opinion: Justice O’Connor
  delivered the opinion of the Court.
  In this case we determine whether the Double Jeopardy Clause requires us to vacate the sentence of death imposed on petitioner Thomas Schiro. For the reasons explained below, we hold that it does not.
  I
  Schiro was convicted and sentenced to death for murder. The body of Laura Luebbehusen was discovered in her home on the morning of February 5, 1981, by her roommate, Darlene Hooper, and Darlene Hooper’s former husband. Darlene Hooper, who had been away, returned to find the home in disarray. Blood covered the walls and floor; Laura Luebbehusen’s semiclad body was lying near the entrance. The police recovered from the scene a broken vodka bottle, a handle and metal portions of an iron, and bottles of various types of liquor.
  The pathologist testified that there were a number of contusions on the body, including injuries to the head. The victim also had lacerations on one nipple and a thigh, and a tear in the vagina, all caused after death. A forensic dentist determined that the thigh injury was caused by a human bite. The cause of death was strangulation.
  Laura Luebbehusen’s car was later found near a halfway house where Schiro was living. Schiro told one counselor at the halfway house he wanted to discuss something “heavy.” App. 53. Schiro later confessed to another counselor that he had committed the murder. After his arrest, he confessed to an inmate in the county jail that he had been drinking and taking Quaaludes the night of the killing, and that he had had intercourse with the victim both before and after killing her.
  Schiro also admitted the killing to his girlfriend', Mary Lee. Schiro told Mary Lee that he gained access to Laura Luebbehusen’s house by telling her his car had broken down. Once in the house, he exposed himself to her. She told him that she was a lesbian, that she had been raped as a child, that she had never otherwise had intercourse before and did not want to have sex. Nonetheless, Schiro raped her numerous times. There was evidence that Schiro forced her to consume drugs and alcohol. When Laura Luebbehusen tried to escape, Schiro restrained and raped her at least once more. Then, as Laura Luebbehusen lay or slept on the bed, Schiro realized that she would have to die so that she would not turn him in. He found the vodka bottle and beat her on the head with it until it broke. He then beat her with the iron and, when she resisted, finally strangled her to death. Schiro dragged her body into another room and sexually assaulted the corpse. After the murder, he attempted to destroy evidence linking him to the crime.
  II
  At the time of the crime, the State of Indiana defined murder as follows:
  “A person who:
  “(1) knowingly or intentionally kills another human being; or
  “(2) kills another human being while committing or attempting to commit arson, burglary, child molesting, criminal deviate conduct, kidnapping, rape or robbery; “commits murder, a felony.” Ind. Code §35-42-1-1 (Supp. 1978).
  Schiro was charged with three counts of murder. In Count I he was charged with “knowingly” killing Laura Luebbehusen; in Count II with killing her while committing the crime of rape; and in Count III with killing her while committing criminal deviate conduct. App. 3-5. The State sought the death penalty for Counts II and III.
  At trial, Schiro did not contest that he had killed Laura Luebbehusen. Indeed, in closing argument, Schiro’s defense attorney stated: “Was there a killing? Sure, no doubt about it. Did Tom Schiro do it? Sure .... There’s no question about it, I’m not going to try . . . and ‘bamboozle’ this jury. There was a killing and he did it.” App. to Brief for Respondent 24. Instead, the defense argued that Schiro either was not guilty by reason of insanity or was guilty but mentally ill, an alternative verdict permitted under Indiana law.
  The jury was given 10 possible verdicts, among them the 3 murder counts described above, the lesser included offenses of voluntary and involuntary manslaughter, guilty but mentally ill, not guilty by reason of insanity, and not guilty. App. 37-38. After five hours of deliberation, the jury returned a verdict of guilty on Count II; it left the remaining verdict sheets blank.
  Under Indiana law, to obtain the death penalty the State is required to establish beyond a reasonable doubt the existence of at least one of nine aggravating factors. Ind. Code' § 35-50-2-9(b) (Supp. 1978). The aggravating factor relevant here is: “[T]he defendant committed the murder by intentionally killing the victim while committing or attempting to commit . . . rape” or another enumerated felony. §35-50 — 2—9(b)(1). Upon proof beyond a reasonable doubt of an aggravating factor, the sentencer weighs the factor against any mitigating circumstances. When the initial conviction is by a jury, the “jury . . . reconvene^] for the sentencing hearing” to “recommend to the court whether the death penalty should be imposed.” §§35-50-2-9(d), (e). The trial judge makes “the final determination of the sentence, after considering the jury’s recommendation.” § 35-50-2-9(e)(2). “The court is not bound by the jury’s recommendation,” however. Ibid.
