Jackie Lee Willingham appeals from an order of the district court denying his petition for a writ of habeas corpus under 28 U.S.C. § 2254. Upon a thorough review of the record and the arguments presented, we conclude Mr. Willingham is not entitled to habeas relief.
In 1995, an OHahoma jury found Mr. Willingham guilty of first degree malice murder. See Okla. Stat. tit. 21, § 701.7. At the penalty phase, the jury rejected the State’s allegation that Mr. Willingham posed a continuing threat to society, see id. § 701.12(7), but found that the murder was especially heinous, atrocious, or cruel (HAC aggravator), see id. § 701.12(4). After weighing the HAC aggravator against the evidence presented in mitigation, the jury determined that Mr. Willingham should be put to death for the crime. The trial court formally imposed the recommended sentence, and the Oklahoma Court of Criminal Appeals (OCCA) affirmed both conviction and sentence on direct appeal. See Willingham v. State, 947 P.2d 1074 (Okla.Crim.App.1997). The OCCA also denied Mr. Willingham’s subsequent appli*920cation for post-conviction relief. See Willingham v. State, No. PC 97 389 (Okla. Crim.App. Mar. 19, 1998) (unpub.).
Mr. Willingham then commenced the instant habeas proceeding, alleging fifteen grounds for relief. The district court denied the petition in its entirety, and Mr. Willingham appealed. The district court granted a certificate of appealability (COA) on ten issues. See generally 28 U.S.C. § 2253(c). Following the case management conference, this court issued its standard order directing that, unless Mr. Willingham submitted a motion to expand the COA within ten days, “[t]he issues to be raised in the opening brief are those set forth by the district court in its order granting a[COA].” Case Management Order, April 18, 2001. No such motion was filed. In accordance with the case management order and § 2253(c), we limit our consideration to the ten issues properly certified for review:1
1. Refusal to Instruct on Second Degree Murder;
2. Use of Victim Impact Evidence;
3. Ineffective Assistance of Counsel;
4. Admission of Willingham’s Post-Arraignment Statements;
5. Prosecutorial Misconduct during Second Stage Closing Argument;
6. Admission of Cumulative Photographs of the Victim;
7. Admission of Willingham’s Videotaped Statement at Crime Scene;
8. Sufficiency of the Evidence Supporting the HAC Aggravator;
9. Use of an Improper Reasonable Doubt Instruction; and
10.Cumulative Error
FACTS
Most of the pertinent facts were established by Mr. Willingham’s own trial testimony and his earlier admissions to the police. On the day of the murder, Mr. Willingham was selling perfume door to door in Lawton, Oklahoma. Working his way through a downtown building, he came to the office occupied by Mrs. Jayne Van Wey. Although she told him she did not wish to purchase any perfume, he continued to press her, adhering to his standard sales procedure of insisting on three “no” answers from a potential customer. The repeated rejections that ensued led to an escalation of the situation to what Mr. Willingham claims was a rude rebuff by Mrs. Van Wey and hostile vulgarity on both sides.
After calling on some other offices in the building, Mr. Willingham noticed Mrs. Van Wey enter a restroom off the hallway near her office. Still angry over their earlier confrontation, he eventually followed her into the restroom, pulled her from a stall, and struck her several times in the face. As she continued to struggle with him, he slammed her head into the wall and let her fall backward onto the floor. When she rolled over and began to push herself up onto her hands and knees, he kicked her in the face with his boot. At that point, all resistance ceased, and he left. Mrs. Van Wey lost consciousness and died asphyxiating on the blood from her injuries.
Shortly after the murder, the police found a sales brochure left at one of the other offices Mr. Willingham had visited. *921Upon contacting the company and speaking with a supervisor, the police learned that a sales team in Lawton would be meeting at a local restaurant later that afternoon. The supervisor also indicated that at least one member of the team, Kevin Longenecker, fit the suspect’s description. The police proceeded to the restaurant and approached the group of salesmen. Detective John Whittington asked about Mr. Longenecker and was told by Mr. Willingham that he was not there. Detective Whittington noticed that Mr. Willingham was extremely uneasy and had a fresh scratch on his neck. After Mr. Willingham offered a facially implausible explanation of the scratch, Detective Whit-tington asked him to come to the police station. The detective said the entire group would need to come, and explained that the police were investigating an attack on a woman (he did not say murder) downtown that day.
