OPINION
¶ 1 James Granvil Wallace pleaded guilty to three counts of first-degree murder and was sentenced to death on each count. This is an automatic appeal from those sentences. See Ariz. R.Crim. P. 31.2(b). We have jurisdiction under Article 6, Section 5(3) of the Arizona Constitution and A.R.S. § 13=4031 (2001).
I.
¶ 2 Wallace lived with Susan Insalaco, his girlfriend, and her two children, sixteen-year-old Anna and twelve-year-old Gabriel, in Susan’s home in Pima County. During their on-again-off-again relationship, Wallace and Susan fought about his drinking and drug use. On January 31, 1984, Wallace came home drunk, and Susan told him to move out. The next day, Susan left for work, and Anna and Gabriel left for school. Wallace woke up around 10:00 a.m., but did not leave the house.
¶ 3 When Anna returned from school around 2:45 p.m., Wallace was hiding behind the front door with a small wooden baseball bat. He struck Anna in the head from behind, and she fell to the ground, but continued breathing and moaning. He struck her in the head ten to twelve more times. Anna was still alive; Wallace then dragged her into *3the bathroom and hit her until the bat broke. He then drove the broken bat into her throat until the bat hit the floor.
¶ 4 Wallace got a pipe wrench to kill Gabriel because he “didn’t want him to suffer like [Anna].” Gabriel arrived around 3:00 p.m. and walked into his bedroom. Wallace followed and hit Gabriel in the head with the wrench. Gabriel fell to the floor, and Wallace hit him in the head ten to twelve more times.
¶ 5 After killing Gabriel, Wallace retrieved Susan’s .22-ealiber handgun from a closet and loaded it in order to commit suicide, but could not bring himself to do so. Susan came home from work around 5:00 p.m. After she set groceries down in the kitchen, Wallace hit her in the head with the pipe wrench. She fell, and Wallace hit her three or four more times. Wallace told the police that he did not use the gun to kill Susan because the neighbors might hear the noise.
¶ 6 Wallace grabbed some clothing and took about ten dollars from Susan’s purse. He then drove to a friend’s apartment, where he spent the night. Wallace told the friend about the murders the next morning, February 2,1984.
¶ 7 Wallace then called the Tucson police and reported, “I just killed three people and I want you to come get me.” The police picked up Wallace outside the friend’s apartment shortly thereafter. In a series of statements, Wallace admitted to the murders, but could not explain why he committed them.
II.
¶ 8 Wallace pleaded guilty to three counts of first-degree murder and two counts of armed robbery. In 1985, a superior court judge found that each murder was committed in an especially heinous, cruel, or depraved manner. AR.S. § 13-703(F)(6) (1984).1 He also found that Susan was murdered for pecuniary gain. A.R.S. § 13-703(F)(5). The judge found one mitigating circumstance, “genuine remorse,” AR.S. § 13-703(G), but concluded it was not sufficiently substantial to call for leniency and sentenced Wallace to death for each murder. Wallace received concurrent twenty-one-year sentences for the armed robberies.
¶ 9 On appeal, this Court vacated the armed robbery convictions, State v. Wallace (Wallace I), 151 Ariz. 362, 366, 728 P.2d 232, 236 (1986), and set aside the pecuniary gain aggravator, id. at 368, 728 P.2d at 238. The Court also found that the cruelty prong of the (F)(6) aggravator had not been established, but held that the murders were gratuitously violent and therefore especially heinous and depraved. Id. at 367, 728 P.2d at 237. The death sentences for the murders of Anna and Gabriel were affirmed; the case was remanded to the superior court for re-sentencing for Susan’s murder. Id. at 370, 728 P.2d at 240.
¶ 10 On remand, the court again sentenced Wallace to death for Susan’s murder. Wallace filed a petition for post-conviction relief, alleging, among other things, ineffective assistance of counsel. Ariz. R.Crim. P. 32. The trial court dismissed the Rule 32 petition.
¶ 11 The direct appeal of the death sentence for Susan’s murder was consolidated with review of the denial of Rule 32 relief. State v. Wallace (Wallace II), 160 Ariz. 424, 425, 773 P.2d 983, 984 (1989). This Court upheld the dismissal of the Rule 32 petition, id. at 426, 773 P.2d at 985, and affirmed the death sentence, id. at 428, 773 P.2d at 987.
¶ 12 Wallace filed a petition for a writ of habeas corpus in federal district court, which denied relief. On appeal, the Ninth Circuit remanded for an evidentiary hearing, holding that Wallace had made a prima facie showing of ineffective assistance of counsel at the penalty phase of his sentencing. Wallace v. Stewart (Wallace III), 184 F.3d 1112, 1117-18 (9th Cir.1999). On remand, the district court found that Wallace had received ineffective assistance of counsel and ordered new sentencing proceedings.