  The primary issue at the sentencing hearing was the weight to be given Schiro’s mitigating evidence. Defense counsel stated to the jury that “I assume by your verdict [at the guilt phase that] you’ve probably decided” that the aggravating circumstance was proved. App. to Brief for Respondent 31-32. He therefore confined his argument to a plea for leniency, citing Schiro’s mental and emotional problems. After considering the statements of counsel, the jury recommended against the death penalty. The trial judge rejected the jury’s recommendation and sentenced Schiro to death. While the case was pending on direct appeal, the Indiana Supreme Court granted the State’s petition to remand the case to the trial court to make written findings of fact regarding aggravating and mitigating circumstances. The trial court found that the State had proved beyond a reasonable doubt that “[t]he defendant committed the murder by intentionally killing the victim while committing or attempting to commit. . . rape.” App. 46. The trial court also found that no mitigating circumstances had been established, and reaffirmed the sentence of death. Id., at 50.
  The sentence was affirmed on direct appeal to the Indiana Supreme Court. Schiro v. State, 451 N. E. 2d 1047 (1983). This Court denied certiorari. Schiro v. Indiana, 464 U. S. 1003 (1983). Schiro sought postconviction relief in state court. Again, the Indiana Supreme Court affirmed the judgment of the trial court. Schiro v. State, 479 N. E. 2d 556 (1985). This Court again denied a petition for a writ of certiorari. Schiro v. Indiana, 475 U. S. 1036 (1986). Schiro then filed a petition for a writ of habeas corpus in the United States District Court for the Northern District of Indiana. The District Judge remanded the case to the Indiana courts for exhaustion of state remedies. The Indiana Supreme Court affirmed the conviction and sentence for a third time. Schiro v. State, 533 N. E. 2d 1201 (1989). In so doing, the Indiana Supreme Court rejected Schiro’s argument that the jury’s failure to convict him on the first murder count operated as an acquittal of intentional murder, and that the Double Jeopardy Clause prohibited the use of the intentional murder aggravating circumstance for sentencing purposes. The Indiana Supreme Court held that “[felony murder] is not an included offense of [murder] and where the jury, as in the instant case, finds the defendant guilty of one of the types of murder and remains silent on the other, it does not operate as an acquittal of the elements of the type of murder the jury chose not to consider.” Id., at 1208. This Court denied certiorari. Schiro v. Indiana, 493 U. S. 910 (1989).
  The Federal District Court then denied Schiro’s federal habeas petition. Schiro v. Clark, 754 F. Supp. 646 (ND Ind. 1990). The Court of Appeals for the Seventh Circuit affirmed. Schiro v. Clark, 963 F. 2d 962 (1992). The Court of Appeals accepted the Indiana Supreme Court’s conclusion that the jury’s verdict was not an acquittal on the Count I murder charge, and that the Double Jeopardy Clause was not violated by the use of the intentional murder aggravating circumstance. The Court of Appeals also concluded that collateral estoppel was not implicated since “the defendant must show that the jury’s verdict actually and necessarily determined the issue he seeks to foreclose” and “Schiro’s conviction for murder/rape did not act as an acquittal with respect to the pure murder charge as a matter of state law.” Id., at 970, n. 7.
  We granted certiorari, 508 U. S. 905 (1993), to consider whether the trial court violated the Double Jeopardy Clause by relying on the intentional murder aggravating circumstance.
  Ill
  The State argues that granting relief to Schiro would require the retroactive application of a new rule, in violation of the principle announced in Teague v. Lane, 489 U. S. 288 (1989) (plurality opinion). Teague analysis is ordinarily our first step when we review a federal habeas case. See, e. g., Graham v. Collins, 506 U.S. 461, 466-467 (1993). The Teague bar to the retroactive application of new rules is not, however, jurisdictional. Collins v. Youngblood, 497 U. S. 37, 40-41 (1990). In this case, the State did not raise the Teague argument in the lower courts. Cf. Parke v. Raley, 506 U. S. 20, 26 (1993). While we ordinarily do not review claims made for the first time in this Court, see, e. g., Taylor v. Freeland & Kronz, 503 U. S. 638, 645-646 (1992), we recognize that the State, as respondent, is entitled to rely on any legal argument in support of the judgment below. See, e. g., Dandridge v. Williams, 397 U. S. 471, 475, n. 6 (1970).
