opinion: JONES v. UNITED STATES
  No. 97-9361.
  Argued February 22, 1999 —
  Decided June 21, 1999
  Thomas, J., announced the judgment of the Court and delivered the opinion of the Court with respect to Parts I, II, and III-B, in which Rehnquist, C. J., and O’Connor, Scalia, and Kennedy, JJ., joined, and an opinion with respect to Part III-A, in which Rehnquist, C. J., and O’Con-nor and Kennedy, JJ., joined. Ginsburg, J., filed a dissenting opinion, in which Stevens and Souter, JJ., joined, and in which Breyer, J., joined as to Parts I, II, III, and V, post, p. 405.
  Timothy Crooks argued the cause for petitioner. With him on the briefs was Timothy W. Floyd.
  Deputy Solicitor General Dreeben argued the cause for the United States. With him on the brief were Solicitor General Waxman, Assistant Attorney General Robinson, Matthew D. Roberts, and Sean Connelly.
  Kent S. Scheidegger and Charles L. Hobson filed a brief for the Criminal Justice Legal Foundation as amicus curiae urging affirmance.
  Justice Thomas
  delivered the opinion of the Court, except as to Part III-A.
  Petitioner was sentenced to death for committing a kid-naping resulting in death to the victim. His sentence was imposed under the Federal Death Penalty Act of 1994, 18 U. S. C. § 3591 et seq. (1994 ed. and Supp. III). We are presented with three questions: whether petitioner was entitled to an instruction as to the effect of jury deadlock; whether there is a reasonable likelihood that the jury was led to believe that petitioner would receive a court-imposed sentence less than life imprisonment in the event that they could not reach a unanimous sentence recommendation; and whether the submission to the jury of two allegedly duplicative, vague, and overbroad nonstatutory aggravating factors was harmless error. We answer “no” to the first two questions. As for the third, we are of the view that there was no error in allowing the jury to consider the challenged factors. Assuming error, arguendo, we think it clear that such error was harmless.
  I
  Petitioner Louis Jones, Jr., kidnaped Private Trade Joy McBride at gunpoint from the Goodfellow Air Force Base in San Angelo, Texas. He brought her to his house and sexually assaulted her. Soon thereafter, petitioner drove Private McBride to a bridge just outside of San Angelo, where he repeatedly struck her in the head with a tire iron until she died. Petitioner administered blows of such severe force that, when the victim’s body was found, the medical examiners observed that large pieces of her skull had been driven into her cranial cavity or were missing.
  The Government charged petitioner with, inter alia, kid-naping with death resulting to the victim, in violation of 18 U. S. C. § 1201(a)(2), an offense punishable by life imprisonment or death. Exercising its discretion under the Federal Death Penalty Act of 1994, 18 U. S. C. § 3591 et seq., the Government decided to seek the latter sentencing option. Petitioner was tried in the District Court for the Northern District of Texas and found guilty by the jury.
  The District Court then conducted a separate sentencing hearing pursuant to § 3593. As an initial matter, the sentencing jury was required to find that petitioner had the requisite intent, see § 3591(a)(2); it concluded that petitioner intentionally killed his victim and intentionally inflicted serious bodily injury resulting in her'death. Even on a finding of intent, however, a defendant is not death eligible unless the sentencing jury also finds that the Government has proved beyond a reasonable doubt at least one of the statutory aggravating factors set forth at §3592. See § 3593(e). Because petitioner was charged with committing a homicide, the Government had to prove 1 of the 16 statutory aggravating factors set forth at 18 U. S. C. § 3592(c) (1994 ed. and Supp. III) (different statutory aggravating factors for other crimes punishable by death are set forth at §§ 3592(b), (d)). The jury unanimously found that two such factors had been proved beyond a reasonable doubt — it agreed that petitioner caused the death of his victim during the commission of another crime, see § 3592(c)(1), and that he committed the offense in an especially heinous, cruel, and depraved manner, see § 3592(c)(6).
  Once petitioner became death eligible, the jury had to decide whether he should receive a death sentence. In making the selection decision, the Act requires that the sentencing jury consider all of the aggravating and mitigating factors and determine whether the former outweigh the latter (or, if there are no mitigating factors, whether the aggravating factors alone are sufficient to warrant a death sentence). §§ 3591(a), 3592, 3593(e). The Act, however, requires more exacting proof of aggravating factors than mitigating ones— although a jury must unanimously agree that the Government established the existence of an aggravating factor beyond a reasonable doubt, § 3593(e), the jury may consider a mitigating factor in its weighing process so long as one juror finds that the defendant established its existence by preponderance of the evidence, §§ 3593(c), (d). In addition to the two statutory aggravators that established petitioner’s death eligibility, the jury also unanimously found two aggravators of the nonstatutory variety had been proved: One set forth victim impact evidence and the other victim vulnerability evidence. As for mitigating factors, at least one juror found 10 of the 11 that petitioner proposed and seven jurors wrote in a factor petitioner had not raised on the Special Findings Form.
  After weighing the aggravating and mitigating factors, the jury unanimously recommended that petitioner be sentenced to death. App. 57-58. The District Court imposed sentence in accordance with the jury’s recommendation pursuant to §3594. The United States Court of Appeals for the Fifth Circuit affirmed the sentence. 132 F. 3d 232 (1998). We granted certiorari, 525 U. S. 809 (1998), and now affirm.
  II
  A
  We first decide the question whether petitioner was entitled to an instruction as to the consequences of jury deadlock. Petitioner requested, in relevant part, the following instruction:
  “In the event, after due deliberation and reflection, the jury is unable to agree on a unanimous decision as to the sentence to be imposed, you should so advise me and I will impose a sentence of life imprisonment without possibility of release....
  “In the event you are unable to agree on [a sentence of] Life Without Possibility of Release or Death, but you are unanimous that the sentence should not be less than Life Without Possibility of Release, you should report that vote to the Court and the Court will sentence the defendant to Life Without the Possibility of Release.” App. 14-15.
  In petitioner’s view, the Eighth Amendment requires that the jurors be instructed as to the effect of their inability to agree. He alternatively argues that we should invoke our supervisory power over the federal courts and require that such an instruction be given.
