Justice Souter
delivered the opinion of the Court.
Under Florida law, after a defendant is found guilty of capital murder, a separate jury proceeding is held as the first of two steps in deciding whether his sentence should be life imprisonment or death. Fla. Stat. §921.141(1) (1991). At the close of such aggravating and mitigating evidence as the prosecution and the defense may introduce, the trial judge charges the jurors to weigh whatever aggravating and mitigating circumstances or factors they may find, and to reach an advisory verdict by majority vote. §921.141(2). The jury does not report specific findings of aggravating and mitigating circumstances, but if, at the second sentencing step, the judge decides upon death, he must issue a written statement of the circumstances he finds. §921.141(3). A death sentence is then subject to automatic review by the Supreme Court of Florida. §921.141(4).
A Florida trial court sentenced petitioner to death after a jury so recommended, and the Supreme Court of Florida affirmed. We must determine whether, as petitioner claims, the sentencer in his case weighed either of two aggravating factors that he claims were invalid, and if so, whether the State Supreme Court cured the error by holding it harmless. We answer yes to the first question and no to the second, and therefore vacate the judgment of the Supreme Court of Florida and remand.
I
On New Year’s Eve 1981, petitioner Dennis Sochor met a woman in a bar in Broward County, Florida. Sochor tried to rape her after they had left together, and her resistance angered him to the point of choking her to death. He was indicted for first-degree murder and kidnaping and, after a jury trial, was found guilty of each offense.
At the penalty hearing, aggravating and mitigating evidence was offered, and the jury was instructed on the possibility of finding four aggravating circumstances, two of which were that
“the crime for which the defendant is to be sentenced was especially wicked, evil, atrocious or cruel, and [that] the crime for which the defendant is to be sentenced was committed in a cold, calculated and premeditated manner, without any pretense of moral or legal justification.” App. 326-327.
The judge then explained to the jury that it could find certain statutory and any nonstatutory mitigating circumstances, which were to be weighed against any aggravating ones. By a vote of 10 to 2, the jury recommended the death penalty for the murder. The trial court adopted the jury’s recommendation, finding all four aggravating circumstances as defined in the jury instructions and no circumstances in mitigation.
The Supreme Court of Florida affirmed. 580 So. 2d 595 (1991). It declined to reverse for unconstitutional vagueness in the trial judge’s instruction that the jury could find as an aggravating factor that “the crime for which the defendant is to be sentenced was especially wicked, evil, atrocious or cruel” (hereinafter, for brevity, the heinousness factor, after the statute’s words “heinous, atrocious, or cruel,” Fla. Stat. § 921.141(5)(h) (1991)). The court held the issue waived for failure to object and the claim lacking merit in any event. 580 So. 2d, at 602-603, and n. 10. The court also rejected Sochor’s claim of insufficient evidence to support the trial judge’s finding of the heinousness factor, citing evidence of the victim’s extreme anxiety and fear before she died. The State Supreme Court did agree with Sochor, however, that the evidence failed to support the trial judge’s finding that “the crime . . . was committed in a cold, calculated, and premeditated manner without any pretense of moral or legal justification” (hereinafter the coldness factor), holding this factor to require a “heightened” degree of premeditation not shown in this case. Id., at 603. The State Supreme Court affirmed the death sentence notwithstanding the error, saying that:
“[1] We... disagree with Sochor’s claim that his death sentence is disproportionate. [2] The trial court carefully weighed the aggravating factors against the lack of any mitigating factors and concluded that death was warranted. [3] Even after removing the aggravating factor of cold, calculated, and premeditated there still remain three aggravating factors to be weighed against no mitigating circumstances. [4] Striking one aggravating factor when there are no mitigating circumstances does not necessarily require resentencing. Robinson v. State, 574 So. 2d 108 (Fla. 1991); Holton v. State, 573 So. 2d 284 (Fla. 1990); James v. State, 453 So. 2d 786 (Fla.), cert. denied, 469 U. S. 1098 ... (1984); Francois v. State, 407 So. 2d 885 (Fla. 1981), cert. denied, 458 U. S. 1122 ... (1982). [5] Under the circumstances of this case, and in comparison with other death cases, we find Sochor’s sentence of death proportionate to his crime. E. g., Hitchcock v. State, 578 So. 2d 685 (Fla. 1990); Tompkins[ v. State, 502 So. 2d 415 (Fla. 1986), cert. denied, 483 U. S. 1033 (1987)]; Doyle[ v. State, 460 So. 2d 353 (Fla. 1984)].” Id., at 604.
