Justice SCALIA delivered the opinion of the Court.

The Supreme Court of Kansas vacated the death sentences of Sidney Gleason and brothers Reginald and Jonathan Carr. Gleason killed one of his co-conspirators and her boyfriend to cover up the robbery of an elderly man. The Carrs' notorious Wichita crime spree culminated in the brutal rape, robbery, kidnaping, and execution-style shooting of five young men and women. We first consider whether the Constitution required the sentencing courts to instruct the juries that mitigating circumstances "need not be proved beyond a reasonable doubt." And second, whether the Constitution required severance of the Carrs' joint sentencing proceedings.

I

A

Less than one month after Sidney Gleason was paroled from his sentence for attempted voluntary manslaughter, he joined a conspiracy to rob an elderly man at knifepoint.1 Gleason and a companion "cut up" the elderly man to get $10 to $35 and a box of cigarettes. 299 Kan. 1127, 1136, 329 P.3d 1102, 1115 (2014). Fearing that their female co-conspirators would snitch, Gleason and his cousin, Damien Thompson, set out to kill co-conspirator Mikiala Martinez. Gleason shot and killed Martinez's boyfriend, and then Gleason and Thompson drove Martinez to a rural location, where Thompson strangled her for five minutes and then shot her in the chest, Gleason standing by and providing the gun for the final shot.

The State ultimately charged Gleason with capital murder for killing Martinez and her boyfriend, first-degree premeditated murder of the boyfriend, aggravating kidnaping of Martinez, attempted first-degree murder and aggravated robbery of the elderly man, and criminal possession of a firearm. He was convicted on all counts except the attempted first-degree murder charge. Id., at 1134-1135, 1146, 329 P.3d, at 1114, 1120. The jury also found that the State proved beyond a reasonable doubt the existence of four aggravating circumstances and unanimously agreed to a sentence of death. Id., at 1146-1147, 329 P.3d, at 1120-1121.

B

In December 2000, brothers Reginald and Jonathan Carr set out on a crime spree culminating in the Wichita Massacre.2 On the night of December 7, Reginald Carr and an unknown man carjacked Andrew Schreiber, held a gun to his head, and forced him to make cash withdrawals at various ATMs.

On the night of December 11, the brothers followed Linda Ann Walenta, a cellist for the Wichita symphony, home from orchestra practice. One of them approached her vehicle and said he needed help. When she rolled down her window, he pointed a gun at her head. When she shifted into reverse to escape, he shot her three times, ran back to his brother's car, and fled the scene. One of the gunshots severed Walenta's spine, and she died one month later as a result of her injuries.

On the night of December 14, the brothers burst into a triplex at 12727 Birchwood, where roommates Jason, Brad, and Aaron lived. Jason's girlfriend, Holly, and Heather, a friend of Aaron's, were also in the house. Armed with handguns and a golf club, the brothers forced all five into Jason's bedroom. They demanded that they strip naked and later ordered them into the bedroom closet. They took Holly and Heather from the bedroom, demanded that they perform oral sex and digitally penetrate each other as the Carrs looked on and barked orders. They forced each of the men to have sex with Holly and then with Heather. They yelled that the men would be shot if they could not have sex with the women, so Holly — fearing for Jason's life — performed oral sex on him in the closet before he was ordered out by the brothers.

Jonathan then snatched Holly from the closet. He ordered that she digitally penetrate herself. He set his gun between her knees on the floor. And he raped her. Then he raped Heather.

Reginald took Brad, Jason, Holly, and Aaron one-by-one to various ATMs to withdraw cash. When the victims returned to the house, their torture continued. Holly urinated in the closet because of fright. Jonathan found an engagement ring hidden in the bedroom that Jason was keeping as a surprise for Holly. Pointing his gun at Jason, he had Jason identify the ring while Holly was sitting nearby in the closet. Then Reginald took Holly from the closet, said he was not going to shoot her yet, and raped her on the dining-room floor strewn with boxes of Christmas decorations. He forced her to turn around, ejaculated into her mouth, and forced her to swallow. In a nearby bathroom, Jonathan again raped Heather and then again raped Holly.

At 2 a.m. — three hours after the mayhem began — the brothers decided it was time to leave the house. They attempted to put all five victims in the trunk of Aaron's Honda Civic. Finding that they would not all fit, they jammed the three young men into the trunk. They directed Heather to the front of the car and Holly to Jason's pickup truck, driven by Reginald. Once the vehicles arrived at a snow-covered field, they instructed Jason and Brad, still naked, and Aaron to kneel in the snow. Holly cried, "Oh, my God, they're going to shoot us." Holly and Heather were then ordered to kneel in the snow. Holly went to Jason's side; Heather, to Aaron.

Holly heard the first shot, heard Aaron plead with the brothers not to shoot, heard the second shot, heard the screams, heard the third shot, and the fourth. She felt the blow of the fifth shot to her head, but remained kneeling. They kicked her so she would fall face-first into the snow and ran her over in the pickup truck. But she survived, because a hair clip she had fastened to her hair that night deflected the bullet. She went to Jason, took off her sweater, the only scrap of clothing the brothers had let her wear, and tied it around his head to stop the bleeding from his eye. She rushed to Brad, then Aaron, and then Heather.

