Chief Justice Rehnquist
delivered the opinion of the Court.
Petitioner murdered and robbed Roger Sarfaty in 1985. In 1986, he murdered and robbed Lloyd Thompson. Petitioner was tried separately for each murder. The Thompson trial occurred first, and an Oklahoma jury found petitioner guilty and sentenced him to death. Petitioner was then tried for the Sarfaty murder. A different Oklahoma jury found him guilty and sentenced him to death. During the sentencing phase of the Sarfaty trial, the State introduced a copy of the judgment and sentence petitioner received for the Thompson murder. Petitioner contends that the admission of evidence regarding his prior death sentence undermined the Sarfaty jury’s sense of responsibility for determining the appropriateness of the death penalty, in violation of the Eighth and Fourteenth Amendments. We disagree and hold that the admission of this evidence did not amount to constitutional error.
In Oklahoma, capital trials are bifurcated into guilt and sentencing phases. Okla. Stat., Tit. 21, § 701.10 (1981). The [4]*4sentencing jury may not impose a death sentence unless it unanimously finds the existence of at least one statutory aggravating circumstance beyond a reasonable doubt, and that any aggravating circumstances outweigh any mitigating circumstances. §701.12. At the sentencing phase of the Sarfaty trial, the State sought to prove four aggravating circumstances, two of which are relevant to our decision: (1) that petitioner had been previously convicted of a violent felony; and (2) that petitioner would constitute a continuing threat to society.1
In attempting to establish these two aggravating circumstances, the State introduced evidence relating to the Thompson murder. The State presented testimony by Thompson’s neighbor concerning her observations the day of the murder, Thompson’s autopsy report, and photographs and fingerprints showing that the defendant in the Thompson case was in fact petitioner. The State also introduced a copy of the judgment and sentence from the Thompson murder conviction. That document revealed that petitioner had been convicted of first-degree murder and had been sentenced to death. App. 5-6. It also showed, and the trial court told the jury, that petitioner planned on appealing from the judgment and sentence. Id., at 7. Petitioner’s counsel objected to the admission of the document. He argued that, regardless of the admissibility of the evidence of petitioner’s conviction, the death sentence petitioner received was not proper for the jury to consider. The trial court overruled the objection and admitted the evidence. Petitioner later presented evidence in mitigation.
Before closing arguments, the trial court instructed the jury. It identified the four aggravating circumstances the State sought to establish and told the jury that “[i]n determining which sentence you may impose in this case, you may [5]*5consider only those [four] circumstances.” Id., at 9. The court then identified the 17 mitigating circumstances offered by petitioner. The jury was instructed that it could not impose the death penalty unless it unanimously found that one or more aggravating circumstances existed beyond a reasonable doubt and that any such circumstances outweighed any mitigating circumstances. Id., at 8-12. In closing, the court admonished the jury:
“You are the determiner of the facts. The importance and worth of the evidence is for you to decide.
“I have made rulings during the second part of this trial. In ruling, I have not in any way suggested to you, nor intimidated [sic] in any way, what you should decide. I do not express any opinion whether or not aggravating circumstances or mitigating circumstances did or did not exist, nor do I suggest to you in any way the punishment to be imposed by you.
“You must not use any kind of chance in reaching a verdict, but you must rest it on the belief of each of you who agrees with it.” Id., at 13.
The jury found that all four aggravating circumstances existed and that they outweighed the mitigating circumstances. It accordingly imposed a death sentence. Petitioner appealed. While his appeal in this case was pending, the Oklahoma Court of Criminal Appeals overturned petitioner’s conviction for the Thompson murder. See Romano v. Oklahoma, 827 P. 2d 1335 (1992) (Romano I). The Oklahoma Court of Criminal Appeals held that petitioner’s trial should have been severed from that of his codefendant; it therefore reversed and remanded for a new trial.2
In his appeal in this case, petitioner argued, inter alia, that the trial court erred by admitting evidence of his conviction and sentence for the Thompson murder. He asserted [6]*6that it was improper to admit the conviction because it was not final at the time of admission, and it had since been overturned. He also contended that the evidence of his death sentence in the Thompson case impermissibly reduced the Sarfaty sentencing jury’s sense of responsibility for its decision, in violation of Caldwell v. Mississippi, 472 U. S. 320 (1985).
The Oklahoma Court of Criminal Appeals affirmed. 847 P. 2d 368, 390 (1993) (Romano II). The Oklahoma court concluded that the evidence regarding petitioner’s prior death sentence was irrelevant. Because the jury was properly instructed in this case, however, it could not be said “that the jury in any way shifted the responsibility for their decision or considered their decision any less significant than they would otherwise.” Ibid. The Court of Criminal Appeals further held that the admission of the evidence “did not so infect the sentencing determination with unfairness as to make the determination to impose the death penalty a denial of due process.” Id., at 391.