  Before we turn to petitioner’s Eighth Amendment argument, a question of statutory interpretation calls for our attention. The Fifth Circuit held that the District Court did not err in refusing petitioner’s requested instruction because it was not substantively correct. See 132 F. 3d, at 242-243. According to the Court of Appeals, § 3593(b)(2)(C), which provides that a new jury shall be impaneled for a new sentencing hearing if the guilt phase jury is discharged for “good cause,” requires the District Court to impanel a second jury and hold a second sentencing hearing in the event of jury deadlock. Id., at 243. The Government interprets the statute the same way (although its reading is more nuaneed) and urges that the judgment below be affirmed on this ground.
  Petitioner, however, reads the Act differently. In his view, whenever the jury reaches a result other than a unanimous verdict recommending a death sentence or life imprisonment without the possibility of release, the duty of sentencing falls upon the district court pursuant to § 3594, which reads:
  “Upon a recommendation under section 3593(e) that the defendant should be sentenced to death or life imprisonment without possibility of release, the court shall sentence the defendant accordingly. Otherwise, the court shall impose any lesser sentence that is authorized by law. Notwithstanding any other law, if the maximum term of imprisonment for the offense is life imprisonment, the court may impose a sentence of life imprisonment without possibility of release.”
  Petitioner’s argument is based on his construction of the term “[otherwise.” He argues that this term means that when the jury, after retiring for deliberations, reports itself as unable to reach a unanimous verdict, the sentencing determination passes to the court.
  As the dissent also concludes, post, at 417-418, petitioner’s view of the statute is the better one. The phrase “good cause” in § 3593(b)(2)(C) plainly encompasses events such as juror disqualification, but cannot be read so expansively as to include the jury’s failure to reach a unanimous decision. Nevertheless, the Eighth Amendment does not require that the jurors be instructed as to the consequences of their failure to agree.
  To be sure, we have said that the Eighth Amendment requires that a sentence of death not be imposed arbitrarily. See, e. g., Buchanan v. Angelone, 522 U. S. 269, 275 (1998). In order for a capital sentencing scheme to pass constitutional muster, it must perform a narrowing function with respect to the class of persons eligible for the death penalty and must also ensure that capital sentencing decisions rest upon an individualized inquiry. Ibid. The instruction that petitioner requested has no bearing on what we have called the “eligibility phase” of the capital sentencing process. As for what we have called the “selection phase,” our cases have held that in order to satisfy the requirement that capital sentencing decisions rest upon an individualized inquiry, a scheme must allow a “broad inquiry” into all “constitutionally relevant mitigating evidence.” Id., at 276. Petitioner does not argue, nor could he, that the District Court’s failure to give the requested instruction prevented the jury from considering such evidence.
  In theory, the District Court’s failure to instruct the jury as to the consequences of deadlock could give rise to an Eighth Amendment problem of a different sort: We also have held that a jury cannot be “affirmatively misled regarding its role in the sentencing process.” Romano v. Oklahoma, 512 U. S. 1, 9 (1994). In no way, however, was the jury affirmatively misled by the District Court's refusal to give petitioner’s proposed instruction. The truth of the matter is that the proposed instruction has no bearing on the jury's role in the sentencing process. Rather, it speaks to what happens in the event that the jury is unable to fulfill its role — when deliberations break down and the jury is unable to produce a unanimous sentence recommendation. Petitioner’s argument, although less than clear, appears to be that a death sentence is arbitrary within the meaning of the Eighth Amendment if the jury is not given any bit of information that might possibly influence an individual juror's voting behavior. That contention has no merit. We have never suggested, for example, that the Eighth Amendment requires a jury be instructed as to the consequences of a breakdown in the deliberative process. On the contrary, we have long been of the view that “[t]he very object of the jury system is to secure unanimity by a comparison of views, and by arguments among the jurors themselves.” Allen v. United States, 164 U. S. 492, 501 (1896). We further have recognized that in a capital sentencing proceeding, the Government has “a strong interest in having the jury express the conscience of the community on the ultimate question of life or death.” Lowenfield v. Phelps, 484 U. S. 231, 238 (1988) (citation and internal quotation marks omitted). We are of the view that a charge to the jury of the sort proposed by petitioner might well have the effect of undermining this strong governmental interest.
  We similarly decline to exercise our supervisory powers to require that an instruction on the consequences of deadlock be given in every capital ease. In drafting the Act, Congress chose not to require such an instruction. Cf. § 3593(f) (district court “shall instruct the jury that, in considering whether a sentence of death is justified, it shall not consider the race, color, religious beliefs, national origin, or sex of the defendant or of any victim and that the jury is not to recommend a sentence of death unless it has concluded that it would recommend a sentence of death for the crime in question no matter what the race, color, religious beliefs, national origin, or sex of the defendant or of any victim may be”). Petitioner does point us to a decision from the New Jersey Supreme Court requiring, in an exercise of that court’s supervisory authority, that the jury be informed of the sentencing consequences of nonunanimity. See New Jersey v. Ramseur, 106 N. J. 123, 304-315, 524 A. 2d 188, 280-286 (1987). Of course, New Jersey’s practice has no more relevance to our decision than the power to persuade. Several other States have declined to require a similar instruction. See, e. g., North Carolina v. McCarver, 341 N. C. 364, 394, 462 S. E. 2d 25, 42 (1995); Brogie v. Oklahoma, 695 P. 2d 538, 547 (Okla. Crim. App. 1985); Calhoun v. Maryland, 297 Md. 563, 593-595, 468 A. 2d 45, 58-60 (1983); Coulter v. Alabama, 438 So. 2d 336, 346 (Ala. Crim. App. 1982); Justus v. Virginia, 220 Va. 971, 979, 266 S. E. 2d 87, 92-98 (1980). We find the reasoning of the 'Virginia Supreme Court in Justus far more persuasive than that of the New Jersey Supreme Court, especially in light of the strong governmental interest that we have recognized in having the jury render a unanimous sentence recommendation:
  “The court properly refused an instruction offered by the defendant which would have told the jury that if it could not reach agreement as to the appropriate punishment, the court would dismiss it and impose a life sentence. While this was a correct statement of law it concerned a procedural matter and was not one which should have been the subject of an instruction. It would have been an open invitation for the jury to avoid its responsibility and to disagree.” Id., at 979, 266 S. E. 2d, at 92.
  In light of the legitimate reasons for not instructing the jury as to the consequences of deadlock, and in light of congressional silence, we will not exercise our supervisory powers to require that an instruction of the sort petitioner sought be given in every case. Cf. Shannon v. United States, 512 U. S. 573, 587 (1994).
