Arizona state prisoner Ramon Martinez-Villareal appeals the district court’s rejection of his petition for writ of habeas corpus on issues relating to the guilt phase of his murder trial in the Arizona Superior Court in Santa Cruz County. Warden Samuel Lewis (“State”) appeals the district court’s grant of the writ on the claim of ineffective assistance of counsel at the sentencing phase of the trial. We affirm the district court’s denial of Martinez-Villareal’s petition as to claims relating to the guilt phase of the trial, but reverse the grant of the writ as to the penalty phase.
FACTUAL AND PROCEDURAL HISTORY
Over the weekend of October 8-10, 1982, Martinez-Villareal burglarized a residence in Tumacaeori, Arizona. Among the missing items were ammunition and several high caliber rifles. Soon afterward, Martinez-Villa-real and an accomplice used these weapons and ammunition to shoot two men to death at a nearby ranch. Following his arrest, Martinez-Villareal boasted that he had killed “because of his pure balls, that he was very *1304macho.” State v. Martinez-Villareal, 145 Ariz. 441, 702 P.2d 670, 673-74, cert. denied, 474 U.S. 975, 106 S.Ct. 339, 88 L.Ed.2d 324 (1985).
Martinez-Villareal was convicted on two counts of first degree murder and one count of burglary. He was sentenced to death for the homicides, to a term of ten years for the burglary, and to a concurrent term of two and one-half years for a burglary to which he pleaded guilty.
Following an unsuccessful direct appeal to the Arizona Supreme Court, see Martinez-Villareal, 702 P.2d at 670-81, Martinez-Villareal’s trial attorney, William Rothstein, filed a petition for post-conviction relief (PCR) pursuant to 17 Ariz.Rev.Stat. Ann. § 32 (“Rule 32”). The PCR petition and a subsequent motion for rehearing were denied by the trial court on April 18, 1986, and May 23, 1986, on the grounds that all the claims raised had already been considered by the Arizona Supreme Court.
On June 11, 1986, Rothstein filed with the district court a “Preliminary Petition for Writ of Habeas Corpus” which contained additional claims not raised in the first PCR petition. After the district court dismissed the preliminary habeas petition on the grounds that it contained unexhausted claims, on June 9, 1986, the Arizona Supreme Court denied review of the denial of the first PCR petition and also denied a stay of execution.
Following dismissal of an amended habeas petition prepared by Rothstein, on June 10, 1986, Arizona lawyer Carla Ryan represented Martinez-Villareal in filing a second habe-as petition asserting Rothstein’s ineffective assistance of counsel at every stage, as well as other unexhausted claims. The district court issued a stay of execution on June 10, 1986, and directed Martinez-Villareal to file another PCR petition on all claims, including ineffective assistance of counsel.
Ryan immediately filed a second PCR petition along with a request that a different lawyer be appointed for Martinez-Villareal. On June 10, 1988, Daniel Davis, Martinez-Villareal’s new court-appointed attorney, filed an amended second PCR petition (“Davis petition”), which raised twenty issues, including Rothstein’s ineffective assistance at trial and sentencing. The trial court summarily denied the Davis petition on July 12,1988.
Davis filed a motion for rehearing on July 28, 1988. On September 27, 1988, the trial court once again “summarily dismissed” all twenty claims. The trial court ruled that under Arizona law no proceedings to assess the claims on the merits were warranted, because the petition presented no material issue of fact or law and therefore offered no colorable claims for review. See Rule 32.6(c). The Arizona Supreme Court denied review without comment, and on October 2, 1989, the U.S. Supreme Court denied the petition for certiorari. Martinez-Villareal v. Arizona, 493 U.S. 874, 110 S.Ct. 205, 107 L.Ed.2d 158 (1989).
Prompted by the Arizona Supreme Court’s notice of intent to issue a new warrant of execution, the Arizona Capital Representation Project filed a thud habeas petition on November 21, 1990. Sean Bruner was appointed to represent Martinez-Villareal on November 26, 1990. Bruner filed a “Motion for Discovery” in February 1991, suggesting for the first time that Martinez-Villareal might be mentally incompetent. The district court deemed this an unexhausted claim and dismissed the third habeas petition without prejudice so that the claim could be presented to the trial court.
Bruner filed a third PCR petition on June 16, 1991. This petition contained thirty-one claims, including ineffective assistance of counsel at trial and on appeal. On August 13, 1991, the third PCR petition and a subsequent motion for rehearing were summarily denied by the trial court. Twenty-eight of the thirty-one claims were found to be procedurally precluded. The remaining three “alleged ‘new grounds’ ” presented no colorable claim for relief. On April 7, 1992, the Arizona Supreme court denied review and on October 5, 1992, the United States Supreme Court denied the petition for certiorari. Martinez-Villareal v. Arizona, 506 U.S. 893, 113 S.Ct. 267, 121 L.Ed.2d 196 (1992).