¶ 13 A sentencing trial was held before a jury in March 2005.2 The jury found that *4Wallace committed the murders in an especially heinous and depraved manner and that evidence of mitigation was insufficient to warrant leniency. He was again sentenced to death on each of the three counts.
III.
¶ 14 Wallace raises a number of issues on appeal. We focus initially on his contention that the superior court erred in instructing the jury on gratuitous violence.
A.
¶ 15 In the aggravation phase, the jury was instructed, over Wallace’s objection, that “[i]n deciding whether the defendant inflicted gratuitous violence, you may consider whether the defendant had available less violent alternatives to cause death.” We determine de novo whether a jury instruction correctly states the law. State v. Tucker, 215 Ariz. 298, 310 ¶ 27, 160 P.3d 177, 189 (2007).
1.
¶ 16 In Wallace I, this Court said,
We believe ... that [Wallace’s] actions clearly amount to “gratuitous violence.” Had defendant’s intent been merely to kill these people, less violent alternatives were readily available to him. Specifically, defendant admits to having had a loaded gun with him that afternoon. He deliberately chose not to use it, however, because the noise would alert neighbors.
151 Ariz. at 367-68, 728 P.2d at 237-38 (internal citation omitted). This language was repeated virtually verbatim in Wallace II. 160 Ariz. at 427-28, 773 P.2d at 986-87.
¶ 17 Only one Arizona case other than Wallace I and II directly addresses whether gratuitous violence can be premised on the availability of a less violent means of causing death. In State v. Styers, the prosecution alleged that the murder was gratuitously violent because the defendant used hyperveloeity bullets. 177 Ariz. 104, 115, 865 P.2d 765, 776 (1993). This Court rejected the argument, “find[ing] no evidence that defendant used these particular bullets because he wanted or intended to inflict greater damage to the victim.” Id. Thus, no case other than Wallace I and II has relied upon the less violent means theory to support a finding of gratuitous violence.3
2.
¶ 18 The instruction in this ease allowed the jury to find gratuitous violence simply because a less violent means of murder was in some way “available.” The instruction did not require proof that the defendant intentionally chose one murder weapon over another. Thus, the jury could have found the (F)(6) aggravator because the gun was in the house at the time the victims were murdered, without regard to whether Wallace thought about using it. We have recently emphasized that “[h]einousness and depravity refer to the mental state and attitude of the perpetrator.” State v. Bocharski, 218 Ariz. 476, 493 ¶83, 189 P.3d 403, 420 (2008) (quoting State v. Jones, 205 Ariz. 445, 449 ¶ 15, 72 P.3d 1264, 1268 (2003)). This state of mind cannot be established without proof that the defendant at least considered and then rejected the “less violent” alternative. The jury here was not so instructed.
¶ 19 Moreover, the instruction given below did not require that the defendant intend to inflict greater violence by forgoing the use of an alternative weapon. We have long stressed that “the statutory concepts of heinous and depraved involve a killer’s vile state *5of mind at the time of the murder.” State v. Gretzler, 135 Ariz. 42, 51, 659 P.2d 1, 10 (1983). The requirement in Styers that the defendant must intend to inflict greater violence by intentionally choosing one weapon over another is aimed at proof of precisely such a state of mind. The instruction here, in contrast, would allow a finding of the (F)(6) aggravator without such a showing and thus was eiToneous under our case law defining gratuitous violence.
3.
¶ 20 Because Wallace objected to the erroneous instruction, we review for harmless error. State v. Henderson, 210 Ariz. 561, 567 ¶ 18, 115 P.3d 601, 607 (2005). Under this standard, the State must “prove beyond a reasonable doubt that the error did not contribute to or affect the verdict.” Id.
¶21 The State has not met this burden. The challenged instruction played a significant role in the State’s closing argument and rebuttal. The prosecutor repeatedly focused on the instruction, asking the jury to find gratuitous violence because Wallace could have killed each victim with “[o]ne shot to the head.” See State v. Anthony, 218 Ariz. 439, 446 ¶ 40, 189 P.3d 366, 373 (2008) (declining to find harmless error when allegation of prior bad act was repeated theme of closing).
¶22 Nor has the State demonstrated beyond a reasonable doubt that the challenged instruction did not affect the jury verdicts. The State presented no evidence that Wallace thought about using the gun to murder Anna or Gabriel, let alone that he chose other weapons in order to inflict greater injury upon them. Thus, under the Styers standard, the challenged instruction was prejudicial.