  B
  Petitioner further argues that the jury was led to believe that if it could not reach a unanimous sentence recommendation he would receive a judge-imposed sentence less severe than life imprisonment, and his proposed instruction as to the consequences of deadlock was necessary to correct the jury’s erroneous impression. Moreover, he contends that the alleged confusion independently warrants reversal of his sentence under the Due Process Clause, the Eighth Amendment, and the Act itself. He grounds his due process claim in the assertion that sentences may not be based on materially untrue assumptions, his Eighth Amendment claim in his contention that the jury is entitled to accurate sentencing information, and his statutory claim in an argument that jury confusion over the available sentencing options constitutes an “arbitrary factor” under § 3595(c)(2)(A).
  To put petitioner’s claim in the proper context, we must briefly review the jury instructions and sentencing procedures used at trial. After instructing the jury on the aggravating and mitigating factors and explaining the process of weighing those factors, the District Court gave the following instructions pertaining to the jury’s sentencing recommendation:
  “Based upon this consideration, you the jury, by unanimous vote, shall recommend whether the defendant should be sentenced to death, sentenced to life imprisonment without the possibility of release, or sentenced to some other lesser sentence.
  “If you unanimously conclude that the aggravating factors found to exist sufficiently outweigh any mitigating factor or factors found to exist, or in the absence of any mitigating factors, that the aggravating factors are themselves sufficient to justify a sentence of death, you may recommend a sentence of death. Keep in mind, however, that regardless of your findings with respect to aggravating and mitigating factors, you are never required to recommend a death sentence.
  “If you recommend the imposition of a death sentence, the court is required to impose that sentence. If you recommend a sentence of life without the possibility of release, the court is required to impose that sentence. If you recommend that some other lesser sentence be imposed, the court is required to impose a sentence that is authorized by the law. In deciding what recommendation to make, you are not to be concerned with the question of what sentence the defendant might receive in the event you determine not to recommend a death sentence or a sentence of life without the possibility of release. That is a matter for the court to decide in the event you conclude that a sentence of death or life without the possibility of release should not be recommended.” App. 43-44.
  The District Court also provided the jury with four decision forms on which to record its recommendation. In its instructions explaining those forms, the District Court told the jury that its choice of form depended on its recommendation:
  “The forms are self-explanatory: Decision Form A should he used if you determine that a sentence of death should not be imposed because the government failed to prove beyond a reasonable doubt the existence of the required intent on the part of the defendant or a required aggravating factor. Decision Form B should be used if you unanimously recommend that a sentence of death should be imposed. Decision Form C or Decision Form D should be used if you determine that a sentence of death should not be imposed because: (1) you do not unanimously find that the aggravating factor or factors found to exist sufficiently outweigh any mitigating factor or factors found to exist; (2) you do not unanimously find that the aggravating factor or factors found to exist are themselves sufficient to justify a sentence of death where no mitigating factor has been found to exist; or (3) regardless of your findings with respect to aggravating and mitigating factors you are not unanimous in recommending that a sentence of death should be imposed. Decision Form C should be used if you unanimously recommend that a sentence of imprisonment for life without the possibility of release should be imposed.
  "Decision Form D should be used if you recommend that some other lesser sentence should be imposed.” Id., at 47-48.
  Petitioner maintains that the instructions in combination with the decision forms led the jury to believe that if it failed to recommend unanimously a sentence of death or life imprisonment without the possibility of release, then it would be required to use Decision Form D and the court would impose a sentence less than life imprisonment. The scope of our review is shaped by whether petitioner properly raised and preserved an objection to the instructions at trial. A party generally may not assign error to a jury instruction if he fails to object before the jury retires or to “stat[e] distinctly the matter to which that party objects and the grounds of the objection.” Fed. Rule Crim. Proc. 30. These timeliness and specificity requirements apply during the sentencing phase as well as the trial. See 18 U. S. C. § 3595(e)(2)(C); see also Fed. Rules Crim. Proc. 1, 54(a). They enable a trial court to correct any instructional mistakes before the jury retires and in that way help to avoid the burdens of an unnecessary retrial. While an objection in a directed verdict motion before the jury retires can preserve a claim of error, Leary v. United States, 895 U. S. 6, 32 (1969), objections raised after the jury has completed its deliberations do not. See Singer v. United States, 380 U. S. 24, 38 (1965); Lopez v. United States, 373 U. S. 427, 436 (1963); cf. United States v. Socony-Vacuum Oil Co., 310 U. S. 150, 238-239 (1940). Nor does a request for an instruction before the jury retires preserve an objection to the instruction actually given by the court. Otherwise, district judges would have to speculate on what sorts of objections might be implied through a request for an instruction and issue rulings on “implied” objections that a defendant never intends to raise. Such a rule would contradict Rule 30’s mandate that a party state distinctly his grounds for objection.
  Petitioner did not voice the objections to the instructions and decision forms that he now raises before the jury retired. See App. 16-33. While Rule 30 could be read literally to bar any review of petitioner’s claim of error, our decisions instead have held that an appellate court may conduct a limited review for plain error. Fed. Rule Crim. Proc. 52(b); Johnson v. United States, 520 U. S. 461, 465-466 (1997); United States v. Olano, 507 U. S. 725, 731-732 (1993); Lopez, supra, at 436-437; Namet v. United States, 373 U. S. 179, 190-191 (1963). Petitioner, however, contends that the Federal Death Penalty Act creates an exception. He relies on language in the Act providing that an appellate court shall remand a case where it finds that “the sentence of death was imposed under the influence of passion, prejudice, or any other arbitrary factor.” § 3595(c)(2)(A). According to petitioner, the alleged jury confusion over the available sentencing options is an arbitrary factor and thus warrants resen-tencing even if he did not properly preserve the objection.
  This argument rests on an untenable reading of the Act. The statute does not explicitly announce an exception to plain-error review, and a congressional intent to create snch an exception cannot be inferred from the overall scheme. Statutory language must be read in context and a phrase “gathers meaning from the words around it.” Jarecki v. G. D. Searle & Co., 367 U. S. 303, 307 (1961); see also Gustafson v. Alloyd Co., 513 U. S. 561, 575 (1995). Here, the same subsection that petitioner relies upon further provides that reversal is warranted where “the proceedings involved any other legal error requiring reversal of the sentence that was properly preserved for appeal under the rules of criminal procedure.” § 3595(c)(2)(C). This language makes clear that Congress sought to impose a timely objection requirement at sentencing and did not intend to equate the phrase “arbitrary factor” with legal error. Petitioner’s broad interpretation of § 3595(c)(2)(A) would drain § 3595(c)(2)(C) of any independent meaning.