On September 4 and 11, 1991, the district court, in order to assure that the stay of *1305execution was still in effect, withdrew all previous orders dismissing various petitions without prejudice.
Bruner filed the fourth habeas petition on March 25,1993. The State filed a motion for summary judgment on July 30, 1993. On July 23, 1994, the district court held an evi-dentiary hearing on the mental competence issues and on Rothstein’s alleged ineffectiveness in failing to request a psychological examination at the time of trial.
On October 20, 1994, the district court denied the petition as it related to claims relating to the validity of the convictions. However, the court granted the writ as to the sentence of death, on the grounds that Rothstein’s assistance was ineffective in the penalty phase of the trial and on appeal. The court found that in the trial’s penalty phase, Rothstein failed to present all of the available evidence as to Martinez-Villareal’s mental state and also failed to have Martinez-Villareal’s mental health investigated. Likewise, the court ruled that with respect to ineffective assistance of counsel on appeal, cause and prejudice was established “to the extent that Rothstein did not have Martinez-Villareal’s mental capacity evaluated.”
The timely appeal and cross-appeal give this court jurisdiction under 28 U.S.C. § 1291.
STANDARD OF REVIEW
We review de novo a district court’s decision to grant or to deny a petition for habeas corpus. Calderon v. Prunty, 59 F.3d 1005, 1008 (9th Cir.1995). We may affirm on any ground supported by the record even if it differs from the rationale of the district court. Bonin v. Calderon, 59 F.3d 815, 823 (9th Cir.1995), cert. denied, — U.S. -, 116 S.Ct. 718, 133 L.Ed.2d 671, reh’g denied, — U.S. -, 116 S.Ct. 977, 133 L.Ed.2d 897 (1996).
PROCEDURAL DEFAULT AND INEFFECTIVENESS OF COUNSEL
The main issue in this case is whether the district court erred in granting the writ as to the sentence of death on the grounds that Rothstein’s assistance was ineffective in the penalty phase of the trial and on appeal. We find that the district court improperly granted the writ. Because Martinez-Villareal has offered no cause for procedurally defaulting his claims of ineffective assistance of counsel, there is no basis on which to address the merits of his claims.
We may address the merits of a procedurally defaulted claim if the petitioner can show cause for the procedural default and actual prejudice as a result of the alleged violations of federal law. Bonin v. Calderon, 77 F.3d 1155 (9th Cir.), cert. denied, — U.S. -, 116 S.Ct. 980, 133 L.Ed.2d 899 (1996). To demonstrate cause, the petitioner must show the existence of “some objective factor external to the defense [which] impeded counsel’s efforts to comply with the State’s procedural rule.” Murray v. Carrier, 477 U.S. 478, 488, 106 S.Ct. 2639, 2645, 91 L.Ed.2d 397 (1986); see also McCleskey v. Zant, 499 U.S. 467, 497, 111 S.Ct. 1454, 1471-72, 113 L.Ed.2d 517, reh’g denied, 501 U.S. 1224, 111 S.Ct. 2841, 115 L.Ed.2d 1010 (1991) (cause is external impediment such as government interference or reasonable unavailability of claim’s factual basis). Lacking cause and prejudice, we may nonetheless consider procedurally barred claims if failure to do so would result in the conviction or execution of “ ‘one who is actually innocent.’ ” Schlup v. Delo, - U.S. -, -, 115 S.Ct. 851, 864, 130 L.Ed.2d 808 (1995).
The district court erred in failing to consider procedural default when it held that the issue of Rothstein’s ineffective assistance at sentencing was properly before it. The last reasoned state court opinion summarily dismissed all procedurally defaulted claims, including ineffective assistance of counsel. See Ylst v. Nunnemaker, 501 U.S. 797, 801, 111 S.Ct. 2590, 2593-94, 115 L.Ed.2d 706 (1991). Not only had Rothstein failed to make any ineffective assistance of counsel claims, but the Davis petition’s claims as to Rothstein’s ineffective assistance of counsel were dismissed expressly for failing to conform to the requirements of Arizona procedure. See Rule 32; Carrier, 477 U.S. at 486, 106 S.Ct. at 2644 (failure to comply with state procedural rules constitutes an independent and *1306adequate ground for a state court’s denial of a claim). On appeal, Martinez-Villareal does not deny that his ineffective assistance of counsel claims were procedurally defaulted.
