
75 P.3d 114 (2003)
206 Ariz. 24
STATE of Arizona, Appellee,
v.
Wayne Benoit PRINCE, Appellant.
No. CR-00-0328-AP.
Supreme Court of Arizona.
August 26, 2003.
*115 Janet A. Napolitano, Arizona Attorney General by Kent E. Cattani, Chief Counsel, Capital Litigation Section and Robert L. Ellman, Assistant Attorney General and James P. Beene, Assistant Attorney General and John P. Todd, Assistant Attorney General, Phoenix and Bruce M. Ferg, Assistant Attorney General, Tucson, Attorneys for State of Arizona.
James J. Haas, Maricopa County Public Defender by James L. Edgar and Charles R. Krull, Phoenix, Attorneys for Wayne Benoit Prince.

SUPPLEMENTAL OPINION
McGREGOR, Vice Chief Justice.
¶ 1 The only issue before us is whether reversible error occurred when a trial judge sentenced Wayne Benoit Prince to death under a procedure that violated Ring v. Arizona, 536 U.S. 584, 122 S.Ct. 2428, 153 L.Ed.2d 556 (2002) (Ring II). We exercise jurisdiction pursuant to Article VI, Section 5.3 of the Arizona Constitution and Arizona Revised Statutes (A.R.S.) section 13-4031 (2001). Based on our review of the record, we cannot conclude that the Ring II violation constituted harmless error.

I.
¶ 2 On March 25, 1998, Prince and his wife Christine Parker were involved in a heated domestic dispute. Christine's son was asleep during the incident, but Cassandra, her thirteen-year-old daughter, attempted to flee the apartment to summon help. Prince was armed with a gun and threatened to kill the children, Christine, and then himself. Eventually, the fight moved into Cassandra's room, where Prince held a pillow around the gun and shot Cassandra in the head. Prince then shot Christine. Christine survived, but Cassandra did not.[1]
¶ 3 A jury found that Prince committed the attempted murder of Christine and the first degree murder of Cassandra. Following the jury's guilty verdict, the trial judge conducted a sentencing hearing to determine whether *116 any aggravating or mitigating circumstances existed. A.R.S. § 13-703 (2001), amended by 2002 Ariz. Sess. Laws, 5th Spec. Sess., ch. 1, § 1. The judge found beyond a reasonable doubt the presence of two aggravating circumstances: (1) Prince committed the murder in an especially heinous, cruel, or depraved manner, A.R.S. section 13-703.F.6; and (2) Prince was an adult at the time he committed the murder and Cassandra was under fifteen years of age, A.R.S. section 13-703.F.9. The judge determined that the mitigating circumstances were not "sufficiently substantial to call for leniency" and sentenced Prince to death for the first degree murder conviction. Id. § 13-703.E.
¶ 4 We affirmed Prince's convictions and his sentence for the attempted murder charge on his direct appeal. State v. Prince, 204 Ariz. 156, 161 ¶ 28, 61 P.3d 450, 455 (2003). This supplemental opinion reviews only Prince's death sentence. Prince raises several arguments to challenge his death sentence. However, we address only the Ring II violation because we conclude that Prince must be resentenced. Because Prince will be resentenced, all other sentencing issues he asserts are moot.

II.
¶ 5 In Ring II, the United States Supreme Court held that Arizona's former capital sentencing scheme violated the right to a jury trial guaranteed by the Sixth Amendment to the United States Constitution. Ring II, 536 U.S. at 609, 122 S.Ct. at 2443. The Court declared that "[c]apital defendants, no less than non-capital defendants ... are entitled to a jury determination of any fact on which the legislature conditions an increase in their maximum punishment." Id. at 589, 122 S.Ct. at 2432. The Court reversed our decision in State v. Ring, 200 Ariz. 267, 25 P.3d 1139 (2001) (Ring I), and remanded for further proceedings consistent with its decision. Ring II, 536 U.S. at 609, 122 S.Ct. at 2443.
¶ 6 Following the Supreme Court's Ring II decision, we consolidated all death penalty cases for which this court had not yet issued a direct appeal mandate to determine whether Ring II requires this court to reverse or vacate the defendants' death sentences. In State v. Ring, 204 Ariz. 534, 555 ¶ 53, 65 P.3d 915, 936 (2003) (Ring III), we held that we will examine a death sentence imposed under Arizona's superseded capital sentencing statutes for harmless error.

III.