Spotting a house with white Christmas lights in the distance, Holly started running toward it for help — naked, skull shattered, and without shoes, through the snow and over barbed-wire fences. Each time a car passed on the nearby road, she feared it was the brothers returning and camouflaged herself by lying down in the snow. She made it to the house, rang the doorbell, knocked. A man opened the door, and she relayed as quickly as she could the events of the night to him, and minutes later to a 911 dispatcher, fearing that she would not live.

Holly lived, and retold this play-by-play of the night's events to the jury. Investigators also testified that the brothers returned to the Birchwood house after leaving the five friends for dead, where they ransacked the place for valuables and (for good measure) beat Holly's dog, Nikki, to death with a golf club.

The State charged each of the brothers with more than 50 counts, including murder, rape, sodomy, kidnaping, burglary, and robbery, and the jury returned separate guilty verdicts. It convicted Reginald of one count of kidnaping, aggravated robbery, aggravated battery, and criminal damage to property for the Schreiber carjacking, and one count of first-degree felony murder for the Walenta shooting. Jonathan was acquitted of all counts related to the Schreiber carjacking but convicted of first-degree felony murder for the Walenta shooting. For the Birchwood murders, the jury convicted each brother of 4 counts of capital murder, 1 count of attempted first-degree murder, 5 counts of aggravated kidnaping, 9 counts of aggravated robbery, 20 counts of rape or attempted rape, 3 counts of aggravated criminal sodomy, 1 count each of aggravated burglary and burglary, 1 count of theft, and 1 count of cruelty to animals. The jury also convicted Reginald of three counts of unlawful possession of a firearm. 300 Kan. 1, 15-16, 331 P.3d 544, 573-574 (2014).

The State sought the death penalty for each of the four Birchwood murders, and the brothers were sentenced together. The State relied on the guilt-phase evidence, including Holly's two days of testimony, as evidence of four aggravating circumstances: that the defendants knowingly or purposely killed or created a great risk of death to more than one person; that they committed the crimes for the purpose of receiving money or items of monetary value; that they committed the crimes to prevent arrest or prosecution; and that they committed the crimes in an especially heinous, atrocious, or cruel manner. Id., at 258-259, 331 P.3d, at 708. After hearing each brother's case for mitigation, the jury issued separate verdicts of death for Reginald and Jonathan. It found unanimously that the State proved the existence of the four aggravating circumstances beyond a reasonable doubt and that those aggravating circumstances outweighed the mitigating circumstances, justifying four separate verdicts of death for each brother for the murders of Jason, Brad, Aaron, and Heather. App. in No. 14-449 etc., pp. 461-492.

C

The Kansas Supreme Court vacated the death penalties in both cases. It held that the instructions used in both Gleason's and the Carrs' sentencing violated the Eighth Amendment because they "failed to affirmatively inform the jury that mitigating circumstances need only be proved to the satisfaction of the individual juror in that juror's sentencing decision and not beyond a reasonable doubt." 299 Kan., at 1196, 329 P.3d, at 1147 (Gleason); 300 Kan., at 303, 331 P.3d, at 733 (Reginald Carr); 300 Kan. 340, 369-370, 329 P.3d 1195, 1213 (2014) (Jonathan Carr). Without that instruction, according to the court, the jury "was left to speculate as to the correct burden of proof for mitigating circumstances, and reasonable jurors might have believed they could not consider mitigating circumstances not proven beyond a reasonable doubt." 299 Kan., at 1197, 329 P.3d, at 1148. This, the court concluded, might have caused jurors to exclude relevant mitigating evidence from their consideration. Ibid.

The Kansas Supreme Court also held that the Carrs' death sentences had to be vacated because of the trial court's failure to sever their sentencing proceedings, thereby violating the brothers' Eighth Amendment right "to an individualized capital sentencing determination." 300 Kan., at 275, 331 P.3d, at 717, 300 Kan., at 368, 329 P.3d, at 1212. According to the court, the joint trial "inhibited the jury's individualized consideration of [Jonathan] because of family characteristics tending to demonstrate future dangerousness that he shared with his brother"; and his brother's visible handcuffs prejudiced the jury's consideration of his sentence. 300 Kan., at 275, 331 P.3d, at 717. As for Reginald, he was prejudiced, according to the Kansas Supreme Court, by Jonathan's portrayal of him as the corrupting older brother. Id., at 276, 331 P.3d, at 717. Moreover, Reginald was prejudiced by his brother's cross-examination of their sister, who testified that she thought Reginald had admitted to her that he was the shooter. Id., at 279, 331 P.3d, at 719. (She later backtracked and testified, "`I don't remember who was, you know, shot by who[m].'" Ibid.) The Kansas Supreme Court opined that the presumption that the jury followed its instructions to consider each defendant separately was "defeated by logic." Id., at 280, 331 P.3d, at 719. "[T]he defendants' joint upbringing in the maelstrom that was their family and their influence on and interactions with one another... simply was not amenable to orderly separation and analysis." Ibid., 331 P.3d, at 719-720. The Kansas Supreme Court found itself unable to "say that the death verdict was unattributable, at least in part, to this error." Id., at 282, 331 P.3d, at 720. We granted certiorari. 575 U.S. ___, 135 S.Ct. 1698, 191 L.Ed.2d 675 (2015).

II

We first turn to the Kansas Supreme Court's contention that the Eighth Amendment required these capital-sentencing courts to instruct the jury that mitigating circumstances need not be proved beyond a reasonable doubt.

