*177OPINION

By the Court,

In 1986, Richard Haberstroh kidnapped a young woman in Clark County, then robbed, sexually assaulted, and murdered her. After his first trial ended in a mistrial, he was convicted at a second trial and sentenced to death. Haberstroh unsuccessfully sought relief on direct appeal and in a prior post-conviction proceeding. In this second post-conviction proceeding, the district court granted partial relief in favor of Haberstroh, vacating his sentence and granting him a new penalty hearing. The State appeals from that part of the district court’s order, and Haberstroh appeals from the part denying the remainder of his petition.

The district court concluded that Haberstroh’s death sentence should be vacated because the jury’s finding of depravity of mind as an aggravating circumstance, without a proper limiting instruction, was unconstitutional. This error is undisputed, and we conclude that it was not harmless beyond a reasonable doubt. The district court otherwise upheld Haberstroh’s conviction, and he raises numerous issues in that regard. We conclude that they do not warrant relief and therefore affirm the district court’s order.

FACTS

Early in the morning on July 21, 1986, Haberstroh abducted a young woman, Donna Kitowski, from a grocery store parking lot in Las Vegas. He took Kitowski into the desert outside the city, robbed her, sexually assaulted her, and strangled her with a ligature. The strangulation caused irreparable brain damage and ultimately Kitowski’s death.

After his arrest, Haberstroh was appointed counsel, Deputy Public Defender George Franzen. Haberstroh pleaded not guilty to various felony charges, including first-degree murder of Kitowski with the use of a deadly weapon. The charges also included kidnapping, sexual assault, attempted robbery, and attempted murder of another victim, Suzette Yake, in a different incident. The week before trial was set to begin, Haberstroh moved to dismiss Franzen and to proceed with his own defense. The district court canvassed Haberstroh extensively to determine if he understood the charges against him, the elements of each crime that the State had to prove, and the possible penalties. The court questioned Haberstroh about his education and prior legal experience. The court advised him that he would not receive any special indulgence by proceeding without counsel and informed him that his appointed counsel *178was an experienced criminal trial lawyer. Haberstroh nevertheless insisted that he be allowed to represent himself. The court granted the motion to dismiss counsel, but ordered Franzen to remain as standby counsel. The trial ended in a mistrial with the jurors voting eleven to one for conviction. A new trial date was set for September 1987. The charges involving Yake were severed from the second trial.

Early in June 1987, Haberstroh informed the district court that he wished to represent himself again at the second trial. On September 15, 1987, just six days before trial, Haberstroh moved to continue the trial and to have Franzen reappointed as defense counsel. The court was pleased to do so and willing to grant a one-week continuance. Franzen stated that he needed at least a month to prepare. When the court refused to continue the trial for longer than one week, Haberstroh, after an off-the-record conversation with Franzen, stated that he was prepared to proceed himself. Franzen again acted as standby counsel.

The second jury found Haberstroh guilty of first-degree murder, first-degree kidnapping, sexual assault, and robbery, each with the use of a deadly weapon. At Haberstroh’s request, Franzen was appointed as counsel for the penalty phase of the trial, but Haberstroh requested that no witnesses be called on his behalf because he did not want his friends and family embarrassed by the publicity. At the end of the penalty phase, the jurors returned a sentence of death. They found no mitigating circumstances and five aggravating circumstances: the murder was committed by a person previously convicted of a felony involving the use or threat of violence, it was committed during the commission of a robbery, it was committed during the commission of first-degree kidnapping, it was committed during the commission of sexual assault, and it involved depravity of mind. Haberstroh also received four consecutive terms of life in prison without possibility of parole for the kidnapping and sexual assault and two consecutive fifteen-year prison terms for the robbery.

This court affirmed Haberstroh’s sentence on direct appeal.1 Haberstroh then sought post-conviction relief, claiming that he had received ineffective assistance of counsel and that his waiver of the right to counsel had not been voluntary and intelligent. After an evidentiary hearing on the matter, the district court denied relief, and this court affirmed the denial.2

In November 1997, Haberstroh filed a petition for a writ of habeas corpus in the district court, raising 43 main issues. In *179September 1998, the district court adopted a stipulation by the parties that some claims would be considered on the merits after an evidentiary hearing, that some other claims would be considered on the merits without the taking of any evidence, and that still other claims had already been rejected by this court and in the State’s view were subject to the doctrine of the law of the case. The parties stipulated that they had substantial evidence to present on any procedural default issues but had “chosen to allow adjudication on the merits for the sake of efficiency and fairness.’ ’

The district court held an evidentiary hearing over several days from July 1999 to June 2001 and granted the habeas petition in part. It concluded that the penalty-phase jury instruction on depravity of mind had been unconstitutional and that the error was not harmless. It therefore vacated the sentence of death and ordered a new penalty hearing. The court decided no other penalty-phase claims and rejected all of Haberstroh’s guilt-phase claims. The State and Haberstroh appealed.

