodriguez; and without the Lewellen-Rodriguez relationship, Lewellen would not have engaged in a drug conspiracy and other crimes with Rodriguez-the impeachment evidence Lewellen failed to disclose in violation of Brady . That reasoning, however, amounts only to a showing of but-for causation, which does not suffice under Monell . Wilson v. Cook Cty. , 742 F.3d 775 , 784 (7th Cir. 2014).

Ruiz-Cortez's second custom fares no better. Failure-to-supervise claims, like failure-to-train claims, are a "tenuous" form of Monell liability. Connick v. Thompson , 563 U.S. 51 , 61, 131 S.Ct. 1350 , 179 L.Ed.2d 417 (2011). This is because such claims seek to hold a municipality liable not for directly inflicting injury, as was the case in Monell , but rather for causing an employee's misconduct. See Bryan Cty. , 520 U.S. at 405 , 117 S.Ct. 1382 ; see also Tuttle , 471 U.S. at 822-23 , 105 S.Ct. 2427 . Municipal failure claims are thus available only in "limited circumstances," City of Canton, Ohio v. Harris , 489 U.S. 378 , 387, 109 S.Ct. 1197 , 103 L.Ed.2d 412 (1989), and they are subject to "rigorous" fault and causation requirements, Bryan Cty. , 520 U.S. at 405 , 117 S.Ct. 1382 . As to fault, here too Ruiz-Cortez must show deliberate indifference. See Connick , 563 U.S. at 61 , 131 S.Ct. 1350 ; Alexander v. City of S. Bend , 433 F.3d 550 , 557 (7th Cir. 2006).

Ruiz-Cortez's failure-to-supervise claim does not meet these high requirements. There is, to start, no issue of fact relating to the City's deliberate indifference. The record does not contain evidence that would have, or should have, notified the City that the informant-handler relationship *600 would devolve into a drug conspiracy and give rise to Brady problems. See Miranda v. Cty. of Lake , 900 F.3d 335 , 345 (7th Cir. 2018). Most conspicuously absent: any evidence that others, besides Lewellen, committed Brady violations like the ones Ruiz-Cortez allegedly suffered. That kind of evidence is normally required for a failure-to-supervise or a failure-to-train claim. Connick , 563 U.S. at 62 , 131 S.Ct. 1350 .

Ruiz-Cortez again cites the Webb Report. But that report, as we explained earlier, deals with police corruption and narcotics crimes generally. It does not criticize the use of criminal informants or mention potential Brady violations. Ruiz-Cortez also emphasizes the magnitude of Rodriguez's work and pay: more than sixty cases worked (most of which occurred after he was caught with bales of marijuana in 1996) and pay totaling about $800,000. Should that record have raised eyebrows? Probably. But it is a stretch to assert, as Ruiz-Cortez does, that Rodriguez's record put the City on notice of the high probability of the injury Ruiz-Cortez eventually suffered. See Connick , 563 U.S. at 61-62 , 131 S.Ct. 1350 . Lewellen's crimes, not Rodriguez's exploits, caused the alleged Brady violation, and nothing presented suggests that an informant's prolific and well-paid record alone indicates that a handler may become so criminally corrupt as to create Brady risks. The record instead shows, at most, negligent supervision on the City's part, but negligence does not suffice under Monell . Bryan Cty. , 520 U.S. at 407 , 117 S.Ct. 1382 .

There is a causation problem, too. Ruiz-Cortez relies again on a but-for line of reasoning, which is insufficient. And the requisite "moving force" causation cannot be reasonably inferred from this record. A municipality's failure to supervise handlers and informants is one thing; it is entirely another for those handlers and informants to conspire to deal drugs, as happened here.

Moving away from Monell 's teachings, Ruiz-Cortez makes a final, novel argument. He contends the district court should not have dismissed the City at summary judgment because it left the jury to decide the Brady claim against Lewellen without learning about the "landscape" of the CPD's corrupt history. This is not an evidentiary argument; Ruiz-Cortez does not argue that the CPD's history was relevant to his Brady claim against Lewellen. See Fed. R. Evid. 401, 402. The argument is instead an end-run to Monell : even if there is no claim against the City, Ruiz-Cortez believes, the City needed to be put on trial to understand its employee's misconduct. Monell is not so easily avoided.

The district court, therefore, correctly dismissed Ruiz-Cortez's Monell claim at summary judgment.

B. Brady Claim Against Lewellen

We move from summary judgment to trial. Ruiz-Cortez challenges the district court's denial of his posttrial motions for judgment as a matter of law (after reconsideration), Fed. R. Civ. P. 50, and for a new trial, Fed. R. Civ. P. 59. Both motions asked the district court to upset the jury's finding that Lewellen did not violate Brady .