¶ 23 As to Susan, Wallace admitted that he considered using the gun, but said he rejected it not to inflict greater injury, but rather to avoid alerting neighbors. Thus, a jury could have concluded that Wallace did not intend to cause greater injury by using the pipe wrench, even if that were the end result. Under Styers, we therefore cannot find the error harmless. See State v. Ring, 204 Ariz. 534, 560 ¶ 79, 65 P.3d 915, 941 (2003) (defining harmless error as “those instances in which no reasonable jury could find that the state failed to prove [the relevant aggravating circumstance] beyond a reasonable doubt”).
4.
¶ 24 In any event, we believe that a “less violent alternative” instruction is not appropriate in gratuitous violence cases. The determination of whether one potential murder weapon is “less violent” than another is fraught with conceptual peril; the violence that attends a murder committed with any particular modality usually depends on the manner in which the weapon is used rather than the nature of the weapon. It is not clear, for example, whether a single blow to the head with a pipe wrench or a baseball bat is more or less violent than a gunshot. The essential issue in gratuitous violence cases is whether “the defendant continued to inflict violence after he knew or should have knoum that a fatal action had occurred.” Bocharski 218 Ariz. at 494 ¶87, 189 P.3d at 421. The defendant’s use of a particular weapon over another available alternative does not establish this state of mind.
5.
¶25 Each of Wallace’s death sentences was based on the same aggravating circumstance — that he committed the murders in an especially heinous and depraved manner. A.R.S. § 13-703(F)(6).4 The State *6alleged three factors to support its allegation that the murders were especially heinous or depraved: gratuitous violence, the senselessness of the crimes, and the helplessness of the victims. See Gretzler, 135 Ariz. at 52, 659 P.2d at 11 (listing factors that establish heinousness and depravity). But senselessness and helplessness, without more, generally do not render a killing especially heinous or depraved. E.g., State v. Murdaugh, 209 Ariz. 19, 33 ¶67, 97 P.3d 844, 858 (2004); State v. Cañez, 202 Ariz. 133, 162 ¶ 109, 42 P.3d 564, 593 (2002); State v. Barreras, 181 Ariz. 516, 523, 892 P.2d 852, 859 (1995).5 Our conclusion that the jury was improperly instructed on the issue of gratuitous violence therefore requires that we vacate the three death sentences.
III.
¶26 Because the erroneous “less violent alternative” instruction requires that we remand for resentencing, it is not necessary for us to address Wallace’s other arguments seeking a new sentencing proceeding. We therefore turn to Wallace’s argument that capital sentences are not warranted because the State failed to present sufficient evidence that the murders were committed with gratuitous violence and thus were especially heinous or depraved.6 See Ariz. R.Crim. P. 20(a) (requiring trial court to “enter a judgment that an aggravating circumstance was not proven if there is no substantial evidence to warrant the allegation”).7
¶ 27 In reviewing a jury’s finding of an aggravating circumstance for sufficiency of the evidence, we take the facts in the light most favorable to the prosecution and ask whether substantial evidence supports the verdict. See State v. Roque, 213 Ariz. 193, 218 ¶ 93, 141 P.3d 368, 393 (2006). “Substantial evidence is such proof that reasonable persons could accept as adequate and sufficient to support a conclusion of defendant’s guilt beyond a reasonable doubt.” Id. (internal quotation marks and citation omitted).
A.
¶28 Recognizing that “our prior eases have not been entirely consistent in describing the showing needed to establish gratuitous violence,” we attempted in Bocharski to clarify the principles governing this theory of heinousness and depravity. 218 Ariz. at 494 ¶ 85, 189 P.3d at 421. We stressed that to prove gratuitous violence, the State must first show that the defendant “inflicted more violence than that necessary to kill.” Id. at 494 ¶86, 189 P.3d at 421. Gratuitous violence requires a specific mental state: “The state must also show that the defendant continued to inflict violence after he knew or should have known that a fatal action had occurred.” Id. at 494 ¶ 87, 189 P.3d at 421.
¶29 We applied these principles in Bocharski to a murder involving twenty-four knife wounds. Id. at 494 ¶ 86, 189 P.3d at 421. Eight of these wounds penetrated deeply into the victim’s face and head. Id. at 494 ¶ 86, 189 P.3d at 421. The medical ex*7aminer testified that at least one of the eight wounds was fatal, and that the fatal wound probably occurred before additional blows were struck. Id. at 494 ¶ 86, 189 P.3d at 421. On that record, we concluded that Bocharski had used more violence than was necessary to kill. Id. at 494 ¶ 86, 189 P.3d at 421.
