OPINION
We -must determine whether a state court’s constitutional error in failing to *294consider certain evidence offered in mitigation of a death sentence can be corrected by the court that committed the error, rather than require the convicted murderer to be sentenced anew, but before a jury.
James Lynn Styers, an Arizona prisoner, was convicted of first degree murder and other charges and sentenced to death. Styers’s first degree murder conviction and his sentence of death were affirmed by the Arizona Supreme Court. State v. Styers, 177 Ariz. 104, 865 P.2d 765, 770 (1993) (“Styers I ”). Styers sought federal habeas corpus, and was denied. On appeal to us, we found that the Arizona Supreme Court had erred in not considering certain mitigation evidence, because it found such evidence was not connected to Styers’s actions at the time of the murder. Styers v. Schriro, 547 F.3d 1026, 1028 (9th Cir. 2008) (“Styers II ”). We reversed and remanded to the district court with instructions to issue a conditional writ ordering Styers’s release from his death sentence unless the State were to initiate proceedings either to correct the constitutional error or to vacate the death sentence and impose a lesser sentence consistent with the law. Id. at 1036. The district court so ordered.
The Arizona Supreme Court conducted an independent review of Styers’s death sentence pursuant to its view of the Arizona statute which provides for independent reviews of all death sentences, A.R.S. § 13-755. State v. Styers, 227 Ariz. 186, 254 P.3d 1132, 1133 (2011) (en banc) (“Styers III”). It again affirmed the death sentence, after expressly considering and weighing the mitigation evidence to which this court’s opinion referred. Styers then moved the district court for an unconditional writ of habeas corpus, arguing that the Arizona Supreme Court was powerless to correct the constitutional error, because the law had changed since Styers I; the death sentence could be imposed only by a jury’s determination of the aggravating factors that rendered Styers eligible for the death penalty. Ring v. Arizona, 536 U.S. 584, 122 S.Ct. 2428, 153 L.Ed.2d 556 (2002). The district court denied Styers’s petition for an unconditional writ. Styers timely appealed.
We review de novo, and we affirm.
I. Facts and Procedural History
In 1989, Styers lived in an apartment with his daughter, a roommate, Styers’s co-defendant Debra Milke,1 and Debra Milke’s four-year-old son, Christopher. Styers provided childcare for Christopher while Milke was at work. On December 2, 1989, Styers borrowed Milke’s car to go to the mall. Christopher wanted to see Santa Claus and joined Styers. On the way to the mall, Styers picked up his friend Roger Scott. Scott, Styers, and Christopher had pizza for lunch and then drove to the desert. The men told Christopher that they were going to look for snakes in the wash.2 They then shot him three times in the head, leaving his body in the wash. State v. Styers, 177 Ariz. 104, 865 P.2d 765, 769 (1998) (“Styers I”).
A jury convicted Styers of first degree murder, conspiracy to commit first degree murder, child abuse, and kidnapping. Id. At sentencing, without a jury, the trial court found three statutory aggravating factors that rendered Styers eligible for the death penalty. Along with mitigating *295evidence as to Styers’s family relationships, military service, and character, Styers submitted evidence of mental health problems including post-traumatic stress disorder (“PTSD”) caused by Styers’s military service. The trial court found no mitigating factors sufficiently substantial to call for leniency. The trial court imposed the death penalty. Id.
Styers appealed his convictions and sentence to the Arizona Supreme Court. The Arizona Supreme Court reversed Styers’s child abuse conviction for insufficiency of evidence and affirmed Styers’s first degree murder, conspiracy, and kidnapping convictions and the death penalty sentence. Id. at 772, 778.