Under Brady , "a defendant's due process rights are violated if the state withholds favorable evidence from the defense that is material to the defendant's guilt or punishment." Sims v. Hyatte , 914 F.3d 1078 , 1087 (7th Cir. 2019). The strain of Brady relevant here is Giglio v. United States , 405 U.S. 150 , 92 S.Ct. 763 , 31 L.Ed.2d 104 (1972), which extends Brady 's holding about exculpatory evidence to "material *601 impeachment evidence." Thompson v. City of Chicago , 722 F.3d 963 , 972 (7th Cir. 2013) ; see also United States v. Bagley , 473 U.S. 667 , 676, 105 S.Ct. 3375 , 87 L.Ed.2d 481 (1985) (rejecting a "distinction between impeachment evidence and exculpatory evidence" under Brady ). Brady applies even if evidence is known only to police officers. Youngblood v. W. Virginia , 547 U.S. 867 , 869, 126 S.Ct. 2188 , 165 L.Ed.2d 269 (2006) ; see also Coleman v. City of Peoria, Ill. , 925 F.3d 336 , 349 (7th Cir. 2019).

Ruiz-Cortez's claim at trial was that Lewellen violated Brady by failing to disclose his corruption and criminal conduct. These facts, as even Lewellen concedes, could have significantly impeached Lewellen's credibility when he acted as the key witness in Ruiz-Cortez's earlier criminal prosecution. See, e.g. , Wearry v. Cain , --- U.S. ----, 136 S. Ct. 1002 , 1007, 194 L.Ed.2d 78 (2016) (withholding impeachment evidence of state's star witness violated Brady ).

1. Rule 50 : Judgment as a Matter of Law

With the Brady rights established, we first turn to the motion for judgment as a matter of law. We review the district court's decision to deny Ruiz-Cortez's Rule 50 motion de novo. Martin v. Milwaukee Cty. , 904 F.3d 544 , 550 (7th Cir. 2018).

Rule 50 states that after a jury verdict a district court may "direct the entry of judgment as a matter of law" if "a reasonable jury would not have a legally sufficient evidentiary basis to find" as the actual jury did. Fed. R. Civ. P. 50(a), (b). This is a high bar. In our Rule 50 review, we give the nonmovant "the benefit of every inference" while refraining from weighing for ourselves the credibility of evidence and testimony. Equal Employment Opportunity Comm'n v. Costco Wholesale Corp. , 903 F.3d 618 , 621 (7th Cir. 2018). We look at the entire trial record, but we must "disregard all evidence favorable" to the movant that "the jury is not required to believe." Reeves v. Sanderson Plumbing Prod., Inc. , 530 U.S. 133 , 150-51, 120 S.Ct. 2097 , 147 L.Ed.2d 105 (2000). This means, in practice, that we accept all evidence in the nonmovant's favor plus the "uncontradicted and unimpeached" testimony from "disinterested" witnesses and, as in this case, the parties' stipulations. Id. Only if no rational jury could have found for the nonmovant may we disturb the jury's verdict. United States v. Funds in the Amount of One Hundred Thousand & One Hundred Twenty Dollars ($100,120.00) , 901 F.3d 758 , 770 (7th Cir. 2018).

Ruiz-Cortez cannot meet Rule 50 's high bar. For Lewellen to have violated Ruiz-Cortez's Brady rights, he must have been conspiring with Rodriguez before Ruiz-Cortez's prosecution-otherwise there was no impeachment material to disclose. But no undisputed evidence established that fact, as Lewellen pointed out in his motion for reconsideration. The stipulations, most notably, did not date the start of Lewellen's crimes. So reading the record in Lewellen's favor, as we must, the jury could have believed that whatever crimes Lewellen committed, he committed after Ruiz-Cortez's prosecution. Or at a minimum, the jury could have concluded that Ruiz-Cortez, the claimant, had not borne his burden to show otherwise.

To be sure, Rodriguez testified to crimes he committed with Lewellen before Ruiz-Cortez's prosecution. In 1998, Rodriguez claimed, Lewellen gave him two kilograms of cocaine, and not long after the pair robbed a drug dealer together. Ruiz-Cortez makes much of this testimony-but the jury was not required to believe it. See Reeves , 530 U.S. at 150-51 , 120 S.Ct. 2097 .

*602 Rodriguez was not a disinterested party; he was a cooperator during Lewellen's prosecution. Nor was his testimony unimpeached; he admitted to perjuring himself before the grand jury, to say nothing of his long rap sheet. The jury, therefore, was not required to accept his testimony. Most of Ruiz-Cortez's remaining Rule 50 arguments ask us to reweigh the evidence, which we cannot do.