A

Before considering the merits of that contention, we consider Gleason's challenge to our jurisdiction. According to Gleason, the Kansas Supreme Court's decision rests on adequate and independent state-law grounds. This argument is a familiar one. We rejected it in Kansas v. Marsh, 548 U.S. 163, 169, 126 S.Ct. 2516, 165 L.Ed.2d 429 (2006). Like the defendant in that case, Gleason urges that the decision below rests only on a rule of Kansas law announced in State v. Kleypas, 272 Kan. 894, 40 P.3d 139 (2001) (per curiam) — a rule later reiterated in State v. Scott, 286 Kan. 54, 183 P.3d 801 (2008) (per curiam). As we stated in Marsh, "Kleypas, itself, rested on federal law." 548 U.S., at 169, 126 S.Ct. 2516. So too does the relevant passage of Scott, which rested on Kleypas's discussion of the constitutional rule that jurors need not agree on mitigating circumstances. See Scott, supra, at 106-107, 183 P.3d, at 837-838. The Kansas Supreme Court's opinion in this case acknowledged as much, saying that "statements from Kleypas implicate the broader Eighth Amendment principle prohibiting barriers that preclude a sentencer's consideration of all relevant mitigating evidence." 299 Kan., at 1195, 329 P.3d, at 1147.

The Kansas Supreme Court's opinion leaves no room for doubt that it was relying on the Federal Constitution. It stated that the instruction it required "protects a capital defendant's Eighth Amendment right to individualized sentencing," that the absence of the instruction "implicat[ed] Gleason's right to individualized sentencing under the Eighth Amendment," and that vacatur of Gleason's death sentence was the "[c]onsequen[ce]" of Eighth Amendment error. Id., at 1196-1197, 329 P.3d, at 1147-1148 (emphasis added).

For this reason, the criticism leveled by the dissent is misdirected. It generally would have been "none of our business" had the Kansas Supreme Court vacated Gleason's and the Carrs' death sentences on state-law grounds. Marsh, 548 U.S., at 184, 126 S.Ct. 2516 (SCALIA, J., concurring). But it decidedly did not. And when the Kansas Supreme Court time and again invalidates death sentences because it says the Federal Constitution requires it, "review by this Court, far from undermining state autonomy, is the only possible way to vindicate it." Ibid. "When we correct a state court's federal errors, we return power to the State, and to its people." Ibid. The state courts may experiment all they want with their own constitutions, and often do in the wake of this Court's decisions. See Sutton, San Antonio Independent School District v. Rodriguez And Its Aftermath, 94 Va. L. Rev. 1963, 1971-1977 (2008). But what a state court cannot do is experiment with our Federal Constitution and expect to elude this Court's review so long as victory goes to the criminal defendant. "Turning a blind eye" in such cases "would change the uniform `law of the land' into a crazy quilt." Marsh, supra, at 185, 126 S.Ct. 2516. And it would enable state courts to blame the unpopular death-sentence reprieve of the most horrible criminals upon the Federal Constitution when it is in fact their own doing.

B

We turn, then, to the merits of the Kansas Supreme Court's conclusion that the Eighth Amendment requires capital-sentencing courts in Kansas "to affirmatively inform the jury that mitigating circumstances need not be proven beyond a reasonable doubt." 299 Kan., at 1197, 329 P.3d, at 1148.

Approaching the question in the abstract, and without reference to our capital-sentencing case law, we doubt whether it is even possible to apply a standard of proof to the mitigating-factor determination (the so-called "selection phase" of a capital-sentencing proceeding). It is possible to do so for the aggravating-factor determination (the so-called "eligibility phase"), because that is a purely factual determination. The facts justifying death set forth in the Kansas statute either did or did not exist — and one can require the finding that they did exist to be made beyond a reasonable doubt. Whether mitigation exists, however, is largely a judgment call (or perhaps a value call); what one juror might consider mitigating another might not. And of course the ultimate question whether mitigating circumstances outweigh aggravating circumstances is mostly a question of mercy — the quality of which, as we know, is not strained. It would mean nothing, we think, to tell the jury that the defendants must deserve mercy beyond a reasonable doubt; or must more-likely-than-not deserve it. It would be possible, of course, to instruct the jury that the facts establishing mitigating circumstances need only be proved by a preponderance, leaving the judgment whether those facts are indeed mitigating, and whether they outweigh the aggravators, to the jury's discretion without a standard of proof. If we were to hold that the Constitution requires the mitigating-factor determination to be divided into its factual component and its judgmental component, and the former to be accorded a burden-of-proof instruction, we doubt whether that would produce anything but jury confusion. In the last analysis, jurors will accord mercy if they deem it appropriate, and withhold mercy if they do not, which is what our case law is designed to achieve.

In any event, our case law does not require capital sentencing courts "to affirmatively inform the jury that mitigating circumstances need not be proved beyond a reasonable doubt." Ibid. In Buchanan v. Angelone, 522 U.S. 269, 118 S.Ct. 757, 139 L.Ed.2d 702 (1998), we upheld a death sentence even though the trial court "failed to provide the jury with express guidance on the concept of mitigation." Id., at 275, 118 S.Ct. 757. Likewise in Weeks v. Angelone, 528 U.S. 225, 120 S.Ct. 727, 145 L.Ed.2d 727 (2000), we reaffirmed that the Court has "never held that the State must structure in a particular way the manner in which juries consider mitigating evidence" and rejected the contention that it was constitutionally deficient to instruct jurors to "`consider a mitigating circumstance if you find there is evidence to support it,'" without additional guidance. Id., at 232-233, 120 S.Ct. 727.