A.
¶ 7 To establish the F.6 aggravating circumstance, the state must prove that the manner in which a defendant killed the victim was especially heinous, cruel, or depraved. A.R.S. § 13-703.F.6. The state needs to prove only one of the heinous, cruel, or depraved components for this aggravating circumstance to apply. State v. Gretzler, 135 Ariz. 42, 51, 659 P.2d 1, 10 (1983). Cruelty refers to the victim's mental and physical suffering, whereas depravity concerns the "mental state and attitude of the perpetrator as reflected in his words and actions." State v. Clark, 126 Ariz. 428, 436, 616 P.2d 888, 896 (1980). The judge found that Cassandra's murder was both especially cruel and depraved.
¶ 8 The trial court concluded that Cassandra contemplated her fate before being shot.[2] Mental anguish encompasses a victim's contemplation of her ultimate fate. State v. Jackson, 186 Ariz. 20, 29, 918 P.2d 1038, 1047 (1996). Few especially cruel findings, however, are predicated solely on an inference that the victim contemplated his or her fate.[3]*117 Previous cases in which we have upheld the cruelty finding, based primarily on the victim's contemplation, have involved other circumstances not present here, from which the anguish can be more readily established. In some cases, the victims witnessed their aggressors shoot or stab a loved one before they were killed or the victims pled for mercy.[4] Other cases have involved a longer, more definite period of captivity.[5] In this case, no witness could quantify the length of time between the point at which Cassandra first experienced mental anguish and the moment that Prince shot Cassandra. The length of time during which a victim contemplates her fate affects whether the victim's mental anguish is sufficient to bring a murder within that group of murders that is especially cruel. See State v. Soto-Fong, 187 Ariz. 186, 204, 928 P.2d 610, 628 (1996) (reversing cruelty finding because victims were killed in rapid succession without any appreciable time to contemplate their fate). Based on this record, we cannot conclude, beyond a reasonable doubt, that a jury hearing the same evidence as did the judge would have interpreted the evidence as he did and found Prince murdered Cassandra in an especially cruel manner.
¶ 9 Depravity describes the defendant's state of mind. State v. Ceja, 126 Ariz. 35, 39, 612 P.2d 491, 495 (1980). The trier of fact considers five factors to determine whether the defendant committed the murder in an especially depraved manner: (1) relishing the murder by the defendant; (2) infliction of gratuitous violence;(3) needless mutilation;(4) senselessness of the crime; and (5) helplessness of the victim. Gretzler, 135 Ariz. at 52, 659 P.2d at 11. The trial judge found only two Gretzler factors present: senselessness and helplessness. The judge found no evidence to suggest Prince relished the murder, inflicted gratuitous violence, or mutilated Cassandra.
¶ 10 "A murder is senseless when it is unnecessary for the defendant to achieve his objective." State v. Hyde, 186 Ariz. 252, 281, 921 P.2d 655, 684 (1996). A child who is physically unable to resist the murder can be considered helpless. See State v. Roscoe, 145 Ariz. 212, 226, 700 P.2d 1312, 1326 (1984) (Roscoe I). The senselessness and helplessness factors tend to reveal less about a defendant's state of mind, however, than do the relishing, gratuitous violence, and mutilation factors. Hyde, 186 Ariz. at 281, 921 P.2d at 684. Therefore, senselessness and helplessness, without the presence of other factors, are usually insufficient to establish depravity beyond a reasonable doubt. See Trostle, 191 Ariz. at 18, 951 P.2d at 883; State v. Gulbrandson, 184 Ariz. 46, 67, 906 P.2d 579, 600 (1995). This court, however, has upheld depravity findings, predicated only on senselessness and helplessness, when a defendant murders a child with whom he maintains a parent or caretaker relationship. State v. Milke, 177 Ariz. 118, 126, 865 P.2d 779, 787 (1993); State v. Styers, 177 Ariz. 104, 116, 865 P.2d 765, 777 (1993); State v. Lopez, 174 Ariz. 131, 144, 847 P.2d 1078, 1091 (1992).
¶ 11 The trial judge concluded that murdering Cassandra was senseless because it was unnecessary to achieve Prince's goal of exacting revenge on Christine. The judge found that thirteen-year-old Cassandra was unable to defend herself against Prince, who was armed with a gun. The trial judge acknowledged that senselessness and helplessness are generally insufficient to establish depravity beyond a reasonable doubt. *118 The judge concluded, however, that senselessness and helplessness were sufficient in this case because Prince maintained a parent-child relationship with Cassandra.
¶ 12 When Prince and Christine first met in May 1996, Cassandra was living in Oregon with her grandparents. Cassandra did not return to Arizona until Prince and Christine had been dating for several months. Prince and Christine had been married approximately one year at the time of the murder. The record includes sparse evidence of the relationship between Prince and Cassandra. A jury could find, as did the judge, that Prince had established and maintained a parent-like status with Cassandra, but the evidence before us of their relationship does not mandate that finding. Therefore, we cannot conclude beyond a reasonable doubt that a jury would have assessed the evidence as did the judge and found that Prince's state of mind was especially depraved.

B.
¶ 13 To establish the F.9 aggravating circumstance, the state must prove that "[t]he defendant was an adult at the time the offense was committed or was tried as an adult and the murdered person was under fifteen years of age." A.R.S. § 13-703.F.9. Christine testified that Cassandra was born on May 16, 1984, and was thirteen at the time of the murder. Prince conceded that the state established that Cassandra was under the age of fifteen. Prince testified that he was born on December 27, 1971. Prince was twenty-six years old at the time of the crime and was tried as an adult. Given the uncontroverted evidence, the Ring II violation with respect to the F.9 factor was harmless.