Sochor petitioned for a writ of certiorari, raising four questions. We granted review limited to the following two: (1) “Did the application of Florida’s [heinousness factor] violate the Eighth and Fourteenth Amendments?” and (2) “Did the Florida Supreme Court’s review of petitioner’s death sentence violate the Eighth and Fourteenth Amendments where that court upheld the sentence even though the trial court had instructed the jury on, and had applied, an improper aggravating circumstance, [in that] the Florida Supreme Court did not reweigh the evidence or conduct a harmless error analysis as to the effect of improper use of the circumstance on the jury’s penalty verdict?” Pet. for Cert. ii; see 502 U. S. 967 (1991).
II
In a weighing State like Florida, there is Eighth Amendment error when the sentencer weighs an “invalid” aggravating circumstance in reaching the ultimate decision to impose a death sentence. See Clemons v. Mississippi, 494 U. S. 738, 752 (1990). Employing an invalid aggravating factor in the weighing process “creates the possibility ... of randomness,” Stringer v. Black, 503 U. S. 222, 236 (1992), by placing a “thumb [on] death’s side of the scale,” id., at 232, thus “creating] the risk [of] treating] the defendant as more deserving of the death penalty,” id., at 235. Even when other valid aggravating factors exist, merely affirming a sentence reached by weighing an invalid aggravating factor deprives a defendant of “the individualized treatment that would result from actual reweighing of the mix of mitigating factors and aggravating circumstances.” Clemons, supra, at 752 (citing Lockett v. Ohio, 438 U. S. 586 (1978), and Eddings v. Oklahoma, 455 U. S. 104 (1982)); see Parker v. Dugger, 498 U. S. 308, 321 (1991). While federal law does not require the state appellate court to remand for resentencing, it must, short of remand, either itself reweigh without the invalid aggravating factor or determine that weighing the invalid factor was harmless error. Id., at 320.
A
Florida’s capital sentencing statute allows application of the heinousness factor if “[t]he capital felony was especially heinous, atrocious, or cruel.” Fla. Stat. §921.141(5)(h) (1991). Sochor first argues that the. jury instruction on the heinousness factor was invalid in that the statutory definition is unconstitutionally vague, see Maynard v. Cartwright, 486 U. S. 356 (1988); Godfrey v. Georgia, 446 U. S. 420 (1980), and the instruction failed to narrow the meaning enough to cure the defect. This error goes to the ultimate sentence, Sochor claims, because a Florida jury is “the sentencer” for Clemons purposes, or at the least one of “the sentencer’s” constituent elements. This is so because the trial judge does not render wholly independent judgment, but must accord deference to the jury’s recommendation. See Tedder v. State, 322 So. 2d 908, 910 (Fla. 1975) (life verdict); Grossman v. State, 525 So. 2d 833, 839, n. 1 (Fla. 1988) (death verdict), cert. denied, 489 U. S. 1071 (1989). Hence, the argument runs, error at the jury stage taints a death sentence, even if the trial judge’s decision is otherwise error free. Cf. Baldwin v. Alabama, 472 U. S. 372, 382 (1985). While Sochor concedes that the general advisory jury verdict does not reveal whether the jury did find and weigh the heinousness factor, he seems to argue that the possibility that the jury weighed an invalid factor is enough to require cure.
This argument faces a hurdle, however, in the rule that this Court lacks jurisdiction to review a state court’s resolution of an issue of federal law if the state court’s decision rests on an adequate and independent state ground, see Herb v. Pitcairn, 324 U. S. 117, 125-126 (1945), as it will if the state court’s opinion “indicates clearly and expressly” that the state ground is an alternative holding, see Michigan v. Long, 463 U. S. 1032, 1041 (1983); see also Harris v. Reed, 489 U. S. 255, 264, n. 10 (1989); Fox Film Corp. v. Muller, 296 U. S. 207, 210 (1935).