DISCUSSION

NRAP 30(b) and the requirement of brevity in appendices

As a preliminary matter, we admonish Haberstroh’s attorney, Assistant Federal Public Defender Michael Pescetta, for filing an appendix containing extensive irrelevant material. Pescetta filed an appendix of 52 volumes and 11,384 pages. In his briefs to this court, however, he did not cite to even a single page in 22 of the volumes, and for most of the other volumes, he cited to only a few pages out of an entire volume. Including thousands of pages of appendix that were not relevant to this appeal violated the Nevada Rules of Appellate Procedure and needlessly burdened this court and its staff. NRAP 30(b) expressly provides that “[bjrevity is required” in appendices and that “all matters not essential to the decision of issues presented by the appeal shall be omitted.”

In response to questions at oral argument in this case, attorney Pescetta asserted that he considered it necessary to impose such a massive record on this court to ensure that he preserves the record for future proceedings in federal court. This response is unacceptable. We do not see how including materials in the record before this court, without relying on them to support issues raised here, could operate to preserve those materials. Moreover, we question what purpose these materials could serve in the federal court if they were of no use to Haberstroh in the proceedings before this court.

We therefore admonish Pescetta for filing an appendix which grossly violates NRAP 30(b) and caution him that we will consider sanctions for similar conduct in the future.

*180Further, counsel for both Haberstroh and the State cited to the appendices without providing volume numbers. This is technically not a violation of NRAP 28(e), which expressly requires every assertion regarding the record only to be supported ‘ ‘by a reference to the page of the transcript or appendix.’ ’ But citation to the specific volume is necessary when appendices or transcripts have multiple volumes, and we direct all appellate attorneys before this court to also cite the volume number in such cases.

Stipulation by the parties in regard to the procedural default rules

We must consider whether it was valid for the parties to stipulate to allow resolution of many of the issues on the merits. We conclude that a stipulation by the parties cannot empower a court to disregard the mandatory procedural default rules.

NRS 34.810(l)(b) provides that a court “shall dismiss” a habeas petition that challenges a conviction resulting from a trial if the grounds for the petition could have been presented in earlier proceedings, absent cause and prejudice. NRS 34.810(2) similarly provides that a successive petition “must be dismissed” if it fails to allege new grounds for relief after a prior determination on the merits, or if it alleges new grounds but the failure to assert them in a prior petition constitutes abuse of the writ, again absent cause and prejudice. Based on this mandatory statutory language, this court in Pellegrini v. State disallowed “the discretionary application of the current procedural bar for waiver.”3 Therefore, a stipulation by the parties cannot empower a court to disregard these statutory requirements.

Haberstroh argues that the stipulation is binding on this court. He cites, for example, Second Baptist Church v. Mount Zion Baptist Church, an opinion by this court that states that “valid stipulations are controlling and conclusive and both trial and appellate courts are bound to enforce them.”4 However, the stipulation in this case is not valid if it contradicts the relevant statutes.

In oral argument before this court, Haberstroh’s counsel argued that application of procedural default rules is not mandatory under this court’s opinion in Phelps v. Director, Prisons.5 In that opinion, this court considered earlier versions of NRS 34.740 and 34.810 and decided that the Legislature did not intend to require a post-conviction habeas petition to show good cause and prejudice on its *181face but instead intended that the State raise waiver or abuse of the writ as affirmative defenses before a petitioner was required to show good cause and prejudice.6 However, the Legislature abrogated this part of Phelps a year later by adding subsections three and four to NRS 34.810 and amending former NRS 34.740.7 As a result, NRS 34.810(3) expressly provides that “the petitioner has the burden of pleading and proving specific facts that demonstrate” both good cause for failing to present a claim or for presenting a claim again and actual prejudice, and NRS 34.745(4) allows courts to look beyond the face of a petition to the courts’ own records in deciding whether to order summary dismissal of the petition.