  We review the instructions, then, for plain error. Under that review, relief is not warranted unless there has been (1) error, (2) that is plain, and (3) affects substantial rights. Johnson, supra, at 467; Olano, supra, at 732. Appellate review under the plain-error doetrine, of course, is circumscribed and we exercise our power under Rule 52(b) sparingly. See United States v. Young, 470 U. S. 1, 15 (1985); United States v. Frady, 456 U. S. 152, 163, and n. 14 (1982); cf. Henderson v. Kibbe, 431 U. S. 145, 154 (1977) (“It is the rare case in which an improper instruction will justify reversal of a criminal conviction when no objection has been made in the trial court”). An appellate court should exercise its discretion to correct plain error only if it “seriously affeet[s] the fairness, integrity, or public reputation of judicial proceedings.” Olano, supra, at 732 (internal quotation marks omitted); Young, supra, at 15; United States v. Atkinson, 297 U. S. 157, 160 (1936).
  Petitioner’s argument — which depends on the premise that the instructions and decision forms led the jury to believe that it did not have to recommend unanimously a lesser sentence — falls short of satisfying even the first requirement of the plain-error doctrine, for we cannot see that any error occurred. We have considered similar claims that allegedly ambiguous instructions caused jury confesión. See, e.g., Victor v. Nebraska, 511 U. S. 1 (1994); Estelle v. McGuire, 502 U. S. 62 (1991); Boyde v. California, 494 U. S. 370 (1990). The proper standard for reviewing such claims is “ ‘whether there is a reasonable likelihood that the jury has applied the challenged instruction in a way* that violates the Constitution.” Estelle, supra, at 72 (quoting Boyde, supra, at 380); see also Victor, supra, at 6 (applying reasonable likelihood standard to direct review of state criminal conviction).
  There is no reasonable likelihood that the jury applied the instructions incorrectly. The District Court did not expressly inform the jury that it would impose a lesser sentence in case of deadlock. It simply told the jury that, if it recommended a lesser sentence, the court would impose a sentence “authorized by the law.” App. 44. Nor did the District Court expressly require the jury to select Decision Form D if it could not reach agreement. Instead, it exhorted the jury “to discuss the issue of punishment with one another in an effort to reach agreement, if you can do so.” Id., at 46.
  Notwithstanding the absence of an explicit instruction on the consequences of nonunanimity, petitioner identifies several passages which, he believes, support the inference that the jury was confused on this point. He trains on that portion of the instructions telling the jurors that the court would decide the sentence if they did not recommend a sentence of death or life without the possibility of release. Petitioner argues that this statement, coupled with two earlier references to a “lesser sentence” option, caused the jurors to infer that the District Court would impose a lesser sentence if they could not unanimously agree on a sentence of death or life without the possibility of release. He maintains that this inference is strengthened by a later instruction: “In order to bring back a verdict recommending the punishment of death or life without the possibility of release, all twelve of you must unanimously vote in favor of such specific penalty.” Id., at 45. According to petitioner, the failure to mention the “lesser sentence” option in this statement strongly implied that, in contradistinction to the first two options, the “lesser sentence” option did not require jury unanimity.
  Petitioner parses these passages too finely. Our decisions repeatedly have cautioned that instructions must be evaluated not in isolation but in the context of the entire charge. See, e. g., Bryan v. United States, 524 U. S. 184, 199 (1998); United States v. Park, 421 U. S. 658, 674 (1975); Cupp v. Naughten, 414 U. S. 141, 147 (1973); Boyd v. United States, 271 U. S. 104, 107 (1926). We agree with the Fifth Circuit that when these passages are viewed in the context of the entire instructions, they lack ambiguity and cannot be given the reading that petitioner advances. See 132 F. 3d, at 244. We previously have held that instructions that might be ambiguous in the abstract can be cured when read in conjunction with other instructions. Bryan, supra, at 199; Victor, supra, at 14-15; Estelle, supra, at 74-75. Petitioner’s claim is far weaker than those we evaluated in Bryan, Victor, and Estelle because the jury in this case received an explicit in-. struction that it had to be unanimous. Just prior to its admonition that the jury should not concern itself with the ultimate sentence if it does not recommend death or life without the possibility of release, the trial court expressly instructed the jury in unambiguous language that any sentencing recommendation had to be by a unanimous vote. Specifically, it stated that “you the jury, by unanimous vote, shall recommend whether the defendant should be sentenced to death, sentenced to life imprisonment without the possibility of release, or sentenced to some other lesser sentence.” App. 43. Other instructions, by contrast, specified when the jury did not have to act unanimously. For example, the District Court explicitly told the jury that its findings on the mitigating circumstances, unlike those on the aggravating circumstances, did not have to be unanimous. To be sure, the District Court could have used the phrase “unanimously” more frequently. But when read alongside an unambiguous charge that any sentencing recommendation be unanimous and other instructions explicitly identifying when the jury need not be unanimous, the passages identified by petitioner do not create a reasonable likelihood that the jury believed that deadlock would cause the District Court to impose a lesser sentence.
  Petitioner also relies on alleged ambiguities in the decision forms and the explanatory instructions. He stresses the fact that Decision Form D (lesser sentence recommendation), unlike Decision Forms B (death sentence) and C (life without the possibility of release), did not contain the phrase “by unanimous vote” and required only the foreperson’s signature. These features of Decision Form D, according to petitioner, led the jury to conclude that nonunanimity would result in a lesser sentence. According to petitioner, the instructions accompanying Decision Form D, unlike those respecting Decision Forms B and C, did not mention unanimity, thereby increasing the likelihood of confusion.
  With respect to this aspect of petitioner’s argument, we agree with the Fifth Circuit that “[although the verdict forms standing alone could have persuaded a jury to conclude that unanimity was not required for the lesser sentence option, any confusion created by the verdict forms was clarified when considered in light of the entire jury instruction.” 132 F. 3d, at 245. The District Court’s explicit instruction that the jury had to be unanimous and its exhortation to the jury to discuss the punishment and attempt to reach agreement, App. 46, malee it doubtful that the jury thought it was compelled to employ Decision Form D in the event of disagreement.
  Petitioner also places too much weight on the fact that Decision Form D required only the foreperson’s signature. Although it only contained a space for the foreperson’s signature, Form D, Like the others, used the phrase “We the jury recommend...,” thereby signaling that Form D represented the jury’s recommendation. Id., at 59. Moreover, elsewhere, the jury foreperson alone signed the jury forms to indicate the jury’s unanimous agreement. Specifically, only the jury foreperson signed the special findings form on which the jury was required to indicate its unanimous agreement that an aggravating factor had been proved beyond a reasonable doubt. Id., at 51-53. In these circumstances, we do not think that the decision forms or accompanying instructions created a reasonable likelihood of confusion over the effect of nonunanimity.