At the police station, Mr. Willingham was advised of his Miranda rights,2 which he waived in writing. He initially denied any involvement in the attack, but after Detective Whittington pointed out what looked like blood on his boots and asked him to tell his side of the story, Mr. Willingham admitted he had beaten Mrs. Van Wey. However, some of the details of his version of the attack did not fit the physical evidence, and he was asked to return to the scene and clarify his account. After again waiving his Miranda rights, Mr. Willingham walked through the crime scene describing the attack, somewhat differently, on videotape.
Thereafter, Mr. Willingham learned that Mrs. Van Wey had died. He was interviewed again to clear up additional questions raised by the physical evidence, and at this point finally admitted he had forcefully kicked Mrs. Van Wey in the head before leaving the restroom. Finally, after two of Mrs. Van Wey’s. credit cards were found in the restaurant where Detective Whittington had first spoken with Mr. Willingham, he was advised of his rights and questioned once more, to explain this new development. He eventually admitted he had not immediately followed Mrs. Van Wey into the restroom but had stopped in her office and taken the cards from her purse first, “to make it look like a robbery.”
Mr. Willingham’s only defense at trial was to challenge the State's case on the element of intent. Specifically, he testified that while he had attacked Mrs. Van Wey out of anger over their prior confrontation, he had not intended to kill or seriously injure her. Accordingly, the defense requested instructions on the lesser offenses of heat-of-passion manslaughter and second degree depraved-mind murder. The trial court granted the first instruction but denied the second. The jury ultimately rejected Mr. Willingham’s intent defense, finding him guilty of first degree malice murder.
STANDARDS OF REVIEW
Mr. Willingham filed his habeas petition after the effective date of the Antiterrorism and Effective Death Penalty Act of 1996 (AEDPA), which therefore governs the proceeding. See Williams v. Taylor, 529 U.S. 420, 429, 120 S.Ct. 1479, 146 L.Ed.2d 435 (2000). This court has summarized the significance of AEDP1A for habeas review as follows:
Under AEDP1A, if a claim was adjudicated on its merits in state court, a petitioner is entitled to federal habeas relief only if he can establish that the state court decision “was contrary to, or *922involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States” or “was based on an unreasonable determination of the facts in light of the evidence presented in the State court proceeding.” 28 U.S.C. § 2254(d)(1), (2). Under § 2254(d)(1), a federal court may grant a writ of habeas corpus only if the state court reached a conclusion opposite to that reached by the Supreme Court on a question of law, decided the case differently than the Supreme Court has decided a case with a materially indistinguishable set of facts, or unreasonably applied the governing legal principle to the facts of the petitioner’s case. See Williams [v. Taylor, 529 U.S. 362, 412-13, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000)]. “Under § 2254(d)(1)’s ‘unreasonable application’ clause ..., a federal habeas court may not issue the writ simply because that court concludes in its independent judgment that the relevant state-court decision applied clearly established federal law erroneously or incorrectly. Rather that application must also be unreasonable.” Williams, [529 U.S. at 411, 120 S.Ct. 1495], “In sum, § 2254(d)(1) places a new constraint on the power of a federal habeas court to grant a state prisoner’s application for a writ of habe-as corpus with respect to claims adjudicated on the merits in state court.” Williams, [529 U.S. at 412, 120 S.Ct. 1495]. AEDP1A also requires federal courts to presume state court factual findings are correct, and places the burden on the petitioner to rebut that presumption by clear and convincing evidence. See 28 U.S.C. § 2254(e)(1).