We realize that the stipulation here preceded our decision in Pellegrini and that Haberstroh relied upon the stipulation and did not present evidence or argument in regard to cause for raising his claims. Under the circumstances of this case, we conclude that we can treat the stipulation as establishing the facts8 to show cause to raise the relevant claims but allowing consideration of the claims’ merits only to determine the question of prejudice. This approach leaves the procedural default rules in effect and allows us to accept the stipulation and decide the appeal.

However, we hold that the parties in a post-conviction habeas proceeding cannot stipulate to disregard the statutory procedural default rules. We direct all counsel in the future not to enter into stipulations like the one in this case and direct the district courts not to adopt such stipulations.

The State’s appeal: the unconstitutional application of depravity of mind as an aggravating circumstance

The State contends that the district court erred in vacating Haberstroh’s death sentence based on the invalid aggravating circumstance of depravity of mind. Given the parties’ stipulation, we accept that cause exists for Haberstroh to raise this claim for the first time in the instant petition. We must decide, therefore, whether the district court correctly concluded that Haberstroh established prejudice under NRS 34.810.

During the penalty phase, the jury was instructed that depravity of mind

*182is characterized by an inherent deficiency of moral sense and rectitude. It consists of evil, corrupt and perverted intent which is devoid of regard for human dignity and which is indifferent to human life. It is a state of mind outrageously, wantonly vile, horrible or inhuman.

The State did not allege torture or mutilation. The jury found that the murder involved depravity of mind as well as four other aggravating circumstances. This instruction provided inadequate guidance to the jury; therefore, the depravity aggravator was not properly found.

In Godfrey v. Georgia, the United States Supreme Court held that States must avoid “the arbitrary and capricious infliction of the death penalty.’ ’9

Part of a State’s responsibility in this regard is to define the crimes for which death may be the sentence in a way that obviates “standardless [sentencing] discretion.” It must channel the sentencer’s discretion by “clear and objective standards” that provide “specific and detailed guidance,” and that “make rationally reviewable the process for imposing a sentence of death.”10

This court has recognized that under Godfrey, absent a properly limiting instruction, the term “depravity of mind” fails to provide the required constitutional guidance to jurors.11 Thus this court construed the relevant statute, former NRS 200.033(8),12 “as requiring torture, mutilation or other serious and depraved physical abuse beyond the act of killing itself, as a qualifying requirement to an aggravating circumstance based in part upon depravity of mind.”13

The instruction given in this case fails to limit the term in a constitutional manner.14 The State does not dispute that the instruction was inadequate, but it argues that the error was harmless or in the alternative that this court should uphold the death sentence after reweighing the four valid aggravators against the nonexistent mitigating evidence.

*183The Supreme Court has held that “the Federal Constitution does not prevent a state appellate court from upholding a death sentence that is based in part on an invalid or improperly defined aggravating circumstance either by reweighing of the aggravating and mitigating evidence or by harmless-error review.”15 It appears that either analysis is essentially the same and that either should achieve the same result.16 Harmless-error review requires this court to “ ‘actually perform a new sentencing calculus’ ” to determine whether the error involving the invalid aggravator was harmless beyond a reasonable doubt.17 “Reweighing involves disregarding the invalid aggravating circumstances and reweighing the remaining permissible aggravating and mitigating circumstances.”18 In any case, we must provide “close appellate scrutiny of the import and effect of invalid aggravating factors to implement the well-established Eighth Amendment requirement of individualized sentencing determinations in death penalty cases.”19

The State stresses that the jury found no mitigating circumstances and that four valid aggravators remain. It therefore argues that the error was harmless beyond a reasonable doubt and the death sentence should stand after reweighing. It cites several cases where this court has upheld death sentences after invalidating an aggravating circumstance.20 Haberstroh counters that jurors need not return a death sentence even if the mitigating circumstances do not outweigh the aggravating.21 Also, in the instant proceedings, he has presented evidence relevant to mitigation.22 The cases cited by *184the State all involve direct appeals, unlike this case, and therefore did not entail reversal of a district court’s decision to grant habeas relief. Since there are no factual findings by the district court involved here, de novo review of this issue may be in order.23

The primary concern of the district court was the emphasis placed on depravity of mind by the prosecutor in closing argument. The record shows that the prosecutor repeatedly employed terms drawn from the jury instruction on depravity of mind, terms such as “depraved,” “vile,” “wanton,” “perverted,” “indifferent,” and “evil.” We share the district court’s concern that this argument likely induced the jurors to rest their sentence to a significant degree on the invalid aggravator.