  Even assuming, arguendo, that an error occurred (and that it was plain), petitioner cannot show that it affected his substantial rights. Any confusion among the jurors over the effect of a lesser sentence recommendation was allayed by the District Court’s admonition that the jury should not concern itself with the effect of such a recommendation. See supra, at 390 (quoting App. 44). The jurors are presumed to have followed these instructions. See Shannon, 512 U. S., at 585; Richardson v. Marsh, 481 U. S. 200, 206 (1987). Even if the jurors had some lingering doubts about the effect of deadlock, therefore, the instructions made clear that they should set aside their concerns and either report that they were unable to reach agreement or recommend a lesser sentence if they believed that this was the only option.
  Moreover, even assuming that the jurors were confused over the consequences of deadlock, petitioner cannot show the confusion necessarily worked to his detriment. It is just as likely that the jurors, loath to recommend a lesser sentence, would have compromised on a sentence of life imprisonment as on a death sentence. Where the effect of an alleged error is so uncertain, a defendant cannot meet his burden of showing that the error actually affected his substantial rights. Cf. Romano, 512 U. S., at 14. In Romano, we considered a similar argument, namely, that jurors had disregarded a trial judge’s instructions and given undue weight to certain evidence. In rejecting that argument, we noted that, even assuming that the jury disregarded the trial judge’s instructions, “[i]t 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.” Ibid. Any speculation on the effect of a lesser sentence recommendation, like the evidence in Romano, would have had such an indeterminate effect on the outcome of the proceeding that we cannot conclude that any alleged error in the District Court’s instructions affected petitioner’s substantial rights. See Park, 421 U. S., at 676; Lopez, 373 U. S., at 436-437.
  III
  A
  Apart from the claimed instructional error, petitioner argues that the nonstatutory aggravating factors found and considered by the jury, see n. 2, supra, were vague, over-broad, and duplicative in violation of the Eighth Amendment, and that the District Court’s error in allowing the jury to consider them was not harmless beyond a reasonable doubt.
  The Eighth Amendment, as the Court of Appeals correctly recognized, see 132 F. 3d, at 250, permits capital sentencing juries to consider evidence relating to the victim’s personal characteristics and the emotional impact of the murder on the victim’s family in deciding whether an eligible defendant should receive a death sentence. See Payne v. Tennessee, 501 U. S. 808, 827 (1991) (“A State may legitimately conclude that evidence about the victim and about the impact of the murder on the victim’s family is relevant to the jury’s decision as to whether or not the death penalty should be imposed. There is no reason to treat such evidence differently than other relevant evidence is treated”). Petitioner does not dispute that, as a general matter, such evidence is appropriate for the sentencing jury’s consideration. See Reply Brief for Petitioner 15. His objection is that the two non-statutory aggravating factors were duplicative, vague, and overbroad so as to render their use in this ease unconstitutional, a point with which the Fifth Circuit agreed, 132 F. 3d, at 250-251, although it ultimately ruled in the Government’s favor on the ground that the alleged error was harmless beyond a reasonable doubt, id., at 251-252.
  The Government here renews its argument that the non-statutory aggravators in this ease were constitutionally valid. At oral argument, however, it was suggested that this case comes to us on the assumption that the nonstatu-tory aggravating factors were invalid because the Government did not cross-appeal on the question. Tr. of Oral Arg. 25. As the prevailing party, the Government is entitled to defend the judgment on any ground that it properly raised below. See, e. g., El Paso Natural Gas Co. v. Neztsosie, 526 U. S. 473, 479 (1999); Northwest Airlines, Inc. v. County of Kent, 510 U. S. 355, 364 (1994) (“A prevailing party need not cross-petition to defend a judgment on any ground properly raised below, so long as that party seeks to preserve, and not to change, the. judgment”). It further was suggested that because we granted certiorari on the Government’s rephrasing of petitioner’s questions and because the third question — “whether the court of appeals correctly held that the submission of invalid nonstatutory aggravating factors was harmless beyond a reasonable doubt” — presumes error, we must assume the nonstatutory aggravating factors were erroneous. Tr. of Oral Arg. 25-27. We are not convinced that the reformulated question presumes error. The question whether the nonstatutory aggravating factors were constitutional is fairly included within the third question presented — we might answer “no” to the question “[w]hether the Court of Appeals correctly held that the submission of invalid nonstatutory aggravating factors was harmless beyond a reasonable doubt,” 525 U. S. 809 (1998), by explaining that the Fifth Circuit was incorrect in holding that there was error. Without a doubt, the Government would have done better to call our attention to the fact that it planned to argue that the nonstatutory aggravating factors were valid at the petitioning stage. But it did not affirmatively concede that the nonstatutory aggravators were invalid, see Brief in Opposition 18-22, and absent such a concession, we think that the Government's argument is properly presented.
  1
  We first address petitioner’s contention that the two non-statutory aggravating factors were impermissibly duplicative. The Fifth Circuit reasoned that “[t]he plain meaning of the term ‘personal characteristics/ used in [nonstatutory aggravator] 3(C), necessarily includes ‘young age, slight stature, background, and unfamiliarity/ which the jury was asked to consider in 3(B).” 132 F. 3d, at 250. The problem, the court thought, was that this duplication led to “double counting” of aggravating factors. Following a Tenth Circuit decision, United States v. McCullah, 76 F. 3d 1087, 1111 (1996), the Fifth Circuit was of the view that in a weighing scheme, “double counting” has a tendency to skew the process so as to give rise to the risk of an arbitrary, and thus unconstitutional, death sentence. 132 F. 3d, at 251. In the Fifth Circuit’s words, there may be a thumb on the scale in favor of death “[i]f the jury has been asked to weigh the same aggravating factor twice.” Ibid.
  We have never before held that aggravating factors could be duplicative so as to render them constitutionally invalid, nor have we passed on the “double counting” theory that the Tenth Circuit advanced in McCullah and the Fifth Circuit appears to have followed here. What we have said is that the weighing process may be impermissibly skewed if the sentencing jury considers an invalid faetor. See Stringer v. Black, 503 U. S. 222, 232 (1992). Petitioner’s argument (and the reasoning of the Fifth and Tenth Circuits) would have us reach a quite different proposition — that if two aggravating factors are “duplicative,” then the weighing process necessarily is skewed, and the factors are therefore invalid.