Martinez-Villareal has not shown cause for the procedural default of his ineffective assistance of counsel claims. Nothing prevented Rothstein or Davis from making a complete investigation of Martinez-Villareal’s mental health or family background; they simply chose not to pursue the evidence that was readily available. The fact that Davis did not present an available claim or that he chose to pursue other claims does not establish cause. Carrier, 477 U.S. at 486, 106 S.Ct. at 2644 (counsel’s failure to recognize the factual or legal basis for a claim or failure to raise the claim despite recognizing it does not constitute cause). Rothstein’s and Davis’s ineffective assistance of counsel in collateral proceedings also does not constitute cause, because the right to counsel does not extend to state collateral proceedings or federal habeas proceedings. Bonin v. Vasquez, 999 F.2d 425, 430 (9th Cir.1993); Bonin v. Calderon, 77 F.3d 1155 (9th Cir.1996). Martinez-Villareal does not argue and the record does not support finding that his execution would constitute a fundamental miscarriage of justice.
Martinez-Villareal’s additional arguments outside of cause do not provide a legitimate basis for lifting the procedural bar. His contention that the Arizona Supreme Court has not regularly and consistently relied on procedural default has no merit. See Carriger v. Lewis, 971 F.2d 329, 333 (9th Cir.1992), cert. denied, 507 U.S. 992, 113 S.Ct. 1600, 123 L.Ed.2d 163, reh’g denied, 508 U.S. 934, 113 S.Ct. 2402, 124 L.Ed.2d 303 (1993) (rejecting argument that Arizona’s reliance on procedural default was so unpredictable and irregular that it does not provide an adequate ground for disposing of claims). Martinez-Villareal has not pointed to any Arizona decisions after our Carriger opinion which show that Arizona has since become inconsistent and irregular in its reliance on procedural default.
In addition, Martinez-Villareal contends that the Arizona Supreme Court’s review for fundamental error on direct appeal prevents, as a matter of state law, procedural preclusion from attaching. This argument has no merit. Under Arizona law, fundamental error review does not prevent subsequent procedural preclusion. See State v. Lopez, 170 Ariz. 112, 822 P.2d 465, 470 (App.1991), rev. denied, (1992) (Sixth Amendment claim precluded following review for fundamental error).
OTHER PROCEDURALLY PRECLUDED CLAIMS
Because Martinez-Villareal either has not contested or has failed to show cause for lifting the procedural bar, we cannot reach the merits of other procedurally defaulted claims. Likewise, we cannot reach the merits of any of Martinez-Villareal’s procedurally precluded claims decided on independent 'state law grounds. Coleman v. Thompson, 501 U.S. 722, 729-30, 111 S.Ct. 2546, 2553-54, 115 L.Ed.2d 640, reh’g denied, 501 U.S. 1277, 112 S.Ct. 27, 115 L.Ed.2d 1109 (1991). The trial court’s failure to distinguish between successive and abusive claims does not render all of the claims reviewable; because the last court reviewing the third PCR petition did not reach the merits of procedurally defaulted federal law claims outside of the three expressly mentioned in its August 13, 1991, order, the procedural bar remains for all but these three claims. Ylst, 501 U.S. at 801, 111 S.Ct. at 2593-94 (1991).
Martinez-Villareal argues, and the district court held, that mental incompetence claims can never be procedurally defaulted, relying on Pate v. Robinson, 383 U.S. 375, 86 S.Ct. 836, 15 L.Ed.2d 815 (1966), and Adams v. Wainwright, 764 F.2d 1356 (11th Cir.1985), cert. denied, 474 U.S. 1073, 106 S.Ct. 834, 88 L.Ed.2d 805 (1986). In Pate, the Court rejected the State’s claim that Robinson had waived his right to a pretrial sanity hearing and thus also the defense of his competence to stand trial by not presenting it to the trial court. Adams cites Pate for the proposition that “the procedural default rule ... does not operate to preclude a defendant who failed to request a competency hearing at trial or pursue a claim of incompetency on direct appeal from contesting his competency *1307to stand trial and be sentenced through post-conviction proceedings.” Adams, 764 F.2d at 1359 (citations omitted).