Equally unavailing is the contention that even if an instruction that mitigating evidence need not be "proven beyond a reasonable doubt" is not always required, it was constitutionally necessary in these cases to avoid confusion. Ambiguity in capital-sentencing instructions gives rise to constitutional error only if "there is a reasonable likelihood that the jury has applied the challenged instruction in a way that prevents the consideration of constitutionally relevant evidence." Boyde v. California, 494 U.S. 370, 380, 110 S.Ct. 1190, 108 L.Ed.2d 316 (1990) (emphasis added). The alleged confusion stemming from the jury instructions used at the defendants' sentencings does not clear that bar. A meager "possibility" of confusion is not enough. Ibid.

As an initial matter, the defendants' argument rests on the assumption that it would be unconstitutional to require the defense to prove mitigating circumstances beyond a reasonable doubt. Assuming without deciding that that is the case, the record belies the defendants' contention that the instructions caused jurors to apply that standard of proof. The defendants focus upon the following instruction: "The State has the burden to prove beyond a reasonable doubt that there are one or more aggravating circumstances and that they are not outweighed by any mitigating circumstances found to exist." App. to Pet. for Cert. in No. 14-452, p. 133 (Instr. 8).3 The juxtaposition of aggravating and mitigating circumstances, so goes the argument, caused the jury to speculate that mitigating circumstances must also be proved beyond a reasonable doubt. 299 Kan., at 1197, 329 P.3d, at 1148. It seems to us quite the opposite. The instruction makes clear that both the existence of aggravating circumstances and the conclusion that they outweigh mitigating circumstances must be proved beyond a reasonable doubt; mitigating circumstances themselves, on the other hand, must merely be "found to exist." That same description, mitigating circumstances "found to exist," is contained in three other instructions, App. to Pet. for Cert. in No. 14-452, at 133 (Instrs. 7, 9, and 10) (emphasis added) — unsurprisingly, since it recites the Kansas statute, see Kan. Stat. Ann. § 21-4624(e) (1995). "Found to exist" certainly does not suggest proof beyond a reasonable doubt. The instructions as a whole distinguish clearly between aggravating and mitigating circumstances: "The State has the burden to prove beyond a reasonable doubt that there are one or more aggravating circumstances ...," and the jury must decide unanimously that the State met that burden. App. to Pet. for Cert. in No. 14-452, at 133 (Instrs. 8 and 10) (emphasis added). "Mitigating circumstances," on the other hand, "do not need to be found by all members of the jury" to "be considered by an individual juror in arriving at his or her sentencing decision." Id., at 131 (Instr. 7). Not once do the instructions say that defense counsel bears the burden of proving the facts constituting a mitigating circumstance beyond a reasonable doubt — nor would that make much sense, since one of the mitigating circumstances is (curiously) "mercy," which simply is not a factual determination.

We reject the Kansas Supreme Court's decision that jurors were "left to speculate as to the correct burden of proof for mitigating circumstances." 299 Kan., at 1197, 329 P.3d, at 1148. For the reasons we have described, no juror would reasonably have speculated that mitigating circumstances must be proved by any particular standard, let alone beyond a reasonable doubt. The reality is that jurors do not "pars[e] instructions for subtle shades of meaning in the same way that lawyers might." Boyde, supra, at 381, 110 S.Ct. 1190. The instructions repeatedly told the jurors to consider any mitigating factor, meaning any aspect of the defendants' background or the circumstances of their offense. Jurors would not have misunderstood these instructions to prevent their consideration of constitutionally relevant evidence.

III

We turn next to the contention that a joint capital-sentencing proceeding in the Carrs' cases violated the defendants' Eighth Amendment right to an "individualized sentencing determination." 300 Kan., at 276, 331 P.3d, at 717.

The Kansas Supreme Court agreed with the defendants that, because of the joint sentencing proceeding, one defendant's mitigating evidence put a thumb on death's scale for the other, in violation of the other's Eighth Amendment rights. Ibid. It accepted Reginald's contention that he was prejudiced by his brother's portrayal of him as the corrupting older brother. And it agreed that Reginald was prejudiced by his brother's cross-examination of their sister, who equivocated about whether Reginald admitted to her that he was the shooter. (Reginald has all but abandoned that implausible theory of prejudice before this Court and contends only that the State "likely would not have introduced any such testimony" had he been sentenced alone. Brief for Respondent in No. 14-450, p. 34, n. 3.) Jonathan asserted that he was prejudiced by evidence associating him with his dangerous older brother, which caused the jury to perceive him as an incurable sociopath.4 Both speculate that the evidence assertedly prejudicial to them would have been inadmissible in severed proceedings under Kansas law. The Kansas Supreme Court also launched a broader attack on the joint proceedings, contending that the joinder rendered it impossible for the jury to consider the Carrs' relative moral culpability and to determine individually whether they were entitled to "mercy." 300 Kan., at 278, 331 P.3d, at 718-719.