Styers filed a federal habeas petition in the district court, challenging his conviction and sentence on various grounds. The district court denied Styers’s petition, and Styers appealed to this court. Styers v. Schriro, 547 F.3d 1026, 1028 (9th Cir. 2008) (“Styers II”). This court affirmed the district court in part, and reversed and remanded in part because when the Arizona Supreme Court conducted its 1993 independent review of Styers’s death sentence, that court “appear[ed] to have imposed a test directly contrary to the constitutional requirement that all relevant mitigating evidence be considered by the sentencing body” when it found that Styers’s PTSD did not qualify as mitigating evidence because it had not affected his actions at the time of the crime. Id. at 1035. Specifically, this court found that the Arizona Supreme Court violated Ed-dings v. Oklahoma, 455 U.S. 104, 102 S.Ct. 869, 71 L.Ed.2d 1 (1982) and Smith v. Texas, 543 U.S. 37, 125 S.Ct. 400, 160 L.Ed.2d 303 (2004), which prohibit consideration of only mitigation evidence causally related to the crime. On remand, the district court entered an order directing that
Petitioner’s Writ of Habeas Corpus as to his sentence of death is granted unless the State of Arizona, within 120 days from entry of this Judgment, initiates proceedings either to correct the constitutional error in Petitioner’s death sentence or to vacate the sentence and impose a lesser sentence consistent with the law.3
The State then moved the Arizona Supreme Court to “remedy its initial independent review of Styers’ death sentence by conducting a new independent review and considering Styers’ PTSD as a mitigating circumstance.” State v. Styers, 227 Ariz. 186, 254 P.3d 1132, 1133 (2011) (en banc) (“Styers III”). Styers objected to the procedure, arguing that by again conducting an independent review under A.R.S. § 13-755, the Arizona Supreme Court had reopened Styers’s case on direct review and Styers’s sentence was no longer final.4 Id. at 1134. Under Teague v. *296Lane, 489 U.S. 288, 109 S.Ct. 1060, 103 L.Ed.2d 334 (1989), if Styers’s sentence was not final when the Arizona Supreme Court conducted its second independent review, Styers would be entitled to all constitutional rules which had been announced at the time of Styers III. These rules would include the requirement of Ring v. Arizona, 536 U.S. 584, 122 S.Ct. 2428, 153 L.Ed.2d 556 (2002), that defendants are entitled to a jury determination of any fact on which their eligibility for the death penalty is conditioned.
The Arizona Supreme Court granted the State’s motion; holding that (1) the Arizona Supreme Court was not required to remand the case to the trial court for a new resentencing, and that (2) even if Styers’s sentence was not final, Ring requires jury findings only of aggravating factors, and the aggravating factors in Styers’s case were not at issue in determining the weight of the mitigating evidence. Styers III, 254 P.3d at 1133-34.
The Arizona Supreme Court did not review its prior Eddings error for harmlessness. Instead, the court reviewed anew whether the mitigation evidence was sufficiently substantial to warrant leniency when weighed against the aggravating factors found by the trial court. Id. at 1135. On its review of the PTSD evidence, the court opined that because Styers had produced no evidence establishing a causal connection between his PTSD and the crime, the PTSD evidence was of little weight. Id. at 1136. The Arizona Supreme Court affirmed Styers’s sentence of death. Id.
Styers then moved the federal district court to enter judgment granting an unconditional writ of habeas corpus on the basis that the state had not complied with the conditional writ of habeas corpus because (1) the constitutional error could not be corrected without resentencing by a jury; (2) the Arizona Supreme Court employed an unconstitutional process in its attempt to cure the constitutional error; and (3) the Arizona Supreme Court failed to correct the constitutional error because it did not properly consider Styers’s mitigation evidence. The district court denied the motion for habeas relief because
[t]he conditional writ of habeas corpus entered in [Styers’s] case gave the State the opportunity to cure the constitutional defect found by the Ninth Circuit. At the request of the State, the Arizona Supreme Court undertook a new independent review of [Styers’s] capital sentence, reweighing the proven aggravating and mitigating circumstances. This remedied the constitutional infirmity found in Styers II and satisfied the condition precedent contained in the condi- ' tional writ.
Styers moved the district court for a certificate of appealability, and the district court granted a certificate of appealability on the issue whether, in correcting Styers’s sentence, the State was required to provide him a jury resentencing. Styers timely appealed.
II. Jurisdiction and Standard of Review
The district court had jurisdiction pursuant to 28 U.S.C. § 2254, and we have jurisdiction pursuant to 28 U.S.C. §§ 1291 and 2253. We review de novo the district court’s denial of the writ of habeas corpus. Harvest v. Castro, 531 F.3d 737, 741 (9th Cir.2008). This court may reverse the dis*297trict court only if the state court ruling “resulted in a decision that was contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States.” 28 U.S.C. § 2254(d)(1).