“If[, however, a] claim was not heard on the merits by the state courts, and the federal district court made its own determination in the first instance, we review the district court’s conclusions of law de novo and its findings of fact, if any, for clear error.” LaFevers v. Gibson, 182 F.3d 705, 711 (10th Cir.1999). If the district court’s factual findings are based only on a review of the state court record, we conduct an independent review. See Smallwood v. Gibson, 191 F.3d 1257, 1264 n. 1 (10th Cir.1999), cert. denied, [531 U.S. 833, 121 S.Ct. 88, 148 L.Ed.2d 49] (2000).
Walker v. Gibson, 228 F.3d 1217, 1225 (10th Cir.2000), cert. denied, 533 U.S. 933, 121 S.Ct. 2560, 150 L.Ed.2d 725 (2001). With this review framework in mind, we turn to the claims raised by Mr. Willingham, first addressing those related solely to his conviction and then those implicating sentencing concerns.
I. Refusal to Instruct on Second Degree Murder
Mr. Willingham argues that he was improperly denied an instruction on second degree depraved-mind murder, citing Beck v. Alabama, 447 U.S. 625, 100 S.Ct. 2382, 65 L.Ed.2d 392 (1980) (invalidating death sentence for first degree murder where jury was not permitted to consider lesser included offense). In light of radical swings in state law as to whether depraved-mind murder even qualifies as a lesser included offense (LIO) of first degree malice murder, this is not simply a straightforward Eighth Amendment claim under Beck and its progeny. A brief history of the pertinent Oklahoma case law will indicate why Mr. Willingham has joined ex post facto and equal protection objections to his Beck claim.
Prior to Mr. Willingham’s direct appeal in 1997, the OCCA considered second degree murder a LIO of first degree murder. Hooks v. Ward, 184 F.3d 1206, 1233 n. 25 (10th Cir.1999) (quoting Boyd v. Ward, 179 F.3d 904, 916 (10th Cir.1999), cert. denied, 528 U.S. 1167, 120 S.Ct. 1188, 145 L.Ed.2d *9231093 (2000)). However, his claim that, the trial court had violated Beck by refusing to instruct on second degree murder prompted the OCCA to take note of a 1976 amendment to the state’s murder scheme that it had theretofore overlooked. Willingham, 947 P.2d at 1081 (“Apparently, our case law failed to recognize this change in the statutes.”). In light of that amendment, second degree depraved-mind murder now requires “an act imminently dangerous to another person,” Okla. Stat. tit. 21, § 701.8(1) — an element that malice murder, which turns on the intent to kill rather than on any particular characterization of the means used to carry out that intent, does not require, see Okla. Stat. tit. 21, § 701.7. Consequently, pursuant to the “statutory elements” test for identifying LIOs in Oklahoma at the time, the OCCA concluded that depraved-mind murder was not a LIO of malice murder and, hence, could not provide a basis for Mr. Willingham’s Beck claim. Willingham, 947 P.2d at 1081-82.
Two years later, however, in Shrum v. State, 991 P.2d 1032 (Okla.Crim.App.1999), the OCCA returned to the view that second degree murder is a LIO of first degree malice murder — this time notwithstanding the 1976 statutory change' — -pursuant to a global reassessment of its approach to LIOs in the murder context. Abandoning the elements test altogether, the OCCA held as a categorical matter “that all lesser forms of homicide are necessarily included and instructions on lesser forms of homicide should be administered if they are supported by the evidence.” Gilson v. State, 8 P.3d 883, 917 (Okla.Crim.App.2000) (summarizing Shrum), cert. denied, 532 U.S. 962, 121 S.Ct. 1496, 149 L.Ed.2d 381 (2001).
This is the legal backdrop against which Mr. Willingham claims Beck entitled him to a LIO instruction on second degree murder. . Should his. Beck claim fail based on the brief break in state law during which second degree murder was not considered a LIO of malice murder, Mr. Will-ingham insists he must be afforded relief under ex post facto and/or equal protection principles.