  Even accepting, for the sake of argument, petitioner’s “double counting” theory, there are nevertheless several problems with the Fifth Circuit’s application of the theory in this ease. The phrase “personal characteristics” as used in factor 3(C) does not obviously include the specific personal characteristics listed in 3(B) — “young age, her slight stature, her background, and her unfamiliarity with San Angelo”— especially in light of the fact that 3(C) went on to refer to the impact of the crime on the victim’s family. In the context of considering the effect of the crime on the victim’s family, it would be more natural to understand “personal characteristics” to refer to those aspects of the victim’s character and personality that her family would miss the most. More important, to the extent that there was any ambiguity arising from how the factors were drafted, the Government’s argument to the jury made clear that 3(B) and 3(C) went to entirely different areas of aggravation — the former clearly went to victim vulnerability while the latter captured the victim’s individual uniqueness and the effect of the crime on her family. See, e. g., 25 Record 2733-2734 (“[Y]ou can consider [the victim’s] young age, her slight stature, her background, her unfamiliarity with the San Angelo area.... She is barely five feet tall [and] weighs approximately 100 pounds. [She is] the ideal victim”); id., at 2734 (“[Y]ou can consider [the victim’s) personal characteristics and the effects of the instant offense on her family.... You heard about this young woman, you heard about her from her mother, you heard about her from her friends that knew her. She was special, she was unique, she was loving, she was caring, she had a lot to offer this world”). As such, even if the phrase “personal characteristics” as used in factor 3(C) was understood to include the specific personal characteristics listed in 3(B), the factors as a whole were not duplicative— at best, certain evidence was relevant to two different aggravating factors. Moreover, any risk that the weighing process would be skewed was eliminated by the District Court’s instruction that the jury “should not simply count the number of aggravating and mitigating factors and reach a deeision based on which number is greater [but rather] should consider the weight and value of each factor.” App. 45.
  2
  We also are of the view that the Fifth Circuit incorrectly concluded that factors 3(B) and 3(C) were unconstitutionally vague. In that court’s view, the nonstatutory aggravating factors challenged here “fail[ed] to guide the jury’s discretion, or [to] distinguish this murder from any other murder.” 132 F. 3d, at 251. The Court of Appeals, relying on our decision in Maynard v. Cartwright, 486 U. S. 356, 361-362 (1988), also was of the opinion that “[t]he use of the terms ‘background,’ ‘personal characteristics,’ and ‘unfamiliarity’ without further definition or instruction left the jury with . . . open-ended discretion.” 132 F. 3d, at 251 (internal quotation marks omitted).
  Ensuring that a sentence of death is not so infected with bias or caprice is our “controlling objective when we examine eligibility and selection factors for vagueness.” Tuilaepa v. California, 512 U. S. 967, 973 (1994). Our vagueness review, however, is “quite deferential.” Ibid. As long as an aggravating factor has a core meaning that criminal juries should be capable of understanding, it will pass constitutional muster. Ibid. Assessed under this deferential standard, the factors challenged here surely are not vague. The jury should have had no difficulty understanding that factor 3(B) was designed to ask it to consider whether the victim was especially vulnerable to petitioner’s attack. Nor should it have had difficulty comprehending that factor 3(C) asked it to consider the victim’s personal traits and the effect of the crime on her family. Even if the factors as written were somewhat vague, the Fifth Circuit was wrong to conclude that the factors were not given further definition, see 132 F. 3d, at 251; as we have explained, the Government’s argument made absolutely clear what each nonstatutory factor meant.
  3
  Finally, we turn to petitioner’s contention that the challenged nonstatutory factors were overbroad. An aggravating factor can be overbroad if the sentencing jury “fairly could conclude that an aggravating circumstance applies to every defendant eligible for the death penalty.” Arave v. Creech, 507 U.S. 463, 474 (1993). We have not, however, specifically considered what it means for a factor to be over-broad when it is important only for selection purposes and especially when it sets forth victim vulnerability or victim impact evidence. Of course, every murder will have an impact on the victim’s family and friends and victims are often chosen because of their vulnerability. It might seem, then, that the factors 3(B) and 3(C) apply to every eligible defendant and thus fall within the Eighth Amendment’s proscription against overbroad factors. But that cannot be correct; if it were, we would not have decided Payne as we did. Even though the concepts of victim impact and victim vulnerability may well be relevant in every case, evidence of victim vulnerability and victim impact in a particular case is inherently individualized. And such evidence is surely relevant to the selection phase decision, given that the sentencer should consider all of the circumstances of the crime in deciding whether to impose the death penalty. See Tuilaepa, 512 U. S., at 976.
  What is of common importance at the eligibility and selection stages is that “the process is neutral and principled so as to guard against bias or caprice in the sentencing decision.” Id., at 973. So long as victim vulnerability and victim impact factors are used to direct the jury to the individual circumstances of the case, we do not think that principle will be disturbed. Because factors 3(B) and 3(C) directed the jury to the evidence specific to this case, we do not think that they were overbroad in a way that offended the Constitution.
  B
  The error in this case, if any, rests in loose drafting of the nonstatutory aggravating factors; as we have made clear, victim vulnerability and victim impact evidence are appropriate subjects for the capital sentencer’s consideration. Assuming that use of these loosely drafted factors was indeed error, we conclude that the error was harmless.
  Harmless-error review of a death sentence may be performed in at least two different ways. An appellate court may choose to consider whether absent an invalid factor, the jury would have reached the same verdict or it may choose instead to consider whether the result would have been the same had the invalid aggravating factor been precisely defined. See Clemons v. Mississippi, 494 U. S. 738, 753-754 (1990). The Fifth Circuit chose to perform the first sort of analysis, and ultimately concluded that the jury would have returned a recommendation of death even had it not considered the two supposedly invalid nonstatutory aggravating factors:
  “After removing the offensive non-statutory aggravating factors from the balance, we are left with two statutory aggravating factors and eleven mitigating factors to consider when deciding whether, beyond a reasonable doubt, the death sentence would have been imposed had the invalid aggravating factors never been submitted to the jury. At the sentencing hearing, the government placed great emphasis on the two statutory aggravating factors found unanimously by the jury— Jones caused the death of the victim during the commission of the offense of kidnapping; and the offense was committed in an especially heinous, cruel, and depraved manner in that it involved torture or serious physical abuse of the victim. Under part two of the Special Findings Form, if the jury had failed to find that the government proved at least one of the statutory aggravating factors beyond a reasonable doubt, then the deliberations would have ceased leaving the jury powerless to recommend the death penalty. Therefore, the ability of the jury to recommend the death penalty hinged on a finding of a least one statutory aggravating factor. Conversely, jury findings regarding the non-statutory aggravating factors were not required before the jury could recommend the death penalty. After removing the two non-statutory aggravating factors from the mix, we conclude that the two remaining statutory aggravating factors unanimously found by the jury support the sentence of death, even after considering the eleven mitigating factors found by one or more jurors. Consequently, the error was harmless because the death sentence would have been imposed beyond a reasonable doubt had the invalid aggravating factors never been submitted to the jury.” 132 F. 3d, at 252.