A different argument from Ruiz-Cortez is worth addressing. At times in his brief, he seems to stray from his core Brady claim and argue that the impeachment evidence was not Lewellen's corruption but rather his use of Rodriguez, a well-paid criminal informant, to arrest Ruiz-Cortez. This alternative theory presents a different obstacle for Ruiz-Cortez: even assuming that Rodriguez's involvement constituted impeachment evidence, the jury could have reasonably found that it was immaterial under Brady . Evidence is material under Brady "if there is a reasonable probability that, had the evidence been disclosed to the defense, the result of the proceeding would have been different." Strickler v. Greene , 527 U.S. 263 , 280, 119 S.Ct. 1936 , 144 L.Ed.2d 286 (1999) (quoting Bagley , 473 U.S. at 682 , 105 S.Ct. 3375 ). Ruiz-Cortez offers no explanation as to why the jury had to accept that his prosecution could have come out differently if Rodriguez's use had been highlighted at his trial. We do not see one either. Criminal informants are commonplace in drug investigations.

A rational jury could have found, based on the evidence it was required to accept, that Ruiz-Cortez had not carried his burden of showing that Lewellen violated Brady . The district court was thus correct to deny Ruiz-Cortez's motion for judgment as a matter of law.

2. Rule 59 : New Trial

Ruiz-Cortez's motion for a new trial is a different matter. We review the district court's denial of that motion for an abuse of discretion, keeping in mind that a legal error can amount to an abuse of discretion. Martinez v. City of Chicago , 900 F.3d 838 , 844 (7th Cir. 2018) ; United States v. Dessart , 823 F.3d 395 , 404 (7th Cir. 2016).

Rule 59 differs from Rule 50. See Mejia v. Cook Cty. , 650 F.3d 631 , 634 (7th Cir. 2011). Unlike Rule 50, a new trial under Rule 59 may be based on "any reason" recognized by federal law. Fed. R. Civ. P. 59(a)(1)(A). This most commonly takes one of two forms: the trial was fundamentally unfair to the movant or the jury's verdict went against the manifest weight of the evidence. Venson v. Altamirano , 749 F.3d 641 , 646 (7th Cir. 2014). Ruiz-Cortez argues that both happened. We begin and end with his argument about unfairness. When errors occurred and the trial was fundamentally unfair as a result, a new trial is appropriate. Christmas v. City of Chicago , 682 F.3d 632 , 643 (7th Cir. 2012).

According to Ruiz-Cortez, the problem started just before trial. The district court ruled in limine that "potential liability" is not "the only reason a defendant may have to invoke the Fifth." It therefore concluded that Lewellen and his lawyers could explain at trial that Lewellen's Fifth Amendment invocation was grounded in reasons other than "the good faith belief that truthful answers may tend to incriminate." At trial, Lewellen followed suit: he invoked his Fifth Amendment right but quickly explained that he would "love to testify" if his criminal case was not on appeal. Ruiz-Cortez's lawyer made an objection, which the court sustained, but it did not instruct the jury to disregard Lewellen's explanation.

*603 The district court's premise was faulty. Witnesses do not enjoy "carte blanche ... to refuse to answer questions." In re High Fructose Corn Syrup Antitrust Litig. , 295 F.3d 651 , 663-64 (7th Cir. 2002). The only valid reason to invoke the Fifth Amendment is a reasonable fear that truthful answers may incriminate the witness. As we have said: "To be privileged ... the answer one would give if one did answer it (and answer it truthfully) must have some tendency to subject the person being asked the question to criminal liability." Id. at 663-64 (emphases added and omitted). The Supreme Court has repeatedly made the same point: "To qualify for the Fifth Amendment privilege, a communication must be testimonial, incriminating , and compelled." Hiibel v. Sixth Judicial Dist. Court of Nevada, Humboldt Cty. , 542 U.S. 177 , 189, 124 S.Ct. 2451 , 159 L.Ed.2d 292 (2004) (emphasis added); see also Fisher v. United States , 425 U.S. 391 , 408, 96 S.Ct. 1569 , 48 L.Ed.2d 39 (1976) (the privilege "applies only when the accused is compelled to make a Testimonial Communication that is incriminating"); Hoffman v. United States , 341 U.S. 479 , 486, 71 S.Ct. 814 , 95 L.Ed. 1118 (1951) (the "protection must be confined to instances where the witness has reasonable cause to apprehend danger from a direct answer"); see also 1 McCormick On Evid. § 120 (7th ed. 2016) ("The privilege applies only if compelled action is incriminating"). It is, of course, a privilege against self-incrimination, not inconvenience or embarrassment.

Lewellen defends the district court's error by citing Evans v. City of Chicago , 513 F.3d 735 (7th Cir. 2008). There, in addressing whether a defendant invoked the Fifth Amendment in bad faith, we said: "denying wrongdoing is different than admitting that there was no basis for invoking the Fifth Amendment." Id. at 744 . The statement is undoubtedly true; a witness may believe that she is innocent but nevertheless recognize that a truthful answer may make her look guilty. That, however, is not what happened here. Lewellen asserted that he had nothing to hide and would testify but for his ongoing, extraneous litigation, unlike the witness in Evans . That is not a valid excuse under the Fifth Amendment.

