Cite as: 527 U. S. 373 (1999)
Opinion of Thomas, J.
leged 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 im-
395
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