Ronald Coleman is a former Chicago police officer who turned to crime. In June 2014, he was assigned to a federal drug investigation task force, which was about to execute numerous search and arrest warrants. Shortly before the operations were set to begin, Coleman telephoned one of the targets-a high school acquaintance-to warn him about the raid. That call led to a single charge of obstruction of justice, in violation of 18 U.S.C. § 1512 (c)(2), and the end of Coleman's law-enforcement career when a jury convicted him. Coleman now argues that he is entitled to a new trial for two primary reasons: evidentiary errors, and the government's use of allegedly perjured testimony. He also urges that the district court committed procedural and substantive errors when selecting his sentence. Because we find no prejudicial error in any of the district court's rulings, we affirm both the conviction and the sentence.

I

Coleman is a lifelong Chicagoan who grew up to become an officer with the Chicago Police Department. In high school, he met cousins Dewan Davis and LaRon Conway. Though Coleman was not close with either of these men after high school, he maintained a casual friendship with them.

In 2014, Coleman served on the team conducting a federal drug investigation dubbed Operation Five Leaf Clover ("the Operation"). In time, the Operation began to focus on several people whom Coleman knew, including Davis. Although Davis was never a target of the Operation, he was identified as an associate of a heroin supplier named Rodney Bedenfield. In June 2014 the Operation was preparing to execute approximately 10 search warrants and numerous arrest warrants. But things went awry when, shortly before the bust, the targets learned about it.

Conway testified that while he was at work on June 9, 2014, he received a call from an unknown woman who told him to call Coleman. This call does not appear in Conway's personal phone records. Conway testified that when he followed the woman's instructions and called Coleman, Coleman warned him about the impending searches and told him to pass the message along to Davis. (Coleman admits that this call took place, but he told the jury that it was about setting up a Father's Day picnic.) Conway did what he was told and warned Davis about the looming raid. Unbeknownst to Coleman, however, the task force knew that something was amiss. The Operation had wiretapped numerous phones as part of its investigation, and so when Davis predictably called Bedenfield, *511 officers heard the two men say that someone "on the task force" had given them a warning call. Davis testified that he understood this person to be Coleman.

After Coleman's warning, Bedenfield moved contraband to a house that the Operation had not known about before. Because they had intercepted the warning, however, officers were monitoring Bedenfield when this move occurred. The Operation then obtained a search warrant for the new house and recovered the contraband placed there.

Based on the warning call, the grand jury indicted Coleman on one count of obstruction of justice. On August 10, 2017, a jury convicted him on that charge. The district court later denied his motion for a new trial and sentenced him to 60 months' imprisonment. On appeal, Coleman raises four objections-two related to the conviction, and two to the sentence.

II

A

Coleman first complains that the government improperly elicited testimony from Conway to the effect that he lied in his initial interviews with law-enforcement agents because he feared retaliation from the Chicago Police Department. Although he objected to this testimony at trial, the ground for that objection was relevance. FED. R. EVID. 401. On appeal, he has gone further and asserted that Conway's testimony was so prejudicial that it deprived him of a fair trial.

We assess the district court's handling of Coleman's relevance objection only for abuse of discretion. United States v. Phillips , 596 F.3d 414 , 416 (7th Cir. 2010). Conway's testimony falls into the category of "threat evidence." We have held that this type of evidence " 'can be relevant to explain a witness' inconsistent statements.' " United States v. Thompson , 359 F.3d 470 , 477 (7th Cir. 2004) (quoting United States v. Thomas , 86 F.3d 647 , 654 (7th Cir. 1996) ). That theory fits these facts. Conway made numerous inconsistent statements to investigators in his earlier interviews. The government thus needed to explain why he had lied, and the threat testimony served that purpose. The district court thus acted within its discretion when it refused to sustain Coleman's objection.

As for the due-process argument, Coleman faces a more difficult standard of review. Because he never made this argument in the district court, we review it only for plain error. See United States v. Saunders , 826 F.3d 363 , 370-71 (7th Cir. 2016).

It is not clear to us that it was error at all to admit this evidence, much less that any such error was so serious that Coleman "probably would not have been convicted but for the error." United States v. Curtis , 280 F.3d 798 , 801 (7th Cir. 2002).

We can assume for present purposes that Conway's testimony was likely to be highly prejudicial. And the prejudice may have been compounded because Conway did not allege a specific threat of retaliation by any member of the Chicago Police Department-just vague fears based on rumors or stories he had supposedly heard. But because Coleman never objected on this basis, the district court was never alerted to the need to weigh the legitimate use of this evidence against its weaknesses and incendiary nature. See United States v. Cox , 536 F.3d 723 , 728 (7th Cir. 2008). Indeed, the amorphous nature of the threats Conway described might have caused the district court to think that Coleman had a strategic reason for not objecting to that evidence, such as *512 a preference for attacking the weaknesses in Conway's story on cross-examination.

Even if the district court did not surmise that Coleman was intentionally refraining from objecting on due-process grounds, the court's failure to strike this testimony sua sponte or to take other remedial action was not plain error. Cf . id. (holding that two government witnesses' testimony that the defendant cooked methamphetamine using the "Nazi method" was not so prejudicial as to create plain error even though it "had almost no probative value"). Furthermore, Coleman had ample opportunity to attack Conway's testimony on cross-examination and in closing argument.