  Nevertheless, the State failed to argue Teague in its brief in opposition to the petition for a writ of certiorari. In deciding whether to grant certiorari in a particular case, we rely heavily on the submissions of the parties at the petition stage. See this Court’s Rule 15.1. If, as in this case, a legal issue appears to warrant review, we grant certiorari in the expectation of being able to decide that issue. Since a State can waive the Teague bar by not raising it, see Godinez v. Moran, 509 U. S. 389, 397, n. 8 (1993), and since the propriety of reaching the merits of a dispute is an important consideration in deciding whether or not to grant certiorari, the State’s omission of any Teague defense at the petition stage is significant. Although we undoubtedly have the discretion to reach the State’s Teague argument, we will not do so in these circumstances.
  IV
  Schiro first argues that he could not be sentenced to death based on the intentional murder aggravating circumstance, because the sentencing proceeding amounted to a successive prosecution for intentional murder in violation of the Double Jeopardy Clause.
  We have recognized that the Double Jeopardy Clause consists of several protections: “It protects against a second prosecution for the same offense after acquittal. It protects against a second prosecution for the same offense after conviction. And it protects against multiple punishments for the same offense.” North Carolina v. Pearce, 395 U. S. 711, 717 (1969) (footnotes omitted). These protections stem from the underlying premise that a defendant should not be twice tried or punished for the same offense. United States v. Wilson, 420 U. S. 332, 339 (1975). The Clause operates as a “bar against repeated attempts to convict, with consequent subjection of the defendant to embarrassment, expense, anxiety, and insecurity, and the possibility that he may be found guilty even though innocent.” United States v. DiFrancesco, 449 U. S. 117, 136 (1980). When a defendant has been acquitted, the “Clause guarantees that the State shall not be permitted to make repeated attempts to convict him.” Wilson, supra, at 343. Where, however, there is “no threat of either multiple punishment or successive prosecutions, the Double Jeopardy Clause is not offended.” 420 U. S., at 344 (footnote omitted). Thus, our cases establish that the primary evil to be guarded against is successive prosecutions: “[T]he prohibition against multiple trials is the controlling constitutional principle.” DiFrancesco, supra, at 132 (internal citations omitted). See also United States v. Martin Linen Supply Co., 430 U. S. 564, 569 (1977).
  Schiro urges us to treat the sentencing phase of a single prosecution as a successive prosecution for purposes of the Double Jeopardy Clause. We decline to do so. Our prior decisions are inconsistent with the argument that a first sentencing proceeding can amount to a successive prosecution. In Stroud v. United States, 251 U. S. 15, 17-18 (1919), we held that where a defendant’s murder conviction was overturned on appeal, the defendant could be resentenced after retrial. Similarly, we found no constitutional infirmity in holding a second sentencing hearing where the first sentence was improperly based on a prior conviction for which the defendant had been pardoned. Lockhart v. Nelson, 488 U. S. 33 (1988). See also North Carolina v. Pearce, supra, at 721 (“[W]e cannot say that the constitutional guarantee against double jeopardy of its own weight restricts the imposition of an otherwise lawful single punishment” upon retrial); Chaffin v. Stynchcombe, 412 U. S. 17, 23-24 (1973) (same). If a second sentencing proceeding ordinarily does not violate the Double Jeopardy Clause, we fail to see how an initial sentencing proceeding could do so.
  We have also upheld the use of prior convictions to enhance sentences for subsequent convictions, even though this means a defendant must, in a certain sense, relitigate in a sentencing proceeding conduct for which he was previously tried. Spencer v. Texas, 385 U. S. 554, 560 (1967). Cf. Moore v. Missouri, 159 U. S. 673, 678 (1895) (“[T]he State may undoubtedly provide that persons who have been before convicted of a crime may suffer severer punishment for subsequent offences than for a first offence”). In short, as applied to successive prosecutions, the Clause “is written in terms of potential or risk of trial and conviction, not punishment.” Price v. Georgia, 398 U. S. 323, 329 (1970).
  Our decision in Bullington v. Missouri, 451 U. S. 430 (1981), is not to the contrary. Bullington was convicted of capital murder. At the first death penalty sentencing proceeding, the jury rejected the death penalty and sentenced him to a term of years. The conviction was overturned; on resentencing the State again sought the death penalty. In Bullington we recognized the general rule that “the Double Jeopardy Clause imposes no absolute prohibition against the imposition of a harsher sentence at retrial.” Id., at 438. Nonetheless, we recognized a narrow exception to this general principle because the capital sentencing scheme at issue “differed] significantly from those employed in any of the Court’s cases where the Double Jeopardy Clause has been held inapplicable to sentencing.” Ibid. Because the capital sentencing proceeding “was itself a trial on the issue of punishment,” ibid., requiring a defendant to submit to a second, identical proceeding was tantamount to permitting a second prosecution of an acquitted defendant, id., at 446.