This expansive reading of Pate has not been followed in other circuits. See Noble v. Barnett, 24 F.3d 582, 588 (4th Cir.1994); Bainter v. Trickey, 932 F.2d 713, 716 (8th Cir.1991); Sawyer v. Whitley, 945 F.2d 812, 823-24 (5th Cir.1991), aff'd 505 U.S. 333, 112 S.Ct. 2514, 120 L.Ed.2d 269, reh’g denied, 505 U.S. 1244, 113 S.Ct. 21, 120 L.Ed.2d 948 (1992). The rule articulated by the Eleventh Circuit is untenable when applied to a case in which the State has raised the defense of procedural default, rather than waiver. The waiver standard does not apply when the State urges procedural default as a defense to a state prisoner’s claims. In Wainwright, 433 U.S. at 73, 97 S.Ct. at 2499, the Court specifically rejected the waiver-based “deliberate by-pass” standard of Fay v. Noia, 372 U.S. 391, 83 S.Ct. 822, 9 L.Ed.2d 837 (1963), as applied to claims of procedural default. In Coleman, the Court made it clear that the cause and prejudice standard applies to all “independent and adequate state procedural defaults.” 501 U.S. at 750-51, 111 S.Ct. at 2565.
The analytical basis of a defense of waiver differs markedly from that of a defense of procedural default. A claim has been “waived” if it was not raised and if the standard of “voluntary relinquishment or abandonment of a known right,” articulated in Fay, is met. In contrast, a finding of procedural default requires only that the claim was rejected by the state court on independent and adequate state procedural grounds. The petitioner can avoid the effect of a procedural default by showing cause and prejudice or manifest injustice.
Claims concerning Martinez-Villareal’s competence to stand trial were not raised until Martinez-Villareal’s third PCR petition. The State’s defense in this case was procedural default, not waiver. Therefore, the district court erred in holding that the claim was not procedurally defaulted.
CLAIMS NOT PRECLUDED IN THIRD PCR PETITION
The three claims in the third PCR petition that the trial court reached on the merits provide no basis for granting the writ. First, as noted previously, Davis’s alleged ineffectiveness in collateral review does not raise a constitutional issue. Second, Martinez-Villa-real has abandoned on appeal the claim that he is entitled to consideration of his exemplary conduct in prison as an additional mitigating factor. See Officers for Justice v. Civil Serv. Comm’n, 979 F.2d 721, 726 (9th Cir.1992), cert. denied, 507 U.S. 1004, 113 S.Ct. 1645, 123 L.Ed.2d 267 (1993). The third issue, Martinez-Villareal’s competence to be executed, was dismissed on state procedural grounds. Because the trial court held that under Arizona law a Rule 32 petition is not the correct procedure for pursuing such a claim, the district court properly found this claim to be premature.
FEDERAL LAW ISSUES SUBJECT TO REVIEW
After applying the rules relating to procedural default and eliminating the issues not argued on appeal, five federal law issues remain open for review. The first three relate to factors considered in imposing the death penalty. The district court consolidated the last two as raising a claim of a right to proportionality review. We hold that the district court did not err in rejecting all of these claims.
1. Pecuniary Gain Factor Not Supported by Evidence
A federal court reviewing the decision of a state court is to use the “rational factfinder” test established in Jackson v. Virginia, 443 U.S. 307, 99 S.Ct. 2781, 61 L.Ed.2d 560, reh’g denied, 444 U.S. 890, 100 S.Ct. 195, 62 L.Ed.2d 126 (1979). “A state court’s finding of an aggravating circumstance in a particular case-including a de novo finding by an appellate court that a particular offense is ‘especially heinous ... or depraved’ — is arbitrary or capricious if and only if no reasonable sentencer could have so concluded.” Lewis v. Jeffers, 497 U.S. 764, 783, 110 S.Ct. 3092, 3103, 111 L.Ed.2d 606, reh’g denied, *1308497 U.S. 1050, 111 S.Ct. 14, 111 L.Ed.2d 829 (1990).
Robbery was a motive for Martinez-Villa-real’s encounter with the two ranch hands. As the Arizona Supreme Court noted on direct appeal, “Lsjubstantial evidence was introduced that [Martinez-Villareal] was at the murder scene to rob McGrew and Estrada and to take McGrew’s pickup truck.” Martinez-Villareal, 702 P.2d at 680. We agree with this characterization of the record. A rational sentencer could have made the finding of pecuniary gain in this case.
2.Unconstitutional Vagueness of Depravity Factor
Martinez-Villareal argues that the “depraved” aggravating factor is unconstitutional as applied in his ease. Under Arizona law, a determination of depravity requires the sentencing court to focus on the defendant’s state of mind. Martinez-Villareal, 702 P.2d at 680. The Arizona Supreme Court there noted that under State v. Gretzler, 135 Ariz. 42, 659 P.2d 1, 10-11, cert. denied, 461 U.S. 971, 103 S.Ct. 2444, 77 L.Ed.2d 1327, reh’g denied, 463 U.S. 1236, 104 S.Ct. 32, 77 L.Ed.2d 1452 (1983), “[depravity includes the apparent relishing of the murder by the killer, the senselessness of the crime and the helplessness of the victim.”