  Petitioner claims that the court’s analysis was so perfunctory as to be infirm. His argument is largely based on the following passage from Clemons: “Under these circumstances, it would require a detailed explanation based on the record for us possibly to agree that the error in giving the invalid ‘especially heinous’ instruction was harmless.” 494 U. S., at 753-754 (emphasis added). Clemons, however, involved quite different facts. There, an “especially heinous” aggravating factor was determined to be unconstitutionally vague. The only remaining aggravating factor was that the murder was committed during a robbery for pecuniary gain. The State had repeatedly emphasized the invalid factor and said little about the valid aggravator. See id., at 753. Despite this, all that the Mississippi Supreme Court said was: “ We likewise are of the opinion beyond a reasonable doubt that the jury’s verdict would have been the same with or without the “especially heinous, atrocious or cruel” aggravating circumstance.’” Ibid. (quoting Clemons v. State, 535 So. 2d 1354, 1364 (Miss. 1988)). We quite understandably required a “detailed explanation based on the record” in those circumstances.
  The same “detailed explanation... on the record” that we required in Clemons may not have been necessary in this case. Cf. Sochor v. Florida, 504 U. S. 527, 540 (1992) (there is no federal requirement that state courts adopt “a particular formulaic indication” before their review for harmless error will pass scrutiny). But even if the Fifth Circuit’s harmless-error analysis was too perfunctory, we think it plain, under the alternative mode of harmless-error analysis, that the error indeed was harmless beyond a reasonable doubt. See § 3595(c)(2) (federal death sentences are not to be set aside on the basis of errors that are harmless beyond a reasonable doubt). Had factors 3(B) and 3(C) been precisely defined in writing, the jury surely would have reached the same recommendation as it did. The Government’s argument to the jury, see, e. g., 25 Record 2733-2734, cured the nonstatutory factors of any infirmity as written. We are satisfied that the jury in this case actually understood what each factor was designed to put before it, and therefore have no doubt that the jury would have reached the same conclusion had the aggravators been precisely defined in writing.
  * * *
  For the foregoing reasons, the judgment of the Court of Appeals is affirmed.
  It is so ordered.
  Justice Scalia joins all but Part III-A of the opinion.
  As phrased on the Special Findings Form returned by the jury, the statutory aggravating factors read:
  “2(A). The defendant LOUIS JONES caused the death of Trade Joy McBride, or injury resulting in the death of Trade Joy McBride, which occurred during the commission of the offense of Kidnapping.”
  “2(C). The defendant LOUIS JONES committed the offense in an espe-dally heinous, cruel, and depraved manner in that it involved torture or serious physical abuse to Trade Joy McBride.” App. 51-52.
  The term “nonstatutory aggravating factor” is used to refer to any aggravating factor that is not specifically described in 18 U. S. C. §3592. Section 3592(c) provides that the jury may consider “whether any other aggravating faetor for which notice has been given exists.” Pursuant to § 3593(a), when the Government decides to seek the death penalty, it must provide notice of the aggravating factors that it proposes to prove as justifying a sentence of death.
  As phrased on the Special Findings Form, the nonstatutory aggravating factors read:
  “3(B). Tracie Joy McBride’s young age, her slight stature, her background, and her unfamiliarity with San Angelo, Texas.
  “3(C). Tracie Joy McBride’s personal characteristics and the effect of the instant offense on Tracie Joy McBride’s family constitute an aggravating factor of the offense.” App. 53.
  The mitigating factors that the jury found as set forth on the Special Findings Form (along with the number of jurors that found for each factor in brackets) are as follows:
  “1. That the defendant Louis Jones did not have a significant prior criminal record.” [6]
  “2. That the defendant Louis Jones’ capacity to appreciate the wrongfulness of the defendant’s conduct or to conform to the requirements of law was significantly impaired, regardless of whether the capacity was so impaired as to constitute a defense to the charge.” [2]
  “3. That the defendant Louis Jones committed the offense under severe mental or emotional disturbance.” [1]
  “4. That the defendant Louis Jones was subjected to physical, sexual, and emotional abuse as a child (and was deprived of sufficient parental protection that he needed).” [4]
  “5. That the defendant Louis Jones served his country well in Desert Storm, Grenada, and for 22 years in the United States Army.” [8]
  “6. That the defendant. Louis Jones is likely to be a well-behaved inmate.” [3]
  "7. That the defendant Louis Jones is remorseful for the crime he committed.” [4]
  "8. That the defendant Louis Jones’ daughter will be harmed by the emotional trauma of her father’s execution.” [9]
  "9. That the defendant Louis Jones was under unusual and substantial internally generated duress and stress at the time of the offense.” [3]
  “10. That the defendant Louis Jones suffered from numerous neurological or psychological disorders at the time of the offense.” [1] Id., at 54-56.
  Seven jurors added petitioner’s ex-wife as a mitigating factor without further elaboration. Id., at 56.
  We have thus approved of the use of a supplemental charge to encourage a jury reporting itself as deadlocked to engage in further deliberations, see Allen v. United States, 164 U. S., at 501, even capital sentencing juries, see Lowenfield v. Phelps, 484 U. S. 281, 237-241 (1988).
  It is not insignificant that the Courts of Appeals to have addressed this question, as far as we are aware, are uniform in rejecting the argument that the Constitution requires an instruction as to the consequences of a jury’s inability to agree. See, e. g., Coe v. Bell, 161 F. 3d 320, 339-340 (CA6 1998); Green v. French, 143 F. 3d 865, 890 (CA4 1998); United States v. Chandler, 996 F. 2d 1073, 1088-1089 (CA11 1993); Evans v. Thompson, 881 F. 2d 117, 123-124 (CA4 1989). Indeed, the Fifth Circuit, in the alternative, reached the same conclusion in this very ease. See 132 F. 3d 232, 245 (1998).