Whatever the merits of defendants' procedural objections, we will not shoehorn them into the Eighth Amendment's prohibition of "cruel and unusual punishments." As the United States as amicus curiae intimates, the Eighth Amendment is inapposite when each defendant's claim is, at bottom, that the jury considered evidence that would not have been admitted in a severed proceeding, and that the joint trial clouded the jury's consideration of mitigating evidence like "mercy." Brief for United States 24, n. 8. As we held in Romano v. Oklahoma, 512 U.S. 1, 114 S.Ct. 2004, 129 L.Ed.2d 1 (1994), it is not the role of the Eighth Amendment to establish a special "federal code of evidence" governing "the admissibility of evidence at capital sentencing proceedings." Id., at 11-12. Rather, it is the Due Process Clause that wards off the introduction of "unduly prejudicial" evidence that would "rende[r] the trial fundamentally unfair." Payne v. Tennessee, 501 U.S. 808, 825, 111 S.Ct. 2597, 115 L.Ed.2d 720 (1991); see also Brown v. Sanders, 546 U.S. 212, 220-221, 126 S.Ct. 884, 163 L.Ed.2d 723 (2006).

The test prescribed by Romano for a constitutional violation attributable to evidence improperly admitted at a capital-sentencing proceeding is whether the evidence "so infected the sentencing proceeding with unfairness as to render the jury's imposition of the death penalty a denial of due process." 512 U.S., at 12, 114 S.Ct. 2004. The mere admission of evidence that might not otherwise have been admitted in a severed proceeding does not demand the automatic vacatur of a death sentence.

In light of all the evidence presented at the guilt and penalty phases relevant to the jury's sentencing determination, the contention that the admission of mitigating evidence by one brother could have "so infected" the jury's consideration of the other's sentence as to amount to a denial of due process is beyond the pale. To begin with, the court instructed the jury that it "must give separate consideration to each defendant," that each was "entitled to have his sentence decided on the evidence and law which is applicable to him," and that any evidence in the penalty phase "limited to only one defendant should not be considered by you as to the other defendant." App. to Pet. for Cert. in No. 14-450, at 501 (Instr. 3). The court gave defendant-specific instructions for aggravating and mitigating circumstances. Id., at 502-508 (Instrs. 5, 6, 7, and 8). And the court instructed the jury to consider the "individual" or "particular defendant" by using four separate verdict forms for each defendant, one for each murdered occupant of the Birchwood house. Id., at 509 (Instr. 10); App. in No. 14-449 etc., at 461-492. We presume the jury followed these instructions and considered each defendant separately when deciding to impose a sentence of death for each of the brutal murders. Romano, supra, at 13, 114 S.Ct. 2004.

The contrary conclusion of the Kansas Supreme Court — that the presumption that jurors followed these instructions was "defeated by logic," 300 Kan., at 280, 331 P.3d, at 719 — is untenable. The Carrs implausibly liken the prejudice resulting from the joint sentencing proceeding to the prejudice infecting the joint trial in Bruton v. United States, 391 U.S. 123, 88 S.Ct. 1620, 20 L.Ed.2d 476 (1968), where the prosecution admitted hearsay evidence of a codefendant's confession implicating the defendant. That particular violation of the defendant's confrontation rights, incriminating evidence of the most persuasive sort, ineradicable, as a practical matter, from the jury's mind, justified what we have described as a narrow departure from the presumption that jurors follow their instructions, Richardson v. Marsh, 481 U.S. 200, 207, 107 S.Ct. 1702, 95 L.Ed.2d 176 (1987). We have declined to extend that exception, id., at 211, 107 S.Ct. 1702 and have continued to apply the presumption to instructions regarding mitigating evidence in capital-sentencing proceedings, see, e.g., Weeks, 528 U.S., at 234, 120 S.Ct. 727. There is no reason to think the jury could not follow its instruction to consider the defendants separately in this case.

Joint proceedings are not only permissible but are often preferable when the joined defendants' criminal conduct arises out of a single chain of events. Joint trial may enable a jury "to arrive more reliably at its conclusions regarding the guilt or innocence of a particular defendant and to assign fairly the respective responsibilities of each defendant in the sentencing." Buchanan v. Kentucky, 483 U.S. 402, 418, 107 S.Ct. 2906, 97 L.Ed.2d 336 (1987). That the codefendants might have "antagonistic" theories of mitigation, Zafiro v. United States, 506 U.S. 534, 538, 113 S.Ct. 933, 122 L.Ed.2d 317 (1993), does not suffice to overcome Kansas's "interest in promoting the reliability and consistency of its judicial process," Buchanan, supra, at 418, 107 S.Ct. 2906. Limiting instructions, like those used in the Carrs' sentencing proceeding, "often will suffice to cure any risk of prejudice." Zafiro, supra, at 539, 113 S.Ct. 933 (citing Richardson, supra, at 211, 107 S.Ct. 1702). To forbid joinder in capital-sentencing proceedings would, perversely, increase the odds of "wanto[n] and freakis[h]" imposition of death sentences. Gregg v. Georgia, 428 U.S. 153, 206-207, 96 S.Ct. 2909, 49 L.Ed.2d 859 (1976) (joint opinion of Stewart, Powell, and Stevens, JJ.). Better that two defendants who have together committed the same crimes be placed side-by-side to have their fates determined by a single jury.