Petitioner sought our review, and we granted certiorari, limited to the following question: “Does admission of evidence that a capital defendant already has been sentenced to death in another case impermissibly undermine the sentencing jury’s sense of responsibility for determining the appropriateness of the defendant’s death, in violation of the Eighth and Fourteenth Amendments?” 510 U. S. 943 (1993). We now affirm.
It is helpful to begin by placing petitioner’s challenge within the larger context of our Eighth Amendment death penalty jurisprudence. We have held that the Eighth Amendment’s concern that the death penalty be both appropriate and not randomly imposed requires the States to perform two somewhat contradictory tasks in order to impose the death penalty.
First, States must properly establish a threshold below which the penalty cannot be imposed. McCleskey v. Kemp, [7]*7481 U. S. 279, 305 (1987). To ensure that this threshold is met, the “State must establish rational criteria that narrow the decisionmaker’s judgment as to whether the circumstances of a particular defendant’s case meet the threshold.” Ibid. As we stated in Lowenfield v. Phelps, 484 U. S. 231 (1988), “[t]o pass constitutional muster, a capital sentencing scheme must ‘genuinely narrow the class of persons eligible for the death penalty and must reasonably justify the imposition of a more severe sentence on the defendant compared to others found guilty of murder.’” Id., at 244 (quoting Zant v. Stephens, 462 U. S. 862, 877 (1983)). In this respect, a State’s sentencing procedure must suitably direct and limit the decisionmaker’s discretion “ ‘so as to minimize the risk of wholly arbitrary and capricious action.’” Id., at 874 (quoting Gregg v. Georgia, 428 U. S. 153, 189 (1976)). Petitioner does not allege that Oklahoma’s sentencing scheme fails to adequately perform the requisite narrowing.
Second, States must ensure that “capital sentencing decisions rest on [an] individualized inquiry,” under which the “character and record of the individual offender and the circumstances of the particular offense” are considered. McCleskey, supra, at 303 (internal quotation marks omitted); see also Clemons v. Mississippi, 494 U. S. 738, 748 (1990). To this end, “States cannot limit the sentencer’s consideration of any relevant circumstance that could cause it to decline to impose the penalty. In this respect, the State cannot channel the sentencer’s discretion, but must allow it to consider any relevant information offered by the defendant.” McCleskey, supra, at 306.
Within these constitutional limits, “the States enjoy their traditional latitude to prescribe the method by which those who commit murder shall be punished.” Blystone v. Pennsylvania, 494 U. S. 299, 309 (1990). This latitude extends to evidentiary rules at sentencing proceedings. See, e.g., Gregg, supra, at 203-204 (approving “the wide scope of evidence and argument allowed at presentence hearings” [8]*8in Georgia). As we observed in California v. Ramos, 463 U. S. 992, 999 (1983):
“In ensuring that the death penalty is not meted out arbitrarily or capriciously, the Court’s principal concern has been more with the procedure by which the State imposes the death sentence than with the substantive factors the State lays before the jury as a basis for imposing death, once it has been determined that the defendant falls within the category of persons eligible for the death penalty.”
See also id., at 1008 (“Once the jury finds that the defendant falls within the legislatively defined category of persons eligible for the death penalty ... the jury then is free to consider a myriad of factors to determine whether death is the appropriate punishment”).
We have also held, in Caldwell v. Mississippi, that the jury must not be misled regarding the role it plays in the sentencing decision. See 472 U. S., at 336 (plurality opinion); id., at 341-342 (O’Connor, J., concurring in part and concurring in judgment). The prosecutor in Caldwell, in remarks which “were quite focused, unambiguous, and strong,” misled the jury to believe that the responsibility for sentencing the defendant lay elsewhere. Id., at 340. The trial judge “not only failed to correct the prosecutor’s remarks, but in fact openly agreed with them.” Id., at 339.
The plurality concluded that the prosecutor’s remarks, along with the trial judge’s affirmation, impermissibly “minimize[d] the jury’s sense of responsibility for determining the appropriateness of death.” Id., at 341. Such a diminution, the plurality felt, precluded the jury from properly performing its responsibility to make an individualized determination of the appropriateness of the death penalty. Id., at 330-331. Justice O’Connor, in her opinion concurring in part and concurring in the judgment, identified more narrowly the infirmity in the prosecutor’s remarks: “In my view, the [9]*9prosecutor’s remarks were impermissible because they were inaccurate and misleading in a manner that diminished the jury’s sense of responsibility.” Id., at 342.