IV.
¶ 14 The judge found that Prince failed to prove, by a preponderance of the evidence, any statutory mitigating circumstances. A.R.S. § 13-703.G. The judge found the presence of five non-statutory mitigating circumstances: (1) Prince was under unusual and substantial stress at the time of the murder; (2) development of religious convictions; (3) genuine remorse; (4) good behavior while incarcerated; and (5) family support. The judge concluded, however, that these circumstances were not "sufficiently substantial to call for leniency." A.R.S. § 13-703.E. The defense presented an expert who testified that Prince suffered from Adjustment Disorder with mixed disturbance of emotions and conduct and borderline intellectual functioning. With respect to the G.1 statutory mitigating factor, the expert testified that Prince's ability to conform his conduct on the night of the murder was significantly impaired. A.R.S. § 13-703.G.1. Although the trial judge found that testimony flawed, we cannot say, beyond a reasonable doubt, that a jury hearing the same evidence as did the judge would have assessed the defense expert's testimony similarly and would have failed to find mental impairment, a statutory mitigating circumstance. A different finding of mitigating circumstances could affect a fact-finder's determination whether the mitigating circumstances are "sufficiently substantial to call for leniency." A.R.S. § 13-703.E.

V.
¶ 15 For the foregoing reasons, we cannot conclude that the Ring II error was harmless in this case. Accordingly, we vacate Prince's death sentence and remand for resentencing under A.R.S. sections 13-703 and 13-703.01 (Supp.2002).
CONCURRING: REBECCA WHITE BERCH, Justice, MICHAEL D. RYAN, Justice.
Justice HURWITZ took no part in the consideration or decision of this case.
JONES, C.J., concurring in part, dissenting in part.
¶ 16 I concur in the result, but dissent from the majority's conclusion that harmless error analysis is appropriate where sentencing determinations are made by the trial judge in the absence of the jury. The right to trial by an impartial jury is fundamental. The sentencing phase is, of itself, a life or death matter. Where a judge, not a jury, determines all questions pertaining to sentencing, *119 I believe a violation of the Sixth Amendment to the Constitution of the United States has occurred. In the aftermath of the Supreme Court's decision in Ring v. Arizona, 536 U.S. 584, 122 S.Ct. 2428, 153 L.Ed.2d 556 (2002) (Ring II), the absence of the jury in the sentencing phase of a capital trial necessarily amounts to structural error. I would remand the case for resentencing, simply on the basis of the Sixth Amendment violation. See State v. Ring, 204 Ariz. 534, 565-67 ¶¶ 105-14, 65 P.3d 915, 946-48 (2003) (Feldman J., concurring in part, dissenting in part) (Ring III).
NOTES
[1]  See State v. Prince, 204 Ariz. 156, 157-58 ¶¶ 2-4, 61 P.3d 450, 451-52 (2003), for a more detailed account of the facts.
[2]  The court found the State did not establish, beyond a reasonable doubt, that Cassandra suffered after being shot.
[3]  See, e.g., State v. Castaneda, 150 Ariz. 382, 393, 724 P.2d 1, 12 (1986) (cruelty based on both physical pain and victim's uncertainty of fate); State v. Rossi, 146 Ariz. 359, 365, 706 P.2d 371, 377 (1985) (same); State v. Gillies, 142 Ariz. 564, 569, 691 P.2d 655, 660 (1984) (circumstances establishing cruelty include victim being raped during her eight-hour captivity, victim's pleas for mercy, victim being pushed from a forty-foot embankment and being beaten to death with a rock); State v. Libberton, 141 Ariz. 132, 139-40, 685 P.2d 1284, 1291-92 (1984) (cruelty based on both contemplation of fate and physical pain); State v. Lambright, 138 Ariz. 63, 75, 673 P.2d 1, 13 (1983) (cruelty based on victim's fear for her life and her sexual assault, as well as physical pain) overruled on other grounds by Hedlund v. Sheldon, 173 Ariz. 143, 840 P.2d 1008 (1992).
[4]  State v. Herrera, 176 Ariz. 21, 34, 859 P.2d 131, 144 (1993) (defendant admitted that before he shot the victim the victim placed his hands in front of his face in a pleading position and begged for mercy); State v. Lavers, 168 Ariz. 376, 392, 814 P.2d 333, 349 (1991) (finding that victim contemplated fate based on victim's statements as well as the victim witnessing the defendant stab her mother); State v. McCall, 139 Ariz. 147, 161, 677 P.2d 920, 934 (1983) (mental anguish for some of the victims based upon loved ones being shot within their hearing and then waiting their turn).
[5]  State v. Trostle, 191 Ariz. 4, 18, 951 P.2d 869, 883 (1997) (victim pled for mercy during thirty minute drive to desert, where victim was murdered); Jackson, 186 Ariz. at 29, 918 P.2d at 1047 (victim begged captors not to hurt her during twenty-five to thirty-minute drive to remote desert area); State v. Miles, 186 Ariz. 10, 17, 918 P.2d 1028, 1035 (1996) (same).