It is improper to vacate a death sentence based on pure "speculation" of fundamental unfairness, "rather than reasoned judgment," Romano, supra, at 13-14, 114 S.Ct. 2004. Only the most extravagant speculation would lead to the conclusion that the supposedly prejudicial evidence rendered the Carr brothers' joint sentencing proceeding fundamentally unfair. It is beyond reason to think that the jury's death verdicts were caused by the identification of Reginald as the "corrupter" or of Jonathan as the "corrupted," the jury's viewing of Reginald's handcuffs, or the sister's retracted statement that Reginald fired the final shots. None of that mattered. What these defendants did — acts of almost inconceivable cruelty and depravity — was described in excruciating detail by Holly, who relived with the jury, for two days, the Wichita Massacre. The joint sentencing proceedings did not render the sentencing proceedings fundamentally unfair.

IV

When we granted the State's petition for a writ of certiorari for the Carrs' cases, we declined to review whether the Confrontation Clause, U.S. Const., Amdt. 6, requires that defendants be allowed to cross-examine witnesses whose statements are recorded in police reports referred to by the State in penalty-phase proceedings. The Kansas Supreme Court did not make the admission of those statements a basis for its vacating of the death sentences, but merely "caution[ed]" that in the resentencing proceedings these out-of-court testimonial statements should be omitted, 300 Kan., at 288, 331 P.3d, at 724. We are confident that cross-examination regarding these police reports would not have had the slightest effect upon the sentences. See Delaware v. Van Arsdall, 475 U.S. 673, 684, 106 S.Ct. 1431, 89 L.Ed.2d 674 (1986).

* * *

The judgments of the Supreme Court of Kansas are reversed, and these cases are remanded for further proceedings not inconsistent with this opinion.

It is so ordered.

Justice SOTOMAYOR, dissenting.

I respectfully dissent because I do not believe these cases should ever have been reviewed by the Supreme Court. I see no reason to intervene in cases like these — and plenty of reasons not to. Kansas has not violated any federal constitutional right. If anything, the State has overprotected its citizens based on its interpretation of state and federal law. For reasons ably articulated by my predecessors and colleagues and because I worry that cases like these prevent States from serving as necessary laboratories for experimenting with how best to guarantee defendants a fair trial, I would dismiss the writs as improvidently granted.

I

In 2014, the Kansas Supreme Court vacated three death sentences — the sentences of Sidney Gleason and the Carr brothers, Reginald and Jonathan — because of constitutional errors in the penalty phases of their trials.

All three men were tried under jury instructions that did not include language previously mandated by the Kansas Supreme Court. The instructions did not state that, under Kansas' statutory scheme, mitigating circumstances need only be proven to an individual juror's satisfaction and not beyond a reasonable doubt. 299 Kan. 1127, 1192-1197, 329 P.3d 1102, 1145-1148 (2014) (Sidney Gleason); 300 Kan. 1, 302-303, 331 P.3d 544, 732-733 (2014) (Reginald Carr); 300 Kan. 340, 368-369, 329 P.3d 1195, 1213 (2014) (Jonathan Carr). The court found that the instructions therefore both undermined Kansas' state law and created a "reasonable likelihood that the jury ... applied the challenged instruction in a way that prevents consideration" of mitigating evidence as required by the Federal Constitution. 299 Kan., at 1191-1197, 329 P.3d, at 1144-1148 (quoting Boyde v. California, 494 U.S. 370, 380, 110 S.Ct. 1190, 108 L.Ed.2d 316 (1990)).

The Kansas Supreme Court also vacated the Carr brothers' death sentences because they were jointly tried at the penalty phase. The court concluded that each brother's particular case for mitigation compromised the other brother's case and therefore that trying them jointly violated the Eighth Amendment right to individualized sentencing. The error was not harmless, the Kansas Supreme Court found, because an "especially damning subset" of the evidence presented might not have been admitted in separate penalty proceedings. 300 Kan., at 275-282, 331 P.3d, at 717-720, 300 Kan., at 369-370, 329 P.3d, at 1212.

The Kansas attorney general requested certiorari, alleging that it would best serve the State's interest for a federal court to intervene and correct the Kansas Supreme Court. This Court complied, even though there was no suggestion that the Kansas Supreme Court had violated any federal constitutional right. The majority now reverses the Kansas Supreme Court on both points.

II

A

Even where a state court has wrongly decided an "important question of federal law," Sup.Ct. Rule 10, we often decline to grant certiorari, instead reserving such grants for instances where the benefits of hearing a case outweigh the costs of so doing. My colleagues and predecessors have effectively set forth many of the costs of granting certiorari in cases where state courts grant relief to criminal defendants: We risk issuing opinions that, while not strictly advisory, may have little effect if a lower court is able to reinstate its holding as a matter of state law. Florida v. Powell, 559 U.S. 50, 66, 130 S.Ct. 1195, 175 L.Ed.2d 1009 (2010) (Stevens, J., dissenting). We expend resources on cases where the only concern is that a State has "`overprotected'" its citizens. Michigan v. Long, 463 U.S. 1032, 1068, 103 S.Ct. 3469, 77 L.Ed.2d 1201 (1983) (Stevens, J., dissenting). We intervene in an intrastate dispute between the State's executive and its judiciary rather than entrusting the State's structure of government to sort it out. See Coleman v. Thompson, 501 U.S. 722, 766-767, 111 S.Ct. 2546, 115 L.Ed.2d 640 (1991) (Blackmun, J., dissenting). And we lose valuable data about the best methods of protecting constitutional rights — a particular concern in cases like these, where the federal constitutional question turns on the "reasonable likelihood" of jury confusion, an empirical question best answered with evidence from many state courts. Cf. Arizona v. Evans, 514 U.S. 1, 30-31, 115 S.Ct. 1185, 131 L.Ed.2d 34 (1995) (GINSBURG, J., dissenting).