III. Analysis
A. Certified Issue: Ring Sentencing
When a constitutional rule is announced, its requirements apply to defendants whose convictions or sentences are pending on direct review or not otherwise final. Griffith v. Kentucky, 479 U.S. 314, 323, 107 S.Ct. 708, 93 L.Ed.2d 649 (1987). The rule announced in Ring, under which “[cjapital defendants are entitled ... to a jury determination of any fact on which the legislature conditions an increase in their maximum punishment,” Ring, 536 U.S. at 589, 122 S.Ct. 2428 is a procedural rule that applies to capital defendants on direct review, see Schriro v. Summerlin, 542 U.S. 348, 358, 124 S.Ct. 2519, 159 L.Ed.2d 442 (2004).
Styers made a Ring claim before the Arizona Supreme Court, arguing that the conditional writ of habeas corpus required that Styers be re-sentenced and that a jury must find the aggravating factors rendering him eligible for the death penalty. The Arizona Supreme Court denied the Ring claim on the ground that Styers’s sentence was final. To prevail, Styers must show that the Arizona Supreme Court’s determination that his conviction was final (and therefore that he was not entitled to a Ring sentencing) “was contrary to, or involved an unreasonable application of, clearly established federal law as determined by the Supreme Court of the United States.” 28 U.S.C. § 2254(d)(1).
The Arizona Supreme Court in Styers III rejected Styers’s contention that the Arizona Supreme Court “must remand this case to the trial court for a new resentenc-ing proceeding because this case is now on ‘direct review.’” Styers III, 254 P.3d at 1133. The court observed
“a judgment of conviction has been rendered, the availability of appeal exhausted, and the time for a petition for certio-rari elapsed or a petition for certiorari finally denied.” Because Styers had exhausted available appeals, his petition for certiorari had been denied, and the mandate had issued almost eight years before Ring was decided, his case was final, and he therefore is not entitled to have his case reconsidered in light of Ring.
Styers III, 254 P.3d at 1133-34 (citing Griffith, 479 U.S. at 328, 107 S.Ct. 708).5 *298The U.S.-Supreme Court has never held that the issuance of a conditional writ of habeas corpus necessarily renders non-final a conviction or sentence that was predicated on constitutional error, and the conditional writ of habeas corpus in this case did not vacate Styers’s death sentence. Therefore, the Arizona Supreme Court’s determination that Styers’s sentence remained final at the time of the second independent review was not contrary to federal law as determined by the Supreme Court of the United States.6,7
B. Uncertified Issue: The Arizona Supreme Court Corrected the Ed-dings Error
Styers also contends that the Arizona Supreme Court failed to correct the Eddings error found by this court in Styers II because it treated Styers’s mitigation evidence as de minimis.
The U.S. Supreme Court has “never held that a specific method for balancing mitigating and aggravating factors in a capital sentencing proceeding is constitutionally required.” Kansas v. Marsh, 548 U.S. 163, 175, 126 S.Ct. 2516, 165 L.Ed.2d 429 (2006). Rather, the Constitution prohibits considering exclusively only that mitigation evidence that bears a relationship to the crime. Tennard v. Dretke, 542 U.S. 274, 284-86, 124 S.Ct. 2562, 159 L.Ed.2d 384 (2004).
Here, when the Arizona Supreme Court conducted its second independent review, it did not preclude consideration of Styers’s PTSD, as it appeared to do in Styers I. There, the Arizona Supreme Court held that PTSD could constitute mitigating evidence in another case, but that it did not warrant leniency because Styers’s PTSD was not causally related to Christopher Milke’s murder. Styers II, 547 F.3d at 1035 (citing Styers I, 865 P.3d at 777-78). In Styers III, the Arizona Supreme Court found that Styers failed to present evidence that his PTSD affected him at the time of the crime and that his actions belied any claim that the disorder did affect him. 254 P.3d at 1135-36. Based on this finding, the Arizona Su*299preme Court considered the mitigating evidence and decided to give it little weight.8 Neither Tennard, 542 U.S. at 285, 124 S.Ct. 2562, nor Eddings, 455 U.S. at 113-15, 102 S.Ct. 869, requires more.
Conclusion
Styers has not shown that the Arizona Supreme Court made a decision contrary to, or involving an unreasonable application of, federal law as determined by the Supreme Court of the United States when it deemed his sentence final, refused to remand his case for a jury resentencing, and instead conducted an independent review under its death penalty statute. For these reasons, we AFFIRM.