The Martinez-Villareal court went on to say:
The evidence in the record shows that the appellant murdered during the course of a robbery in which his victims were unarmed and offered no apparent resistance. Martinez-Villareal bragged that he murdered to show “machismo.” Murdering another human being to show manliness constitutes depravity in that the killer senselessly takes life to demonstrate his superiority over his victims. This horrific form of ego gratification constitutes a manifest disregard for the fundamental principles upon which our society is based. The victims were unarmed. The murders were “senseless,” and appellant “relished” his deed as is apparent by his statement to Meza-Monreal. We find appellant’s behavior depraved within the statutory terms and as construed by this court.
702 P.2d at 680.
We hold that under Jeffers, a rational sentencer could have found that shooting defenseless victims only to show manliness was depraved. In addition, in response to Martinez-Villareal’s argument that the depravity factor contradicts the pecuniary gain factor, we agree with the district court’s determination that there can be more than one motivation for a crime.
3. Depravity a Non-Statutory Factor
Martinez-Villareal contends that the sentencing judge relied on the depravity factor because Martinez-Villareal showed “machismo,” which is not a statutory aggravating factor. We disagree. The trial court found that the unnecessary killing of helpless victims to show machismo was depraved. The question is not whether machismo is a separate aggravating factor, but whether a rational factfinder could find depravity given the facts of this case. As we held above, the depravity finding is supported by the evidence on the record.
4. Right to Proportionality Review
The final two claims allege (1) that there was no meaningful basis for distinguishing Martinez-Villareal’s case from others in which the death penalty was not imposed, and (2) that imposing the death penalty in this case is not proportional “when compared to other cases in Arizona in which the death penalty is imposed.” Following the district court, we will consider the two claims together as raising a claim of a right to proportionality review.
Since Pulley v. Harris, 465 U.S. 37, 104 S.Ct. 871, 79 L.Ed.2d 29 (1984), there is no federal constitutional requirement of an inter-case proportionality analysis of death sentences. The Arizona Supreme Court independently addresses the question of proportionality of the death sentence. Martinez-Villareal, 702 P.2d at 680. It specifically did so in this case. Id. Martinez-Villareal argues that if state law requires proportionality review, federal habeas *1309relief may be available if the state’s failure to conform to its own law is a separate violation of federal due process. This is true as a general matter of federal law. See Evitts v. Lucey, 469 U.S. 387, 393, 105 S.Ct. 830, 834, 83 L.Ed.2d 821, reh’g denied, 470 U.S. 1065, 105 S.Ct. 1783, 84 L.Ed.2d 841 (1985).
However, this generality will not prevail in the face of specific Supreme Court authority on the question of the adequacy of a state’s proportionality review. A similar challenge to the adequacy of an Arizona Supreme Court proportionality review was specifically rejected in Walton v. Arizona, 497 U.S. 639, 656, 110 S.Ct. 3047, 3058-59, 111 L.Ed.2d 511, reh’g denied, 497 U.S. 1050, 111 S.Ct. 14, 111 L.Ed.2d 828 (1990). Because the Arizona Supreme Court “plainly undertook its proportionality review in good faith” and found that Martinez-Villareal’s sentence “was proportional to the sentence imposed in cases similar to his[,] the Constitution does not require us to look behind that conclusion.” Id.
Martinez-Villareal does not contend that the Arizona Supreme Court did its proportionality review in bad faith, but that it was incorrect in its analysis. In effect he is asking for de novo review by this court. This is not a proper function of federal courts reviewing a state death penalty decision. See Jeffers, 497 U.S. at 779, 110 S.Ct. at 3101-02 (court of appeals erred in conducting a de novo, case-by-case comparison of state cases with the facts of the instant case).
CONCLUSION
We AFFIRM the district court’s denial of Martinez-Villareal’s petition as to claims relating to the guilt-innocence phase of the trial, but REVERSE the grant of the writ on claims relating to the penalty phase, and REMAND with instructions to enter judgment denying the petition for writ of habeas corpus.1
AFFIRMED in part, REVERSED in part and REMANDED with instructions.
. To eliminate any ambiguity, we reiterate that the claim of Martinez-Villareal's current incompetence was denied as premature by the district court. That decision was not contested on appeal. Our instruction to enter judgment denying the petition is not intended to affect any later litigation of that question.