A. Beck Claim
In fact, the district court did rely on the window of unfavorable state LIO law to deny Mr. Willingham’s Beck claim. Invoking Hopkins v. Reeves, 524 U.S. 88, 95-100, 118 S.Ct. 1895, 141 L.Ed.2d 76 (1998), for the principle that Beck is not violated if a state court refuses to instruct on an offense that, under state law, is not a LIO of first degree murder, the district court held that the OCCA’s construction of the second degree murder statute on his direct appeal controlled and defeated his Beck claim. We agree: While Hopkins indicated that state courts may not frustrate the values embodied in Beck through arbitrary interpretation of hierarchical murder schemes, see Hopkins, 524 U.S. at 100, 118 S.Ct. 1895; see also Bagby v. Sowders, 894 F.2d 792, 794-95 (6th Cir.1990) (en banc), no such impropriety has been demonstrated here. As explained above, the OCCA’s rejection of Mr. Willingham’s Beck claim was grounded in a reasoned, albeit belated, application of the prevailing LIO standard to the controlling statutory definitions of the offenses involved.
Before turning to Mr. Willingham’s resultant ex post facto argument, we briefly consider two other bases for rejecting his Beck claim which would not implicate any ex post facto problem. First, the state trial court did instruct the jury on first degree heat of passion manslaughter, which suggests the district court could have denied the Beck claim because, under Schad v. Arizona, 501 U.S. 624, 111 S.Ct. 2491, 115 L.Ed.2d 555 (1991), “[t]he Beck *924requirement is satisfied so long as the jury-had the option of at least one lesser included offense, even if there are other lesser included offenses also supported by the evidence.” James v. Gibson, 211 F.3d 543, 555 (10th Cir.2000), cert. denied, 531 U.S. 1128, 121 S.Ct. 886, 148 L.Ed.2d 794 (2001). However, Schad’s qualification on Beck presumes that the LIO presented to the jury had evidentiary support in the record, as otherwise it would not have provided a true third option to obviate the death-or-acquittal dilemma Beck was intended to resolve. Valdez v. Ward, 219 F.3d 1222, 1242 (10th Cir.2000), cert. denied, 532 U.S. 979, 121 S.Ct. 1618, 149 L.Ed.2d 481 (2001); see Schad, 501 U.S. at 648, 111 S.Ct. 2491 (explaining that, while Beck dilemma can be obviated by one LIO, “[t]hat is not to suggest that Beck would be satisfied by instructing the jury on just any [LIO], even one without any support in the evidence”); cf. Roberts v. Louisiana, 428 U.S. 325, 334-35, 96 S.Ct. 3001, 49 L.Ed.2d 974 (1976) (invalidating, as arbitrary, state procedure allowing juries to avoid death penalty through use of LIOs regardless of supporting evidence). Here, both the OCCA and the district court held that the evidence did not warrant a heat of passion manslaughter instruction, and the trial record bears out that determination. The minimal nature of the alleged provocation, and the length of time between that provocation and the murder, during which Mr. Willingham made other office calls showing nothing remarkable in his demeanor, clearly undercut this LIO. Thus, we cannot rely on Schad to provide an alternative rationale for rejecting Mr. Willingham’s Beck claim.
A second possibility is that the evidence simply did not warrant the second degree murder instruction Mr. Willingham insists that he should have received. The OCCA’s opinion is unclear on this question. At one point the OCCA did note, as one of three bases upon which Beck “can be distinguished from this case,” that “Beck only requires an instruction on lesser included offenses when the evidence supports such an instruction,” but then went on to'discuss the inadequacy of the evidence solely with respect to the manslaughter instruction. Willingham, 947 P.2d at 1082-83. The district court, which relied exclusively on the Hopkins rationale cited above, also did not assess whether the trial evidence would have warranted a second degree murder instruction in any event.
Our own review of the trial record leads us to conclude that, had a second degree murder instruction otherwise been available under state LIO law, the evidence was legally sufficient to warrant such a charge. The critical elements of depraved-mind murder are that the death was “caused by conduct which was imminently dangerous to another person” and that “the conduct [was] not done with the intention of taking the life of any particular individual.” Id. at 1081. The former element is clearly established by the violent nature of Mr. Willingham’s physical assault on Mrs. Van Wey, and the latter element, while ultimately rejected by the jury’s verdict, was nevertheless a plausible option on the evidence — indeed, as the OCCA noted, lack of intent to Mil was the “only theory of defense at trial,” id. at 1080.