B

The cases here demonstrate yet another cost of granting certiorari to correct a state court's overprotection of federal rights: In explaining that the Federal Constitution does not protect some particular right, it is natural to buttress the conclusion by explaining why that right is not very important. In so doing, the Court risks discouraging States from adopting valuable procedural protections even as a matter of their own state law.

State experimentation with how best to guarantee a fair trial to criminal defendants is an essential aspect of our federalism scheme. See, e.g., Linde, First Things First: Rediscovering the States' Bill of Rights, 9 U. Balt. L. Rev. 379, 393 (1980). The Federal Constitution guarantees only a minimum slate of protections; States can and do provide individual rights above that constitutional floor. See, e.g., Brennan, The Bill of Rights and the States: the Revival of State Constitutions as Guardians of Constitutional Rights, 61 N.Y. U. L. Rev. 535, 548-550 (1986). That role is particularly important in the criminal arena because state courts preside over many millions more criminal cases than their federal counterparts and so are more likely to identify protections important to a fair trial. Compare Court Statistics Project, Examining the Work of State Courts: An Analysis of 2010 State Court Caseloads 19-21 (2012), with Dept. of Justice, Bureau of Justice Statistics, Federal Justice Statistics 2011-2012, pp. 19-20 (Jan. 2015) (Tables 11 and 12).

The majority's opinion in these cases illustrates how an unnecessary grant of certiorari can lead to unexpected costs by disrupting this sort of state experimentation. Take the first question presented in these cases. The majority's actual holding is that the Eighth Amendment does not require an instruction specifying that mitigating factors need not be proven beyond a reasonable doubt. Ante, at 642-643. The Eighth Amendment has nothing to say about whether such an instruction is wise as a question of state law or policy. But the majority nonetheless uses this Court's considerable influence to call into question the logic of specifying any burden of proof as to mitigating circumstances. The majority claims that while assessing an aggravating factor is "a purely factual determination," assessing mitigation involves "a judgment call (or perhaps a value call)" and is thus not amenable to burdens of proof. Ante, at 642. Short of dividing the mitigating factor "into its factual component and its judgmental component," and issuing burden-of-proof instructions only as to the former, the majority wonders "whether it is even possible to apply a standard of proof to the mitigating-factor determination." Ibid.

By this observation, and with no experience with the needs of juries, the majority denigrates the many States that do specify a burden of proof for the existence of mitigating factors as a matter of state law, presumably under the belief that it is, in fact, "possible" to do so.* Brief for Respondent in No. 14-452, pp. 28-29, and n. 6. Some States even recommend an instruction specifying that mitigating factors need not be proven beyond a reasonable doubt. See, e.g., Idaho Jury Instr., Crim., ICJI 1718, Jury Deliberations (2010); Okla. Jury Instr., Crim., OUJI-CR 4-78 (2015).

The majority's discussion of severance likewise short circuits state experimentation. The majority is not content to hold that the Eighth Amendment does not, strictly speaking, require severance of capital penalty proceedings. Instead, it goes on to explain why joint capital sentencing proceedings are not only permissible under the Federal Constitution but are, in fact, preferable as a policy matter: "Better that two defendants who have together committed the same crimes be placed side-by-side to have their fates determined by a single jury." Ante, at 646. The majority even intimates that severed proceedings may be worse for defendants: "To forbid joinder in capital-sentencing proceedings would, perversely, increase the odds of `wanto[n] and freakis[h]' imposition of death sentences." Ibid. (quoting Gregg v. Georgia, 428 U.S. 153, 206-207, 96 S.Ct. 2909, 49 L.Ed.2d 859 (1976) (joint opinion of Stewart, Powell, and Stevens, JJ.)).

So much for Ohio's, Georgia's, and Mississippi's sentencing regimes, all of which routinely allow severance at both phases of capital proceedings. See Ga.Code Ann. § 17-8-4 (2013) (upon request, defendants must be tried separately in capital cases); Miss.Code Ann. § 99-15-47 (2015) (same); Ohio Rev.Code Ann. § 2945.20 (Lexis 2014) (capital defendants shall be tried separately unless good cause is shown for a joint trial). There is no evidence that any of those three States adopted a severance regime based on a misunderstanding of the Eighth Amendment. But without any empirical foundation or any basis in experience, the majority asserts that such regimes may increase the odds of arbitrariness.

The majority claims that we "`return power to the State, and to its people,'" when we explain that the Federal Constitution does not require a particular result. Ante, at 641-642 (emphasis deleted). But that is only so when the Court is able to pass solely on the federal constitutional ground and not the wisdom of a state holding on an equivalent question. Though the Court pretends that it sends back cases like this one with a clean slate, it rarely fully erases its thoughts on the virtues of the procedural protection at issue. By placing a thumb on the scale against a State adopting — even as a matter of state law — procedural protections the Constitution does not require, the Court risks turning the Federal Constitution into a ceiling, rather than a floor, for the protection of individual liberties.

III

I see no reason why these three cases out of the Kansas Supreme Court warranted our intervention given the costs that I have just described and those described by my predecessors and colleagues, see supra, at 647-648. No federal right has been compromised. And nobody disputes that the State of Kansas could, as a matter of state law, reach the same outcome.