  This case is manifestly different. Neither the prohibition against a successive trial on the issue of guilt nor the Bullington prohibition against a second capital sentencing proceeding is implicated here — the State did not reprosecute Schiro for intentional murder, nor did it force him to submit to a second death penalty hearing. It simply conducted a single sentencing hearing in the course of a single prosecution. The state is entitled to “one fair opportunity” to prosecute a defendant, Bullington, supra, at 446 (internal quotation marks omitted), and that opportunity extends not only to prosecution at the guilt phase, but also to present evidence at an ensuing sentencing proceeding.
  V
  Schiro also contends that principles of constitutional collateral estoppel require vacation of his death sentence. In Ashe v. Swenson, 397 U. S. 436 (1970), we held that the Double Jeopardy Clause incorporates the doctrine of collateral estoppel in criminal proceedings. See also Dowling v. United States, 493 U. S. 342,347 (1990). Collateral estoppel, or, in modern usage, issue preclusion, “means simply that when an issue of ultimate fact has once been determined by a valid and final judgment, that issue cannot again be litigated between the same parties in any future lawsuit.” Ashe, 397 U. S., at 443. Schiro reasons that the jury acquitted him of “intentionally” murdering Laura Luebbehusen, and that as a result, the trial court was precluded from finding the existence of the aggravating circumstance that he “committed the murder by intentionally killing the victim while committing or attempting to commit . . . rape.” We do not address whether collateral estoppel could bar the use of the “intentional” murder aggravating circumstance, because Schiro has not met his burden of establishing the factual predicate for the application of the doctrine, if it were applicable, namely, that an “issue of ultimate fact has once been determined” in his favor. Ibid.
  The Indiana Supreme Court concluded that the jury verdict did not amount to an acquittal on the intentional murder count. Schiro v. State, 533 N. E. 2d, at 1201. Ordinarily on habeas review, we presume the correctness of state court findings of fact. See 28 U. S. C. § 2254(d). Cf. also Cichos v. Indiana, 385 U. S. 76, 79-80 (1966). The preclusive effect of the jury’s verdict, however, is a question of federal law which we must review de novo. Cf. Ashe v. Swenson, 397 U. S., at 444.
  We must first determine “whether a rational jury could have grounded its verdict upon an issue other than” Schiro’s intent to kill. Ibid. Cf. 18 C. Wright, A. Miller, & E. Cooper, Federal Practice and Procedure § 4421, p. 192 (1981) (“Issue preclusion attaches only to determinations that were necessary to support the judgment entered in the first action”). To do so, we “examine the record of a prior proceeding taking into account the pleadings, evidence, charge, and other relevant matter....” Ashe v. Swenson, supra, at 444 (internal quotation marks omitted). The burden is “on the defendant to demonstrate that the issue whose relitigation he seeks to foreclose was actually decided in the first proceeding.” Dowling, 493 U. S., at 350. In Dowling, for example, the defendant contended that because he had been acquitted of a robbery, the jury must have concluded that he had not been present at the crime. Ibid. In rejecting that argument, we considered the fact that during the trial there was a discussion between the lawyers and the judge where it was asserted that the intruder’s identity was not a factual issue in the case. Id., at 351. Because there were “any number of possible explanations for the jury’s acquittal verdict,” the defendant had “failed to satisfy his burden of demonstrating” that he was not one of the intruders. Id., at 352.
  Applying these principles, we find that the jury could have grounded its verdict on an issue other than Schiro’s intent to kill. The jury was not instructed to return verdicts on all the counts listed on the verdict sheets. In fact, there are indications in the record that the jury might have believed it could only return one verdict. In closing argument at the guilt phase, defense counsel told the jury that it would “have to go back there and try to figure out which one of eight or ten verdicts . . . that you will return back into this Court.” App. to Brief for Respondents 17. The prosecution also told the jury that “you are only going to be allowed to return one verdict.” Id., at 27. Although the jury instructions indicated to the jury that more than one verdict was possible, id, at 27-28, on this record it is impossible to tell which of these statements the jury relied on. The dissent concludes that the jury acquitted on Count I for lack of intent, based on the fact that the only way the jury could have expressed that conclusion was by leaving the Count I verdict form blank, as it did. What stands in the way of such an inference, however, is that the jury would also have acted as it did after reaching a guilty verdict on Count II but without ever deliberating on Count I. In short, since it was not clear to the jury that it needed to consider each count independently, we will not draw any particular conclusion from its failure to return a verdict on Count I.