The Supreme Court of Florida said this about petitioner’s claim that the trial judge’s instruction on the heinousness factor was unconstitutional:
“Sochor’s next claim, regarding alleged errors in the penalty jury instructions, likewise must fail. None of the complained-of jury instructions were objected to at trial, and, thus, they are not preserved for appeal. Vaught v. State, 410 So. 2d 147 (Fla. 1982). In any event, Sochor’s claims here have no merit.
580 So. 2d, at 602-603, and n. 10.
The quoted passage indicates with requisite clarity that the rejection of Sochor’s claim was based on the alternative state ground that the claim was “not preserved for appeal,” and Sochor has said nothing in this Court to persuade us that this state ground is either not adequate or not independent. Hence, we hold ourselves to be without authority to address Sochor’s claim based on the jury instruction about the heinousness factor.
B
Sochor maintains that the same Eighth Amendment violation occurred again when the trial judge, who both parties agree is at least a constituent part of “the sentencer,” weighed the heinousness factor himself. To be sure, Sochor acknowledges the rule in Walton v. Arizona, 497 U. S. 639 (1990), where we held it was no error for a trial judge to weigh an aggravating factor defined by statute with impermissible vagueness, when the State Supreme Court had construed the statutory language narrowly in a prior case. Id., at 653. We presumed that the trial judge had been familiar with the authoritative construction, which gave significant guidance. Ibid. Sochor nonetheless argues that Walton is no help to the State, because Florida’s heinousness factor has not been subjected to the limitation of a narrow construction from the State Supreme Court.
In State v. Dixon, 283 So. 2d 1 (1973), cert. denied, 416 U. S. 943 (1974), the Supreme Court of Florida construed the statutory definition of the heinousness factor:
“It is our interpretation that heinous means extremely wicked or shockingly evil; that atrocious means outrageously wicked and vile; and, that cruel means designed to inflict a high degree of pain with utter indifference to, or even enjoyment of, the suffering of others. What is intended to be included are those capital crimes where the actual commission of the capital felony was accompanied by such additional acts as to set the crime apart from the norm of capital felonies — the conscienceless or pitiless crime which is unnecessarily torturous to the victim.” 283 So. 2d, at 9.
Understanding the factor, as defined in Dixon, to apply only to a “conscienceless or pitiless crime which is unnecessarily torturous to the victim,” we held in Proffitt v. Florida, 428 U. S. 242 (1976), that the sentencer had adequate guidance. See id., at 255-256 (opinion of Stewart, Powell, and Stevens, JJ.).
Sochor contends, however, that the State Supreme Court’s post-Proffitt cases have not adhered to Dixon’s limitation as stated in Proffitt, but instead evince inconsistent and over-broad constructions that leave a trial court without sufficient guidance. And we may well agree with him that the Supreme Court of Florida has not confined its discussions on the matter to the Dixon language we approved in Proffitt, but has on occasion continued to invoke the entire Dixon statement quoted above, perhaps thinking that Proffitt approved it all. See, e. g., Porter v. State, 564 So. 2d 1060 (1990), cert. denied, 498 U. S. 1110 (1991); Cherry v. State, 544 So. 2d 184, 187 (1989), cert. denied, 494 U. S. 1090 (1990); Lucas v. State, 376 So. 2d 1149, 1153 (1979).
But however much that may be troubling in the abstract, it need not trouble us here, for our review of Florida law indicates that the State Supreme Court has consistently held that heinousness is properly found if the defendant strangled a conscious victim. See Hitchcock v. State, 578 So. 2d 685, 692-693 (1990), cert. denied, 502 U. S. 912 (1991); Holton v. State, 573 So. 2d 284, 292 (1990); Tompkins v. State, 502 So. 2d 415, 421 (1986); Johnson v. State, 465 So. 2d 499, 507, cert. denied, 474 U. S. 865 (1985); Adams v. State, 412 So. 2d 850, cert. denied, 459 U. S. 882 (1982). Cf. Rhodes v. State, 547 So. 2d 1201, 1208 (1989) (strangulation of semiconscious victim not heinous); Herzog v. State, 439 So. 2d 1372 (1983) (same). We must presume the trial judge to have been familiar with this body of case law, see Walton, 497 U. S., at 653, which, at a minimum, gave the trial judge “[some] guidance,” id., at 654. Since the Eighth Amendment requires no more, we infer no error merely from the fact that the trial judge weighed the heinousness factor. While Sochor responds that the State Supreme Court’s interpretation of the heinousness factor has left Florida trial judges without sufficient guidance in other factual situations, we fail to see how that supports the conclusion that the trial judge was without sufficient guidance in the case at hand. See generally Maynard v. Cartwright, 486 U. S., at 361-364.