Four valid aggravators remain in this case. Of course, the weighing of aggravating and mitigating circumstances is not a simplistic, mathematical process.24 Three of the remaining aggravators— that the murder was committed during a robbery, a first-degree kidnapping, and a sexual assault — involve the circumstances of the murder itself and can be viewed in effect as one major aggravator. The fourth aggravator is that Haberstroh was previously convicted of a felony involving the use or threat of violence — an escape from federal custody in which Haberstroh threatened a jailer with a shank. The weight of these aggravating circumstances is not so great that we are convinced beyond a reasonable doubt that the jury would have returned a death sentence even without the invalid finding of depravity of mind, especially considering the emphasis the prosecution placed on depravity. We are also cognizant that the jury heard no mitigating evidence and that Haberstroh would now offer evidence in mitigation. We conclude that Haberstroh has established prejudice under NRS 34.810, and we affirm the district court’s order vacating the death sentence and granting a new penalty hearing.

Haberstroh’s appeal: numerous claims

As a petitioner for post-conviction relief, Haberstroh cannot rely on conclusory claims for relief but must plead and prove specific facts demonstrating good cause and actual prejudice.25

Because we have concluded that Haberstroh’s death sentence should be vacated, we do not discuss cognizable claims challeng*185ing the validity of his death sentence unless they are likely to arise again or are based on grounds that would prohibit another death sentence from being imposed or executed.

Claims not raised before

The following claims were apparently not raised before the instant petition, but cause exists under the parties’ stipulation for Haberstroh to raise them for the first time. We conclude that he fails to demonstrate prejudice in regard to any of them, however.

Haberstroh contends that prosecutors argued at the penalty hearing that he was found at the jail with a metal object that could be sharpened into a “shank” while they withheld exculpatory evidence that the object was a digging tool belonging to another inmate. He argues that this violated Brady v. Maryland.26 Because the issue is likely to arise again, we consider whether Haberstroh has established prejudice. As a preliminary point, even though Haberstroh did not want mitigating evidence presented, he did want his counsel to counter the State’s case regarding this metal object. This claim is nevertheless meritless. Haberstroh has not shown that the State withheld exculpatory evidence. The record shows that another inmate admitted to and was disciplined for using the metal object as a digging tool and slipping it into Haberstroh’s cell to avoid detection shortly before Haberstroh was found with it. But these facts still do not contradict the evidence or argument presented by the State. Regardless of the source of the metal object, Haberstroh did not discard it or report it to jail authorities — rather, he placed it in his pocket. And the evidence that it could have been fashioned into a shank is undisputed.

Haberstroh asserts that in defending himself he was denied adequate access to legal materials and was appointed an inexperienced investigator who lacked adequate funding and access to Haberstroh. Haberstroh does not explain how the lack of legal materials or limited investigation prejudiced him. This remains a conclusory claim that does not entitle him to any relief.

Haberstroh claims that the prosecution misled the defense in regard to the appearance of another suspect. The police eliminated Gary Huber as a suspect in the crimes committed against Suzette Yake, prosecuted in Haberstroh’s first trial but not the second. In the first trial, a detective testified that Huber did not look like *186Haberstroh. Haberstroh points out that Huber’s sister told police that she “would have sworn” that a composite drawing was of her brother. Evidently this drawing appeared in a newspaper and was intended to depict the suspect in this case, i.e., Haberstroh. Haberstroh therefore asserts that the prosecution concealed exculpatory evidence that Huber closely resembled him, in violation of Brady.27 This evidence was not material: Haberstroh has failed to show how its disclosure would have made a different result reasonably probable.

Haberstroh contends that the district court erred in excluding evidence that tanning would not have obscured his tattoos. Because witnesses who identified him as the perpetrator did not report seeing his tattoos, he says that excluding the evidence violated his due process right to present a defense. This evidence also was immaterial because two witnesses were certain in their identifications of Haberstroh. On the night and at the scene of the abduction, one had spoken with Haberstroh for about two hours and heard his plan to abduct a victim, and the other had observed Haberstroh for about twenty minutes and saw him abduct the victim. Haberstroh thus fails to show any prejudice resulting from exclusion of evidence regarding tanning and his tattoos.

Haberstroh claims that the trial judge, District Judge Addeliar Guy, was hostile to the defense in imposing undue court security, including armed guards with a shoot-to-kill order. Haberstroh also complains that, being popularly elected, district judges cannot be impartial. Haberstroh cites to the record where Judge Guy denied issuing such an order and lifted a requirement that the parties stay behind their respective tables in the courtroom. These facts do not bear out the claim that the judge was hostile to the defense.