As Justice O’Connor supplied the fifth vote in Caldwell, and concurred on grounds narrower than those put forth by the plurality, her position is controlling. See Marks v. United States, 430 U. S. 188, 193 (1977); Gregg, supra, at 169, n. 15. Accordingly, we have since read Caldwell as “relevant only to certain types of comment — those that mislead the jury as to its role in the sentencing process in a way that allows the jury to feel less responsible than it should for the sentencing decision.” Darden v. Wainwright, 477 U. S. 168, 184, n. 15 (1986). Thus, “[t]o establish a Caldwell violation, a defendant necessarily must show that the remarks to the jury improperly described the role assigned to the jury by local law.” Dugger v. Adams, 489 U. S. 401, 407 (1989); see also Sawyer v. Smith, 497 U. S. 227, 233 (1990).
Petitioner argues that Caldwell controls this case. He contends that the evidence of his prior death sentence impermissibly undermined the sentencing jury’s sense of responsibility, in violation of the principle established in Caldwell. We disagree. The infirmity identified in Caldwell is simply absent in this case: Here, the jury was not affirmatively misled regarding its role in the sentencing process. The evidence at issue was neither false at the time it was admitted, nor did it even pertain to the jury’s role in the sentencing process. The trial court’s instructions, moreover, emphasized the importance of the jury’s role. As the Court of Criminal Appeals observed:
“The jury was instructed that it had the responsibility for determining whether the death penalty should be imposed.... It was never conveyed or intimated in any way, by the court or the attorneys, that the jury could shift its responsibility in sentencing or that its role in any way had been minimized.” Romano II, 847 P. 2d, at 390.
[10]*10We do not believe that the admission of evidence regarding petitioner’s prior death sentence affirmatively misled the jury regarding its role in the sentencing process so as to diminish its sense of responsibility. The admission of this evidence, therefore, did not contravene the principle established in Caldwell.
That this case is different from Caldwell only resolves part of petitioner’s challenge. In addition to raising a “Caldwell” claim, petitioner presents a more general contention: He argues that because the evidence of his prior death sentence was inaccurate and irrelevant, the jury’s consideration of it rendered his sentencing proceeding so unreliable that the proceeding violated the Eighth Amendment. See Lockett v. Ohio, 438 U. S. 586, 604 (1978) (plurality opinion); Woodson v. North Carolina, 428 U. S. 280, 305 (1976). The Oklahoma court agreed that the “evidence of the imposition of the death penalty by another jury is not relevant in determining the appropriateness of the death sentence for the instant offense.” Romano II, supra, at 391. That the evidence may have been irrelevant as a matter of state law, however, does not render its admission federal constitutional error. See Estelle v. McGuire, 502 U. S. 62, 67 (1991).
Some of the cases upon which petitioner relies for support, to be sure, do hold that the Constitution bars the introduction of certain evidence at sentencing proceedings. But these cases are plainly inapposite. Petitioner cites, for example, Dawson v. Delaware, 503 U. S. 159 (1992). There we held that the trial court erred by admitting evidence, at Dawson’s capital sentencing proceeding, regarding Dawson’s membership in a white racist prison gang known as the Aryan Brotherhood. See id., at 162-163. It was constitutional error, however, only because the admission violated “Dawson’s First Amendment rights.” Id., at 167. Dawson thus involved application of the principle first enunciated in Zant: An aggravating circumstance is invalid if “it authorizes a jury to draw adverse inferences from conduct that is [11]*11constitutionally protected.” 462 U. S., at 885. Petitioner does not argue that the admission of evidence regarding his prior death sentence allowed the jury to consider, in aggravation, constitutionally protected conduct. Accordingly, our decisions in Dawson and Zant do not support petitioner’s contention.
Petitioner also cites Johnson v. Mississippi, 486 U. S. 578 (1988), but it, too, is inapposite. There we reversed the imposition of Johnson’s death sentence because the only evidence supporting an aggravating factor turned out to be invalid, and because the Mississippi Supreme Court refused to reweigh the remaining, untainted aggravating circumstances against the mitigating circumstances. Id., at 586, 590, n. 8. Similarly, in this case the only evidence supporting the “prior violent felony” aggravating circumstance was the judgment from petitioner’s conviction for the Thompson murder. That evidence, like the evidence in Johnson, was rendered invalid by the reversal of petitioner’s conviction on appeal.