III
Sochor also claims that when “the sentenced weighed the coldness factor there was Eighth Amendment error that went uncorrected in the State Supreme Court.
A
First, Sochor complains of consideration of the coldness factor by the jury, the first step in his argument being that the coldness factor was “invalid” in that it was unsupported by the evidence; the second step, that the jury in the instant case “weighed” the coldness factor; and the third and last step, that in Florida the jury is at least a constituent part of “the sentencer” for Clemons purposes. The argument fails, however, for the second step is fatally flawed. Because the jury in Florida does not reveal the aggravating factors on which it relies, we cannot know whether this jury actually relied on the coldness factor. If it did not, there was no Eighth Amendment violation. Thus, Sochor implicitly suggests that, if the jury was allowed to rely on any of two or more independent grounds, one of which is infirm, we should presume that the resulting general verdict rested on the infirm ground and must be set aside. See Mills v. Maryland, 486 U. S. 367, 376-377 (1988); cf. Stromberg v. California, 283 U. S. 359, 368 (1931). Just this Term, however, we held it was no violation of due process that a trial court instructed a jury on two different legal theories, one supported by the evidence, the other not. See Griffin v. United States, 502 U. S. 46 (1991). We reasoned that although a jury is unlikely to disregard a theory flawed in law, it is indeed likely to disregard an option simply unsupported by evidence. Id., at 59-60. We see no occasion for different reasoning here, and accordingly decline to presume jury error.
B
Sochor next complains that Eighth Amendment error in the trial judge’s weighing of the coldness factor was left uncured by the State Supreme Court.
1
We can start from some points of agreement. The parties agree that, in Florida, the trial judge is at least a constituent part of “the sentencer” for Clemons purposes, and there is, of course, no doubt that the trial judge “weighed” the coldness factor, as he said in his sentencing order. Nor is there any question that the coldness factor was “invalid” for Clemons purposes, since Parker applied the Clemons rule where a trial judge had weighed two aggravating circumstances that were invalid in the sense that the Supreme Court of Florida had found them to be unsupported by the evidence. See 498 U. S., at 311. It follows that Eighth Amendment error did occur when the trial judge weighed the coldness factor in the instant case. What is in issue is the adequacy of the State Supreme Court’s effort to cure the error under the rule announced in Clemons, that a sentence so tainted requires appellate reweighing or review for harmlessness.
2
We noted in Parker that the Supreme Court of Florida will generally not reweigh evidence independently, 498 U. S., at 319 (citing Hudson v. State, 538 So. 2d 829, 831 (per curiam), cert. denied, 493 U. S. 875 (1989); Brown v. Wainwright, 392 So. 2d 1327, 1331-1332 (1981) (per curiam)), and the parties agree that, to this extent at least, our perception of Florida law was correct. The State argues, nonetheless, that, in this case, the State Supreme Court did support the death verdict adequately by performing harmless-error analysis. It relies on the excerpt from the state court’s opinion quoted above, and particularly on the second through fourth sentences, as “declaring] a belief that” the trial judge’s weighing of the coldness factor “was harmless beyond a reasonable doubt” in that it “did not contribute to the [sentence] obtained.” Chapman v. California, 386 U. S. 18, 24 (1967). This, however, is far from apparent. Not only does the State Supreme Court’s opinion fail so much as to mention “harmless error,’’ see Yates v. Evatt, 500 U. S. 391, 406 (1991), but the quoted sentences numbered one and five expressly refer to the quite different enquiry whether Sochor’s sentence was proportional.
The State tries to counter this deficiency by arguing that the four cases cited following the fourth sentence of the quoted passage were harmless-error cases, citation to which was a shorthand signal that the court had reviewed this record for harmless error as well. But the citations come up short. Only one of the four cases contains language giving an explicit indication that the State Supreme Court had performed harmless-error analysis. See Holton v. State, 573 So. 2d 284, 293 (1990) (“We find the error was harmless beyond a reasonable doubt”). The other three simply do not, and the result is ambiguity.