Coleman also argues that Conway's testimony about retaliation was prompted by an improper leading question. He is correct that the government's question, "Were you afraid for you[r] family?" was leading and thus generally improper on direct examination. The government's contention to the contrary in this court is simply wrong. A question is leading when it suggests the answer the witness should give. "Since [fearing for one's family] is unusual, the question would be unlikely to be asked unless an affirmative answer was expected." United States v. Cephus , 684 F.3d 703 , 708 (7th Cir. 2012). But even when they are improper, leading questions rarely give rise to plain error. See United States v. Durham , 645 F.3d 883 , 891 (7th Cir. 2011). This is because "in the face of a sustained objection, most lawyers can rephrase a leading question to elicit the desired testimony." Id. That is especially likely when the leading question elicits the same response that a witness would have given if asked a neutral question. See United States v. Miller , 782 F.3d 793 , 799-800 (7th Cir. 2015). In this case, Conway had previously told investigators that he feared retaliation from the Chicago Police Department, and so there is no reason to think that the government's leading question changed his testimony. We thus find no reversible error in the district court's failure to take some action with respect to Conway's retaliation testimony.

B

Coleman also asserts that he should receive a new trial because the government knowingly used perjured testimony. He is referring to Conway's description of the call he received from the unknown woman; that call set in motion the chain of calls warning the suspects about the impending raids. A defendant seeking a new trial because of the use of perjured testimony must show: "(1) the prosecution's case included perjured testimony; (2) the prosecution knew, or should have known, of the perjury; and (3) there is a likelihood that the false testimony affected the judgment of the jury." United States v. Saadeh , 61 F.3d 510 , 523 (7th Cir. 1995).

It is doubtful that Coleman can meet even the first of these criteria. All we know is that the phone call from the unknown woman to Conway did not show up on Conway's personal phone records. But there may have been other phones available, such as a work phone. And the lack of a record was not something the government was trying to hide. To the contrary, it was the government that introduced the phone records that undercut Conway's story. That fact is also inconsistent with Coleman's theory that the government was engaged in the knowing use of perjured testimony.

And there is yet another problem with this line of argument: even if the government knew (or should have known) that Conway was giving false testimony about the woman's call, so did Coleman. During closing argument, Coleman used Conway's *513 testimony about the call from the mysterious, unidentified woman to argue that Conway was a liar whom the jury should not believe. When a defendant has, and takes advantage of, the opportunity to cross-examine, discredit, and expose a witness's perjury, the likelihood that perjured testimony will have "affected the judgment of the jury" is greatly diminished. See id. ; see also Long v. Pfister , 874 F.3d 544 , 549 (7th Cir. 2017) ( en banc ) (suggesting that when "the prosecutor fails to correct a falsehood, but the defense knows about that falsehood and corrects it ... there is no constitutional violation"). The district court did not abuse its discretion in refusing to grant a new trial for this reason.

III

Finally, we turn to Coleman's complaints about his sentence. He first argues that the district court erroneously found that he perjured himself when he testified at trial that his phone call with Conway was about a Father's Day picnic, and then imposed an enhancement under the Sentencing Guidelines for obstruction of justice. U.S.S.G. § 3C1.1. Second, he argues that his 60-month sentence is unreasonable and a violation of the Eighth Amendment to the U.S. Constitution.

We review the district court's findings in support of the obstruction enhancement deferentially. United States v. Cherry , 855 F.3d 813 , 815-16 (7th Cir. 2017). We find the court's decision well supported. When relying on perjured testimony for the application of the section 3C1.1 offense-level enhancement, "the district court should make a finding as to all the factual predicates necessary for a finding of perjury: false testimony, materiality, and willful intent." United States v. Chychula , 757 F.3d 615 , 619 (7th Cir. 2014) (quoting United States v. Riney , 742 F.3d 785 , 790 (7th Cir. 2014) ). Coleman's version of the telephone call was inconsistent with the other testimony. More importantly, it was the jury's prerogative to decide whom to believe, and the jury chose not to believe Coleman. The district court found that Coleman's testimony was "calculated to confuse the jury," but that it was a lie "not very well told." Coleman offers no reason to overturn these assessments.

We need say only a word or two about Coleman's arguments that his sentence is substantively unreasonable and unconstitutional. The fact that he can point to other cases in which law-enforcement officers have committed crimes and received lower sentences tells us very little, especially since it appears that none of his comparators was convicted of obstruction of justice. Coleman's sentence was 37 months below the recommended guidelines range for someone with an offense level of 30 and a criminal-history category of I (97 to 121 months). Indeed, even without the obstruction enhancement, his sentence would have been 28 months below the recommended guidelines range. "We presume the district court's imposition of a below-[g]uidelines sentence to be reasonable." United States v. Jones , 696 F.3d 695 , 699 (7th Cir. 2012). Coleman offers no reason why that presumption has been overcome here.

Because his sentence was reasonable, it also falls well outside the Eighth Amendment's prohibition on cruel and unusual punishments. See id. ("If the sentence is within the statutory limits, a claim of cruel and unusual punishment is normally without merit."); see also Harmelin v. Michigan , 501 U.S. 957 , 965, 111 S.Ct. 2680 , 115 L.Ed.2d 836 (1991) ("[T]he Eighth Amendment contains no proportionality guarantee.").

* * *

*514 We AFFIRM Coleman's conviction and sentence.