  The decision forms read as follows:
  “DECISION FORM A
  “We the jury have determined that a sentence of death should not be imposed because the government has failed to prove beyond a reasonable doubt the existence of the required intent on the part of the defendant or a required aggravating factor.”
  “DECISION FORM B
  “Based upon consideration of whether the aggravating factor or factors found to exist sufficiently outweigh any mitigating factor or factors found to exist, or in the absence of any mitigating factors, whether the aggravating factor or factors are themselves sufficient to justify a sentence of death, we recommend, by unanimous vote, that a sentence of death be imposed.”
  “DECISION FORM C
  “We the jury recommend, by unanimous verdict, a sentence of life imprisonment without the possibility of release.”
  “DECISION FORM D
  “We the jury recommend some other lesser sentence.” App. 57-59.
  Petitioner does not argue that the District Court’s instructions on the lesser sentence option, standing alone, constituted reversible error although the parties agree that, after the jury found petitioner guilty of kidnaping resulting in death, the only possible sentences were death and a life sentence. See Brief for Petitioner 18-19; Brief for United States 13, n. 2; see also 18 U. S. C. § 1201. Petitioner made such an argument below; the Fifth Circuit, however, concluded that the instructions as to the lesser sentence option did not rise to the level of plain error. 132 F. 3d, at 246-248.
  Petitioner concedes that the Boyde standard applies to the extent that he is advancing a constitutional claim, but relying on our prior decision in Andres v. United States, 333 U. S. 740, 752 (1948), he contends that a more lenient standard applies to the extent that he seeks relief under the statute directly. Our decisions in Boyde and Estelle, however, foreclose that reading of Andres. In Boyde we noted that our prior decisions, including Andres, had been “less than clear” in articulating a single workable standard for evaluating claims that an instruction prevented the jury’s consideration of constitutionally relevant evidence. 494 U. S., at 378. In order to supply “a single formulation for this Court and other courts to employ in deciding this kind of federal question,” we announced the “reasonable likelihood” standard. Id., at 379. We made this same point later in Estelle, noting that “[i]n Boyde ... we made it a point to settle on a single standard of review for jury instructions — the Reasonable likelihood’ standard — after considering the many different phrasings that had previously been used by this Court.” 502 U. S., at 72-73, n. 4.
  The relevant portion of the instruction read: “You will also recall that I previously told you that all twelve of you had to unanimously agree that a particular aggravating circumstance was proved beyond a reasonable doubt before you consider it. Quite the opposite is true with regard to mitigating factors. A finding with respect to a mitigating factor may be made by any one or more of the members of the jury, and any member who finds by a preponderance of the evidence the existence of a mitigating factor may consider such factor established for his or her weighing of aggravating and mitigating factors regardless of the number of other jurors who agree that such mitigating factor has been established.” App. 43.
  Petitioner also urges us to take cognizance of two affidavits prepared after the jury had returned its sentencing recommendation. One affidavit, attached to petitioner’s new trial motion, was executed by an investigator for the federal public defender after a juror had contacted the public defender’s office. Id., at 66-68. The other affidavit, attached to petitioner’s motion to reconsider the District Court’s order denying his motion for a new trial, was executed by one of the jurors. Id., at 78-80. The Fifth Circuit ruled that petitioner could not rely on these affidavits to undermine the jury’s sentencing recommendation. 132 F. 3d, at 245-246. Petitioner did not raise this independent determination in any of his questions presented, and we do not believe that the issue is fairly included within them. We therefore decline review of this ruling by the Fifth Circuit. See this Court’s Rule 14.1(a); Berkemer v. McCarty, 468 U. S. 420, 443, n. 38 (1984).
  The dissent would treat this aspect of the Government’s argument as waived. Post, at 420-421, n. 24. As Justice Ginsburg explained, for a unanimous Court, in Caterpillar Inc. v. Lewis, 519 U. S. 61 (1996): "Under this Court’s Rule 15.2, a nonjurisdietional argument not raised in a respondent’s brief in opposition to a petition for a writ of certiorari ‘may be deemed waived.’” Id., at 75, n. 13 (emphasis added). But we have not done so when the issue not raised in the brief in opposition was "predicate to an intelligent resolution of the question presented.” Ohio v. Robinette, 519 U. S. 33, 38 (1996) (internal quotation marks omitted); see also Caterpillar, 519 U. S., at 75, n. 13. In those instances, we have treated the issue not raised in opposition as fairly included within the question presented. This is certainly such a case. Assessing the error (including whether there was error at all) is essential to an intelligent resolution of whether any such error was harmless. Moreover, here, as in Caterpillar, “[t]he parties addressed the issue in their briefs and at oral argument.” Ibid. By contrast, in the cases that the dissent looks to for support for its position, there were good reasons to decline to exercise our discretion. In Roberts v. Galen of Va., Inc., 525 U. S. 249, 253-254 (1999) (per curiam), the "claims [we declined to consider did] not appear to have been sufficiently developed below for us to assess them,” and in South Central Bell Telephone Co. v. Alabama, 526 U. S. 160, 171 (1999), the argument respondent raised for the first time in its merits brief was “so far-reaching an argument” that “[w]e would normally expect notice [of it],” especially when, unlike this case, the respondent’s argument did not appear to have been raised or considered below.
  The Tenth Circuit, in a decision subsequent to McCullah, has emphasized that factors do not impermissibly overlap unless one “necessarily subsumes” the other. Cooks v. Ward, 165 F. 3d 1283, 1289 (1998).
  Petitioner argues that the term “personal characteristics” was so vague that the jury may have thought it could consider the victim’s race and the petitioner’s race under factor 3(C). In light of the remainder of the factor and the Government’s argument with respect to the factor, we fail to see that possibility. In any event, in accordance with the Death Penalty Act’s explicit command in § 3593(f), the District Court instructed the jury not to consider race at all in reaching its decision. App. 47. Jurors are presumed to have followed their instructions. See Richardson v. Marsh, 481 U. S. 200, 206 (1987).
  We reiterate the point we made in Tuilaepa v. California, 512 U. S. 967 (1994) — we have held only a few, quite similar factors vague, see, e. g., Maynard v. Cartwright, 486 U. S. 356 (1988) (whether murder was “especially heinous, atrocious, or cruel”), while upholding numerous other factors against vagueness challenges, see 512 U. S., at 974 (collecting cases).