Although we do not mean here to require a particular formulaic indication by state courts before their review for harmless federal error will pass federal scrutiny, a plain statement that the judgment survives on such an enquiry is clearly preferable to allusions by citation. In any event, when the citations stop as far short of clarity as these do, they cannot even arguably substitute for explicit language signifying that the State Supreme Court reviewed for harmless error.
IV
In sum, Eighth Amendment error occurred when the trial judge weighed the coldness factor. Since the Supreme Court of Florida did not explain or even “declare a belief that” this error “was harmless beyond a reasonable doubt” in that “it did not contribute to the [sentence] obtained,” Chapman, supra, at 24, the error cannot be taken as cured by the State Supreme Court’s consideration of the case. It follows that Sochor’s sentence cannot stand on the existing record of appellate review. We vacate the judgment of the Supreme Court of Florida and remand the case for proceedings not inconsistent with this opinion.
It is so ordered.
“10. .... We reject without discussion Sochor’s ... claims ... that the instructions as to the aggravating factors of heinous, atrocious, or cruel and cold, calculated, and premeditated were improper ....”
Justice Stevens’s dissenting conclusion that we do have jurisdiction, post, at 547-549, is mistaken. First, the suggestion'that Soehor’s pretrial motion objecting to the vagueness of Florida’s heinousness factor preserved his objection to the heinousness instruction to the jury, post, at 547, ignores the settled rule of Florida procedure that, in order to preserve an objection, a party must object after the trial judge has instructed the jury. See, e. g., Harris v. State, 438 So. 2d 787, 795 (Fla. 1983), cert. denied, 466 U. S. 963 (1984); Vazquez v. State, 518 So. 2d 1348, 1350 (Fla. App. 1987); Walker v. State, 473 So. 2d 694, 697-698 (Fla. App. 1985). While the rule is subject to a limited exception for an advance request for a specific jury instruction that is explicitly denied, see, e. g., State v. Heathcoat, 442 So. 2d 955, 957 (Fla. 1983); Buford v. Wainwright, 428 So. 2d 1389, 1390 (Fla.), cert. denied, 464 U. S. 956 (1983); De Parias v. State, 562 So. 2d 434, 435 (Fla. App. 1990), Sochor gets no benefit from this exception, because he never asked for a specific instruction.
Second, Justice Stevens states that “the Florida Supreme Court, far from providing us with a plain statement that petitioner’s claim was procedurally barred, has merely said that the claim was not preserved for appeal, and has given even further indication that petitioner’s claim was not procedurally barred by proceeding to the merits, albeit in the alternative.” Post, at 547-548 (citations and internal quotation marks omitted). It is difficult to comprehend why the State Supreme Court’s statement that “the claim was not preserved for appeal” would not amount to “a plain statement that petitioner’s claim was procedurally barred,” especially since there is no reason to believe that error of the kind Sochor alleged cannot be waived under Florida law, see this note, infra. It is even more difficult to comprehend why the fact that the State Supreme Court rested upon this state ground merely in the alternative would somehow save our jurisdiction. See supra, at 533.
Third, Justice Stevens suggests that, in holding Sochor’s claim waived, the Supreme Court of Florida implied that the claim did not implicate “fundamental error,” and that this in turn implied a rejection of So-chor’s claim of “error,” presumably because all federal constitutional error (or at least the kind claimed by Sochor) would automatically be “fundamental.” Post, at 548-549. To say that this is “the most reasonable explanation,” Michigan v. Long, 463 U. S. 1032, 1041 (1983), of the court’s summary statement that Sochor’s claim was “not preserved for appeal,” see 580 So. 2d, at 602-603, is an Olympic stretch, see Harris v. Reed, 489 U. S. 255, 274-276 (1989) (Kennedy, J., dissenting). In any event, we know of no Florida authority supporting Justice Stevens’s suggestion that all federal constitutional error (or even the kind claimed by Sochor) would be automatically “fundamental.” Indeed, where, as here, valid aggravating factors would remain, instructional error involving another factor is not “fundamental.” See Occhicone v. State, 570 So. 2d 902, 906 (Fla. 1990), cert. denied, 500 U. S. 938 (1991).
Finally, Justice Stevens’s suggestion that the State waived its independent-state-ground defense, post, at 548-549, forgets that this defense goes to our jurisdiction and therefore cannot be waived. See supra, at 533.