Thus, the Hopkins analysis discussed above, which rests on the temporary swing in Oklahoma LIO law conclusively disadvantageous to Mr. Willingham, appears to be the only rationale available for rejecting the Beck claim on the merits. As a result, Mr. Willingham’s ex post facto objection cannot be avoided.
*925B. Ex Post Facto (i.e., Due Process3) Claim
It might appear that this claim, which arose only in response to the OCCA’s new construction of the amended second degree murder statute in its decision on Mr. Willingham’s direct appeal, has never been exhausted in state court. However, Mr. Willingham raised it in a petition for rehearing from that decision, which was denied without explanation by the OCCA. Under Aycox v. Lytle, 196 F.3d 1174, 1177-78 (1999), the latter disposition could still be entitled to deference under § 2254(d), even though it would be left to the federal courts to articulate an appropriate rationale for the OCCA’s summary decision. As it happens, the OCCA explained in a later case why the change in LIO law effected by its decision on Mr. Willingham’s appeal did not violate any ex post facto prohibition. In Phillips v. State, 989 P.2d 1017, 1034 (Okla.Crim.App. 1999), the OCCA rejected an essentially identical claim for the following reason:
Although Willingham was handed down six (6) months after the trial in this case, the law upon which the decision that second degree depraved mind murder is not a lesser included offense of malice murder was based was the 1976 amendment to the statute. Therefore, as the statutory language upon which this Court relied for its authority was in effect at the time of the murder and trial in this case, it appears that no possible ex post facto violation is present.
The problem with this rationale, which might be upheld under § 2254(d) in the context of a retroactive legislative change as a reasonable application of Ex Post Facto Clause jurisprudence, is that, as noted in footnote 3 above, Mr. Willingham’s claim arises, rather, under the Due Process Clause and is therefore governed by somewhat different principles never considered by the OCCA.
The Supreme Court recently clarified that “due process limitations on the retroactive application of judicial interpretations of criminal statutes” apply to those decisions “that are ‘unexpected and indefensible by reference to the law which had been expressed prior to the conduct in issue.’ ” Rogers, 532 U.S. at 461, 121 S.Ct. 1693 (quoting Bowie v. City of Columbia, 378 U.S. 347, 354, 84 S.Ct. 1697, 12 L.Ed.2d 894 (1964) (quotation omitted)). This court employed appropriate due process standards in this context before Rogers’ clarification/reaffirmation of Bouie. Of particular relevance here is Fultz v. Embry, 158 F.3d 1101 (10th Cir.1998), in which we held that a state decision, much like Willingham, belatedly interpreting and applying legislative amendments “a number of years ... after passage of these new laws” was an example of the sort of foreseeable decision whose retroactive application was constitutionally permissible. Id. at 1103-04.
Of course, the question whether the OCCA’s decision in Willingham was “unexpected and indefensible” also depends on the merit or plausibility of its holding in light of the legal principles and statutory language on which it was based. In that regard, it should be clear from what has been said above that the OCCA’s application of its statutory elements test to the amended second degree murder statute *926cannot be characterized as “indefensible,” even if the OCCA’s prior failure to acknowledge the statutory change made its sudden attention to the matter “unexpected.” Further, the OCCA’s later reversal of position in Shrum reflected a global reassessment of its approach to the LIO question — resulting in its abandonment of the straightforward but inflexible elements test for a broader approach permitting instruction on any lesser homicide offense supported by the trial record — and, thus, Shrum’s contrary result does not suggest that the OCCA’s analysis in Willingham was indefensible on its own terms. In sum, we hold that Mr. Willingham has failed to make out a due process violation under the Rogers-Bouie standard.
C. Equal Protection Claim
Mr. Willingham argues that when the OCCA “restored the law preceding Will-ingham, in Shrum," but “left out in the cold those few cases [denying LIO claims] which had begun with Willingham,” the OCCA “irrationally denied [him] the protections mandated by Beck and afforded Oklahoma capital defendants both before and after him,” thereby violating his right to equal protection under the law. Aplt. Br. at 25-26. This contention merits little comment. In light of the preceding discussion of the OCCA’s reasoning in Will-ingham and Shrum, the charge of irrational discrimination is unfounded. Moreover, as Mr. Willingham concedes, he did not raise this equal protection issue below (nor has he exhausted it in the state courts).