Haberstroh contends that his constitutional rights were violated because the district court failed, and in one instance refused, to have some proceedings reported. He says that the lack of a complete record prevents him from demonstrating error, but he does not allege what error or errors might have occurred. Moreover, he improperly cites only his own habeas petition to support his contention.28 He thus fails to provide any facts or argument demonstrating prejudice.

*187Haberstroh claims that he did not receive a transcript of the first trial until shortly before the second trial. He says this prejudiced him because “the trial witnesses changed their testimony repeatedly.” This claim remains conclusory. Haberstroh does not describe a single instance of such changed testimony or how it prejudiced him.

Haberstroh alleges that the State peremptorily dismissed a prospective juror who was African-American in violation of Batson v. Kentucky.29 During jury selection, Haberstroh asked for an explanation after the prosecutor dismissed a black juror. The district court noted that another black juror remained on the jury and stated that it saw no improper pattern of challenges by the prosecution. The prosecutor nevertheless responded. He noted that two or three black jurors had served in the first trial without challenge, and he explained that he dismissed the prospective juror for not being “as quick on the uptake as I’d like.” Haberstroh calls this explanation “facially pretextual” and asserts that other, unchallenged jurors appeared no more “quick” than the one that was dismissed. This assertion remains unsupported by reference to any specific facts. Haberstroh fails to show that any Batson violation occurred.

Haberstroh contends that the district court erred when it did not sua sponte remove a juror who knew a close friend of the victim and was familiar with the facts of the case. Haberstroh says that the juror had even discussed the case with the friend, but this is inaccurate. The juror had only spoken to the friend’s mother. The court questioned the juror extensively, and she stated that she could be fair and impartial. Haberstroh questioned her briefly and did not challenge her. Haberstroh invokes his right to an impartial jury and cites the United States and Nevada Constitutions, but he offers no specific authority or argument for his contention that the district court had a duty to strike the juror despite Haberstroh’s own decision to allow her to serve. Contentions unsupported by specific argument or authority should be summarily rejected on appeal.30

Haberstroh claims that the deadly weapon enhancement was improperly applied to his noncapital sentences because the jury instruction defining “deadly weapon” was unconstitutionally vague and there was no evidence that he used a deadly weapon. This claim has no merit. An eyewitness testified that shortly before the *188crimes Haberstroh displayed a handgun and a ligature and expressed a plan to use them to abduct a victim. NRS 193.165(1) provides in pertinent part that “any person who uses a firearm or other deadly weapon ... in the commission of a crime shall be punished by” an additional, consecutive prison term equal to the term prescribed for the crime.31 This court has held that the Legislature has “attributed to firearms a per se deadly status; proof of a firearm’s deadly capabilities is not required.”32 And the jury was so instructed. Even assuming that the jury instruction was otherwise vague in its general definition of “deadly weapon,” given the evidence that Haberstroh used a firearm, we conclude that he was not prejudiced.

Haberstroh asserts that the death penalty in Nevada is applied in an arbitrary and capricious manner, permitting “juries an unlimited ability to impose a death sentence, regardless of the circumstances of the case.” This claim remains completely conclusory without any specific facts or argument to support it. Haberstroh contends that the death penalty is cruel and unusual punishment under any circumstances and especially in his case because of his mental impairments. He also contends that his confinement on death row for more than fourteen years raises a presumption of inhuman or degrading treatment. This court has consistently rejected such arguments.33 Haberstroh claims that lethal injection involves the unnecessary infliction of pain, in violation of the Eighth and Fourteenth Amendment prohibition against the gratuitous infliction of suffering. However, he fails to provide any facts demonstrating that pain inflicted during lethal injection is unnecessary or gratuitous.