¶ 30 We were unable, however, to conclude that the State had sufficiently proved the required mental state. Id. at 495 ¶ 91, 189 P.3d at 422. We noted first that, although the medical examiner had opined about the likely timing of the fatal wound, the expert was unable to conclusively determine the sequence of the wounds. Id. at 494-95 ¶88, 189 P.3d at 421. Moreover, the medical examiner’s testimony demonstrated that the victim was alive when each of the wounds was inflicted. Id. at 494-95 ¶ 88, 189 P.3d at 421. This “uncertainty about the timing of the fatal wound” made it “difficult to conclude ... that Bocharski knew or should have known that he had already struck a fatal wound yet continued to attack the victim.” Id. at 494-95 ¶ 88, 189 P.3d at 422.
¶31 We also stressed in Bocharski that the knife injuries occurred in rapid succession — “all the injuries were likely inflicted within a minute,” id. at 495 ¶ 89, 189 P.3d at 422 — and involved a single weapon. Id. at 495 ¶ 90, 189 P.3d at 422. We contrasted those facts with prior decisions finding gratuitous violence, cases involving prolonged assaults and multiple weapons, circumstances that allowed an inference that the defendant possessed the requisite mental state. Id. at 495 ¶¶ 89-90, 189 P.3d at 422. We concluded that “[bjecause Bocharski used only a knife to inflict the wounds and completed his attack very rapidly, we find it unlikely he knew or should have known he had inflicted a fatal wound but continued nonetheless to inflict more violence.” Id. at 495 ¶ 90, 189 P.3d at 422.
1.
¶32 Under the standard enunciated in Bocharski we conclude that there was sufficient evidence to submit the issue of gratuitous violence to the jury with respect to the murder of Anna. She was struck over the head with a baseball bat until her skull was crushed. The assault began in the living room of the home; it continued after Wallace dragged Anna into the bathroom, where he struck her with the bat until it broke and then shoved the remaining jagged edge through her throat.
¶33 The medical examiner testified that Anna died from head injuries. Thus, Wallace’s final act was not necessary to kill her. Moreover, the length and savagery of the attack would allow a properly instructed jury to infer that Wallace either knew or should have known that he had inflicted sufficient violence to kill, but nonetheless continued the attack.
¶ 34 We reach a similar conclusion with respect to the murder of Gabriel. The attack involved ten to twelve blows with a pipe wrench. The result of the attack was horrific — not only was Gabriel’s skull crushed, his brain was exposed and extruded, and brain matter was found on the floor at the crime scene. Although the medical examiner was unable to conclusively determine which blow was fatal or the order of the injuries, the nature of the attack and its results support an inference that Wallace either knew or should have known he had struck enough blows to kill yet continued his attack.
¶ 35 Whether the State can prove this aggravating circumstance on remand beyond a reasonable doubt is not the issue before us; we conclude only that the evidence warranted submission of the (F)(6) aggravator to the jury with respect to the murders of Anna and Gabriel.
2.
¶36 We cannot conclude, however, that the issue of gratuitous violence was properly submitted to the jury with respect to the murder of Susan. The attack involved four or five blows to the head with the pipe wrench over a relatively brief period. As in Bocharski the blows were apparently struck in rapid succession with the same implement that caused death.
¶ 37 The medical examiner, although suggesting that any of the blows that struck *8Susan “might have” been fatal, was unable to opine as to which blow was fatal, let alone whether sufficient injury to kill had already been inflicted before the final blow. But even if we assume that to be the case, the evidence would not allow a jury reasonably to conclude that Wallace possessed the requisite mental state. Although the assault on Susan was brutal and reprehensible, it “came in an attempt ... to kill the victim, not to engage in violence beyond that necessary to kill.” State v. Anderson, 210 Ariz. 327, 355 ¶ 123, 111 P.3d 369, 397 (2005). We conclude that the State did not present sufficient evidence to prove the defendant had the required mental state.
B.
¶ 38 At the time Wallace murdered Susan, the penalty for first-degree murder was “death or imprisonment ... for life, without possibility of parole [for] twenty-five calendar years.” A.R.S. § 13-703(A) (1984).8 Because we have concluded that the sole aggravating circumstance alleged should not have been submitted to the jury for Susan’s murder, Wallace is not eligible for the death penalty on that count, and we must reduce his sentence to life in prison. We order that this sentence be served consecutively to the sentences imposed on remand for the murders of Anna and Gabriel.
IV.
¶ 39 For the reasons above, we (1) vacate the three death sentences imposed on Wallace; (2) remand for new sentencing proceedings for the murders of Anna and Gabriel; and (3) order that Wallace be sentenced to life imprisonment pursuant to A.R.S. § 13-703(A) (1984) for the murder of Susan, such sentence to be served consecutively to the sentences imposed on remand for the other two murders.
CONCURRING: RUTH V. McGREGOR, Chief Justice, REBECCA WHITE BERCH, Vice Chief Justice, MICHAEL D. RYAN, Justice, and DONN KESSLER, Judge *