  The jury instructions on the issue of intent to kill were also ambiguous. Under Indiana law, a person who either “knowingly or intentionally kills another human being” or “kills another human being while committing or attempting to commit... rape” is guilty of “murder.” Ind. Code §35-42-1-1 (Supp. 1978). Thus, intent to kill is not required for a felony murder conviction. Schiro reasons that since the jury found him guilty of felony murder in the course of a rape, but failed to convict him of intentional murder, the jury must have found that he did not have an intent to kill.
  We do not so interpret the jury’s failure to convict on Count I, however. Although the jury was provided with the state law definition of murder, App. 21, the judge also instructed the jury that the State had to prove intent for both felony and intentional murder: “To sustain the charge of murder, the State must prove . . . [t]hat the defendant engaged in the conduct which caused the death of Laura Luebbehusen [and] [t]hat when the defendant did so, he knew the conduct would or intended the conduct to cause the death of Laura Luebbehusen.” Id, at 22-23 (emphasis added). This instruction did not differentiate between the two ways of proving “murder” under Indiana law. The jury was further told that “[t]he instructions of the court are the best source as to the law applicable to this case.” Id., at 20. The jury may well have believed, therefore, that it was required to find a knowing or intentional killing in order to convict Schiro on any of the three murder counts. In sum, in light of the jury instructions, we find that as a matter of law the jury verdict did not necessarily depend on a finding that Schiro lacked an intent to kill.
  Although not necessary to our conclusion, we note that there is additional evidence in the record indicating that Schiro’s intent to kill was not a significant issue in the case. The defense primarily confined its proof at trial to showing that Schiro was insane, and did not dispute that Schiro had committed the murder. At no point during the guilt phase did defense counsel or any of the defense witnesses assert that Schiro should be acquitted on Count I because he lacked an intent to kill. Indeed, we have located no point in the transcript of the proceedings where defense counsel or defense witnesses even discussed the issue of Schiro’s intent to kill. Schiro argues that his intent to kill was put in issue by the insanity defense. But, even if that were so, the jury did not accept this defense. Even defense counsel apparently believed that Schiro’s intent was not an issue in the case. After the jury returned its verdict of guilty on Count II, and reconvened to consider the appropriate sentence, defense counsel indicated his belief that by convicting Schiro on Count II, the jury had found that he had an intent to kill:
  “The statute... provides for aggravating circumstances. There is one listed in this case, and one which you may consider. And that one is that the murder was committed, was intentionally committed in the commission of rape and some other things. I assume by your verdict Friday, or Saturday, that you’ve probably ... decided that issue. In finding him guilty of murder in the commission of rape, I’m assuming you’ve decided beyond a reasonable doubt that it was done in the commission of a rape, and so that aggravating circumstance most likely exists in your mind.” App. to Brief for Respondent 31-32.
  Finally, we observe that a jury finding of intent to kill is entirely consistent with the evidence presented at trial. By Schiro’s own admission, he decided to kill Laura Luebbehusen after she tried to escape and he realized she would go to the police. In addition, the physical evidence suggested a deliberate, rather than unintentional, accidental, or even reckless, killing. The victim was repeatedly beaten with a bottle and an iron; when she resisted, she was strangled to death.
  We have in some circumstances considered jury silence as tantamount to an acquittal for double jeopardy purposes. Green v. United States, 355 U. S. 184, 190-191 (1957); Price v. Georgia, 398 U. S., at 329. The failure to return a verdict does not have collateral estoppel effect, however, unless the record establishes that the issue was actually and necessarily decided in the defendant’s favor. As explained above, our cases require an examination of the entire record to determine whether the jury could have “grounded its verdict upon an issue other than that which the defendant seeks to foreclose from consideration.” Ashe, 397 U. S., at 444 (internal quotation marks omitted). See also Dowling, 493 U. S., at 350. In view of Schiro’s confession to the killing, the instruction requiring the jury to find intent to kill, and the uncertainty as to whether the jury believed it could return more than one verdict, we find that Schiro has not met his “burden ... to demonstrate that the issue whose relitigation he seeks to foreclose was actually decided” in his favor. Ibid.
  The judgment of the Court of Appeals is affirmed.
  So ordered.
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