Lewellen also downplays his errant explanation, but it clearly mattered. When a defendant in a civil case invokes the Fifth Amendment, juries are permitted, but not required, to draw a negative inference against the defendant. E.g. , Baxter v. Palmigiano , 425 U.S. 308 , 318, 96 S.Ct. 1551 , 47 L.Ed.2d 810 (1976) ; Thompson v. City of Chicago , 722 F.3d 963 , 976 (7th Cir. 2013). Key to the trial was whether the jury would draw such an inference against Lewellen and find that he sat on evidence of his crimes in violation of Brady . And key to the jury's decision was its understanding of when a defendant may properly invoke the Fifth Amendment. If the jury believed that Lewellen could invoke the Fifth Amendment on the simple ground that there was other ongoing litigation-and not because truthful answers may have incriminated him, as Lewellen indicated-the jury was almost certainly less likely to penalize Lewellen for his invocation.

Perhaps the error would not have misled the jury if there had been a clarifying instruction. The district court, however, did not give one during or after Lewellen's testimony, and it rejected Ruiz-Cortez's effort to explain to the jury when a Fifth Amendment invocation is proper. The court opted instead not to instruct the jury on the Fifth Amendment's limits, telling the jury only that it could, but did not have to, infer from Lewellen's assertion that his answers "would have been adverse." We do not quarrel with this instruction in the *604 abstract. 1 Cf. Empress Casino Joliet Corp. v. Balmoral Racing Club, Inc. , 831 F.3d 815 , 834 (7th Cir. 2016) (approving of a similar instruction); Evans , 513 F.3d at 741 (similar). But in this case, with Lewellen's innocent but improper explanation firmly on the record, the jury could well have mistakenly believed that extraneous litigation was a valid reason to invoke the Fifth Amendment.

As we noted earlier, we cannot be sure why the district court rejected Ruiz-Cortez's explanatory instruction because the conference was held off the record. (Ruiz-Cortez later stated his objection on the record, which was wise for preservation purposes, but that part of the transcript does not detail the district court's reasoning.) When critical moments of a trial happen off the record, it makes appellate review difficult. A court should make every reasonable effort to ensure there is a record for its decisions. See also 28 U.S.C. § 753 (b) (describing when court reporters must transcribe court proceedings). And litigants should remember their obligation to develop a record. Accord Fed. R. App. P. 10 ; McBride v. Hanks , 202 F.3d 274 (7th Cir. 1999). Yet even with a missing record, here, we have little trouble concluding that Lewellen's explanation plus a noncorrective jury instruction led to an unfair trial for Ruiz-Cortez.

Lewellen also makes an argument about Brady materiality, which is really one about harmless error. Setting aside Lewellen's "love to testify" statement and the instruction, Lewellen argues, the evidence at trial allowed the jury to conclude that Lewellen's crimes were not material in Ruiz-Cortez's prosecution. Recall that materiality under Brady requires only a "reasonable probability" that the result would be different. Where, as here, the impeachment evidence is about the government's star witness, it is often material. See, e.g. , Wearry , 136 S. Ct. at 1007 ; Kyles v. Whitley , 514 U.S. 419 , 441-42, 115 S.Ct. 1555 , 131 L.Ed.2d 490 (1995). Even more importantly, here, the prosecution itself conceded materiality. In moving to vacate Ruiz-Cortez's conviction, the government admitted that, with Lewellen's crimes in the open, there was "virtually no admissible evidence of defendant's guilt." When the government admits that a prosecution should not have even happened, materiality is not a close call. 2

We do not order a new trial lightly. See, e.g. , Thompson , 722 F.3d at 980 . And we, of course, recognize the skill and experience of the district court overseeing this case. The errors that played out at trial, however, misinformed the jury about the central question it faced: whether to infer from Lewellen's invocation that he was, in fact, corrupt when he testified against Ruiz-Cortez. It had been told, contrary to *605 the law, that extraneous litigation was reason enough to invoke the Fifth Amendment, and no correction was ever made. No doubt a "significant chance exists" that those errors "affected the outcome of the trial," especially in light of the evidence of Lewellen's corruption before Ruiz-Cortez's prosecution. Mihailovich v. Laatsch , 359 F.3d 892 , 913 (7th Cir. 2004). Because we order a new trial on these grounds, we need not address Ruiz-Cortez's remaining Rule 59 arguments.

III. Conclusion

For these reasons, we affirm the dismissal of the claims against the City. We vacate the judgment in favor of Lewellen and remand for a new trial.