Here, however, the Oklahoma Court of Criminal Appeals struck the “prior violent felony” aggravator, reweighed the three untainted aggravating circumstances against the mitigating circumstances, and still concluded that the death penalty was warranted. See Romano II, supra, at 389, 393-394. The Court of Criminal Appeals’ approach is perfectly consistent with our precedents, including Johnson, where we remanded without limiting the Mississippi Supreme Court’s authority to reweigh the remaining aggravating circumstances against the mitigating circumstances. See 486 U. S., at 590; id., at 591 (White, J., concurring); see also Clemons, 494 U. S., at 744-750. Contrary to petitioner’s assertion, Johnson does not stand for the proposition that the mere admission of irrelevant and prejudicial evidence requires the overturning of a death sentence.
Petitioner’s argument, pared down, seems to be a request that we fashion general evidentiary rules, under the guise of interpreting the Eighth Amendment, which would govern [12]*12the admissibility of evidence at capital sentencing proceedings. We have not done so in the past, however, and we will not do so today. The Eighth Amendment does not establish a federal code of evidence to supersede state evidentiary rules in capital sentencing proceedings. Cf. Payne v. Tennessee, 501 U. S. 808, 824-825 (1991); Blystone, 494 U. S., at 309.
Petitioner finally argues that the introduction of the evidence in question violated the Due Process Clause of the Fourteenth Amendment. It is settled that this Clause applies to the sentencing phase of capital trials. See, e.g., Payne, supra, at 825; Clemons, supra, at 746 (“[C]apital sentencing proceedings must of course satisfy the dictates of the Due Process Clause”).
We believe the proper analytical framework in which to consider this claim is found in Donnelly v. DeChristoforo, 416 U. S. 637, 643 (1974). There we addressed a claim that remarks made by the prosecutor during his closing argument were so prejudicial as to violate the defendant’s due process rights. We noted that the case was not one in which the State had denied a defendant the benefit of a specific constitutional right, such as the right to counsel, or in which the remarks so prejudiced a specific right as to amount to a denial of that right. Id., at 643. Accordingly, we sought to determine whether the prosecutor’s remark “so infected the trial with unfairness as to make the resulting conviction a denial of due process.” Ibid. We concluded, after an “examination of the entire proceedings,” that the remarks did not amount to a denial of constitutional due process. Ibid.
The relevant question in this case, therefore, is whether the admission of evidence regarding petitioner’s prior death sentence so infected the sentencing proceeding with unfairness as to render the jury’s imposition of the death penalty a denial of due process. See Sawyer, 497 U. S., at 244 (observing that “[t]he Caldwell rule was . .. added to [Donnelly’s] existing guarantee of due process protection against [13]*13fundamental unfairness”); see also Darden, 477 U. S., at 178-181 (in analyzing allegedly improper comments made by prosecutor during closing argument of guilt-innocence stage of capital trial, “[t]he relevant question is whether the prosecutors’ comments ‘so infected the trial with unfairness as to make the resulting conviction a denial of due process’ ” (quoting Donnelly, supra, at 643)). Under this standard of review, we agree with the Oklahoma Court of Criminal Appeals that the admission of this evidence did not deprive petitioner of a fair sentencing proceeding.
The evidence that petitioner received a death sentence for murdering Thompson was deemed irrelevant by the Oklahoma Court of Criminal Appeals. See Romano II, 847 P. 2d, at 391. However, if the jurors followed the trial court’s instructions, which we presume they did, see Richardson v. Marsh, 481 U. S. 200, 206-207, 211 (1987), this evidence should have had little — if any — effect on their deliberations. Those instructions clearly and properly described the jurors’ paramount role in determining petitioner’s sentence, and they also explicitly limited the jurors’ consideration of aggravating factors to the four which the State sought to prove. Regardless of the evidence as to petitioner’s death sentence in the Thompson case, the jury had sufficient evidence to justify its conclusion that these four aggravating circumstances existed. Although one of the aggravating circumstances proved invalid when petitioner’s conviction for the Thompson murder was overturned on appeal, the other three remained untainted and still outweighed the mitigating circumstances. See Romano II, supra, at 389, 393-394. In short, the instructions did not offer the jurors any means by which to give effect to the evidence of petitioner’s sentence in the Thompson murder, and the other relevant evidence presented by the State was sufficient to justify the imposition of the death sentence in this case.
Even assuming that the jury disregarded the trial court’s instructions and allowed the evidence of petitioner’s prior [14]*14death sentence to influence its decision, it is impossible to know how this evidence might have affected the jury. It seems equally plausible that the evidence could have made the jurors more inclined to impose a death sentence, or it could have made them less inclined to do so. Either conclusion necessarily rests upon one’s intuition. To hold on the basis of this record that the admission of evidence relating to petitioner’s sentence in the Thompson case rendered petitioner’s sentencing proceeding for the Sarfaty murder fundamentally unfair would thus be an exercise in speculation, rather than reasoned judgment.
The judgment of the Oklahoma Court of Criminal Appeals is
Affirmed.