Perhaps most importantly, both of the questions on which the Court granted certiorari turn on specific features of Kansas' sentencing scheme. As a result, the Kansas Supreme Court's opinion is unlikely to have much salience for other States. If the Kansas Supreme Court was wrong, its wrong opinion will not subvert federal law on a broader scale.

First, the Kansas court's decision on the jury instruction question aimed to "both preserv[e] the [state] statute's favorable distinction and protec[t] a capital defendant's Eighth Amendment right to individualized sentencing by ensuring jurors are not precluded from considering all relevant mitigating evidence." 299 Kan., at 1196, 329 P.3d, at 1147 (emphasis added). The Kansas Supreme Court's decision was thus informed by a combination of federal and state considerations. A decision that expressly relies on a State's unique statutory scheme — as did the Kansas Supreme Court's here — has limited potential for influencing other States.

It is not absurd to conclude that a juror unfamiliar with the mechanics of the law might be confused by Kansas' jury instructions, which almost always mention aggravating and mitigating instructions in the same breath. Id., at 1196-1197, 329 P.3d, at 1147-1148. The Kansas Supreme Court's opinion rested largely on the specific language and ordering of that State's instructions. Other States' jury instructions may be less likely to have the same effect.

Moreover, the decision below was made against the unique backdrop of trial courts' failure to implement the Kansas Supreme Court's earlier demands for a change to jury instructions in capital cases. In a 2001 case, the Kansas Supreme Court considered the jury instructions insufficiently confusing to reverse the judgment, but sufficiently confusing to demand higher clarity going forward: "[A]ny instruction dealing with the consideration of mitigating circumstances should state (1) they need to be proved only to the satisfaction of the individual juror in the juror's sentencing decision and not beyond a reasonable doubt and (2) mitigating circumstances do not need to be found by all members of the jury in order to be considered in an individual juror's sentencing decision." State v. Kleypas, 272 Kan. 894, 1078, 40 P.3d 139, 268. The Kansas pattern instructions were then revised to include consideration (2), but — "inexplicably," as the court noted in Gleason — not consideration (1). 299 Kan., at 1193, 329 P.3d, at 1145. The Kansas Supreme Court reiterated the two requirements for any jury instruction in 2008, see State v. Scott, 286 Kan. 54, 106-108, 183 P.3d 801, 837, and the pattern instructions were finally changed in 2011, see 299 Kan., at 1193, 329 P.3d, at 1145. But Gleason and the Carr brothers were tried in the 10-year delay between the Kansas Supreme Court's initial admonition and when the jury instructions were finally edited. The Kansas Supreme Court's opinion in Gleason may have rested in part on a "broader Eighth Amendment principle," but it also rested on some lower courts' failure to give instructions reflecting the Kansas Supreme Court's "repeated recognition of the required content." 299 Kan., at 1195, 329 P.3d, at 1146, 1147. Given this context, the Kansas Supreme Court's decision is particularly unlikely to undermine other States or the Federal Constitution.

The same goes for the severance question. The Kansas Supreme Court's decision depended on the "especially damning subset" of the aggravating evidence presented that may not have been admitted in a severed proceeding under Kansas' capital punishment scheme and evidentiary rules, such as evidence that one brother was a bad influence on the other. Ibid. But the difference between a joint penalty phase and a severed penalty phase may be of limited significance in States where the same evidence may be admitted in joint and severed proceedings. Cf. Brown v. Sanders, 546 U.S. 212, 217, 126 S.Ct. 884, 163 L.Ed.2d 723 (2006); L. Palmer, The Death Penalty in the United States: A Complete Guide to Federal and State Laws 137 (2d ed. 2014). It thus seems to me unlikely that the Kansas Supreme Court's opinion would have proven instructive in other States, even though it was couched in the language of the Federal Constitution.

IV

There may, of course, be rare cases where certiorari is warranted in which a state prosecutor alleges that a State's highest court has overprotected a criminal defendant. These circumstances may include: Where a state court's decision in favor of a criminal defendant implicates another constitutional right, see, e.g., Nebraska Press Assn. v. Stuart, 427 U.S. 539, 547, 96 S.Ct. 2791, 49 L.Ed.2d 683 (1976); where a state court indicates a hostility to applying federal precedents, Florida v. Meyers, 466 U.S. 380, 383, 104 S.Ct. 1852, 80 L.Ed.2d 381 (1984) (per curiam) (Stevens, J., dissenting); or where a state court's grant of relief is particularly likely to destabilize or significantly interfere with federal policy. None of those circumstances, and no comparable interest, is present in these cases.

The Carr brothers committed acts of "almost inconceivable cruelty and depravity," and the majority is understandably anxious to ensure they receive their just deserts. (So anxious, in fact, that it reaches out to address a question on which we did not grant certiorari at all. Ante, at 646). But I do not believe that interest justifies not only "correcting" the Kansas Supreme Court's error but also calling into question the procedures of other States.

The standard adage teaches that hard cases make bad law. See Northern Securities Co. v. United States, 193 U.S. 197, 364, 24 S.Ct. 436, 48 S.Ct. 679 (1904) (Holmes, J., dissenting). I fear that these cases suggest a corollary: Shocking cases make too much law. Because I believe the Court should not have granted certiorari here, I respectfully dissent.