Claims already decided by this court

This court has already decided on the merits some of the grounds for relief raised in the instant petition. A court must dismiss a successive habeas petition in regard to such grounds, unless the petitioner proves specific facts that demonstrate good cause for presenting the claims again and actual prejudice.34 The doctrine of the law of the case also precludes reconsideration of these claims. The law of a first appeal is the law of the case in all later appeals *189in which the facts are substantially the same, and that law cannot be avoided by more detailed and precisely focused argument made after reflecting upon previous proceedings.35

Haberstroh complains that the prosecutor committed misconduct at the trial. However, in his direct appeal Haberstroh claimed that the prosecutor committed misconduct in the penalty phase, and this court rejected the claim.36 This is now the law of the case. The parties stipulated that this issue should be considered on its merits, but that does not alter the force of the law of the case established by our prior decision. Haberstroh also contends that his conviction must be reversed because he was forced to choose between proceeding to trial with unprepared counsel or representing himself. This court has also considered and rejected this claim.37

In addition, Haberstroh stipulated below that certain claims (numbered 4-7, 9, 12, 13, 16, 19-21, 23-26, 33, and 34 in his district court habeas petition) already “have been fairly presented” to this court and rejected on the merits. Such a stipulation of fact is valid.38 Haberstroh raises some of these claims on appeal39 but has *190not shown good cause for presenting them again. Therefore, they also are precluded by the law of the case as well as procedurally barred.40

CONCLUSION

The jury’s finding of depravity of mind as an aggravating circumstance was improper because there was no jury instruction limiting the term in a constitutional manner. This error was not harmless beyond a reasonable doubt. We therefore affirm the district court’s order vacating Haberstroh’s death sentence and granting a new penalty hearing. We also affirm the order insofar as it otherwise upholds Haberstroh’s conviction.

agree, concurring in part and dissenting in part:

I concur with the majority opinion in affirming the decision of the district court to uphold Haberstroh’s conviction, in admonishing Haberstroh’s attorneys for filing an appendix containing irrelevant material, and in disapproving stipulations regarding procedural default rules. I dissent from the majority’s affirmance of the district court’s decision to vacate the death sentence and to grant a new penalty hearing. Although the jury instruction on depravity of mind was inadequate and the aggravating circumstance is invalid, four valid aggravators remain, and there is no mitigating evidence. I therefore conclude that the error was harmless and that this court should uphold the death sentence.

The majority is correct that de novo review is appropriate because there are no relevant factual findings by the district court. And despite the district court’s concern about the prosecutor’s final argument, independent review of the record shows that the prosecutor did not emphasize depravity of mind more than any of the other four aggravators. Moreover, the prosecutor’s comments served a dual purpose. The prosecutor was not simply arguing that the State had proven “depravity”; he was also arguing why the aggravating circumstances were not outweighed by any mitigating circumstances and that death was the appropriate penalty. At various points in his argument, the prosecutor used terms found in the instruction on depravity of mind, such as “vile,” “wanton,” “perverted,” “indifferent,” and “evil.” The use of this language, for these purposes, was not per se improper. Furthermore, the prosecutor did not place inordinate stress on depravity of mind in comparison to the other aggravating circumstances or other considera*191tions. In his opening final argument, the prosecutor discussed a number of points: the jury’s responsibility for deciding the sentence in a capital case; the framework for making that decision and the five alleged aggravators generally; the three felony aggravators specifically; the character of Haberstroh and the circumstances of the crime; his prior crimes and use of a shank; his recent possession of a metal object which could be fashioned into a shank; and the sentencing factors of rehabilitation, deterrence, protection of society, and punishment. The prosecutor referred to the depraved nature of the murder, but did not suggest that jurors should consider that factor to be of primary importance. In his closing argument, the prosecutor again addressed a number of points: the general framework for deciding on a sentence; the defense argument that there was still a chance that Haberstroh could ultimately be proved innocent; the credibility of the State’s witnesses and the strength of the State’s case in the guilt phase; the victim; the lack of mitigating circumstances and the existence of all five aggravating circumstances; and the appropriateness of death as the penalty. The record does not show that the prosecutor’s argument sought or worked to convince the jurors to base their sentence particularly on depravity of mind.

Four valid aggravators remain in this case. The murder was committed: during the commission of robbery, during the commission of first-degree kidnapping, during the commission of sexual assault, and by a person who was previously convicted of a felony involving the use or threat of violence. In reweighing the valid aggravating circumstances, we have no mitigating circumstances to counter them. The balance overwhelmingly favors death, as this court’s decisions in similar cases indicate.1Haberstroh chose not to present mitigating evidence, and his belated offer of such evidence is of no consequence to the decision before this court.2 This murder was unprovoked and extremely callous and brutal. The failure to give a limiting instruction on depravity of mind was *192harmless error: I have no reasonable doubt that the jury would have returned a death sentence even without the invalid aggravator. Haberstroh has failed to establish prejudice under NRS 34.810, and this court should reverse the district court’s order on this point.