II. Admission of Post-Arraignment Statements
Immediately upon his arrest, Mr. Will-ingham waived his Fifth Amendment rights and confessed to the attack on Mrs. Van Wey. He does not challenge that confession. Rather, he objects on Sixth Amendment grounds to the admission of two statements he gave shortly after his arraignment, which he later recanted, relating to (1) his pre-murder theft of Mrs. Van Wey’s credit cards, from a purse she had left in her office, to deflect suspicion for the ensuing attack by making it look like a robbery (but which had the unintended effect of supporting the State’s case on intent, since such a cover made no sense if he planned to leave her alive to tell the police about the attack); and (2) an assault on an officer in the Marines years earlier (relevant to the continuing threat aggravator). At trial, he insisted he stole the credit cards only after the attack on Mrs. Van Wey (for no plausible reason he could explain), and simply denied the latter assault.
Mr. Willingham’s right to counsel had certainly attached when he made the statements in question, i.e., “after the initiation of adversary judicial criminal proceedings ... by way of ... arraignment.” United States v. Baez-Acuna, 54 F.3d 634, 637 (10th Cir.1995) (quotation omitted). However, he does not dispute police testimony that repeated Miranda (Fifth Amendment) waivers were effected at this time. Such waivers can suffice for Sixth Amendment purposes as well, depending on two further factual considerations: whether the later contact was initiated by the police or the suspect, and whether the suspect expressly invoked his right to counsel before that contact. Under Michigan v. Jackson, 475 U.S. 625, 106 S.Ct. 1404, 89 L.Ed.2d 631 (1986), and Patterson v. Illinois, 487 U.S. 285, 108 S.Ct. 2389, 101 L.Ed.2d 261 (1988), the Sixth Amendment permits re-initiation of police questioning pursuant to Miranda procedures if the suspect has not requested the professional representation to which he is entitled, but, once he has made such a request, subsequent contact is permitted only if the suspect initiates it himself, even if the *927police otherwise adhere to Miranda safeguards.
Thus, the district court properly focused on whether Mr. Willingham requested counsel during his arraignment. The court noted that the OCCA had addressed the two “statements made by [Mr. Willingham] after his initial appearance, but before he filled out and submitted his [formal, post-arraignment] application for appointed counsel,” and had concluded that “[t]he' record indicates [Mr. Willingham] did not request counsel until [his subsequent written application].” Willingham, 947 P.2d at 1079. The district court deemed this a factual finding presumptively correct under § 2254(e)(1), and then considered whether' Mr. Willingham’s affidavit averring that he asked the judge to appoint counsel at his arraignment constituted the “clear and convincing evidence” necessary to rebut the presumption. This is a difficult question, because the arraignment was not recorded and there is no evidence in the record to counter Mr. Willingham’s account (the OCCA denied his request for an evidentiary hearing on post-conviction, when he first submitted his affidavit).
The district court ultimately elected to resolve the matter through harmless error analysis.4 With respect to the assault in the Marines, the district court held it was merely cumulative to other admissions Mr. Willingham had made about fighting and, thus, was harmless. We agree. Moreover, we note that the primary focus of this evidence — the continuing threat ag-gravator — was not found by the jury in any event.
In contrast, the timing and, by inference, purpose of Mr. Willingham’s theft of the credit cards was clearly relevant to the crucial element of intent for first degree murder. However, the district court held that the physical evidence led to the inescapable conclusion that Mr. Willingham stole the cards before the attack, so his admission to the same effect was harmless. The court was referring to the fact that, despite the large quantity of blood in the washroom, and. associated stains on the doorknob, hallway carpet, and Mr. Willing-ham’s clothes, there was no blood in Mrs. Van Wey’s office or on her purse. Two additional points support the .district court’s analysis. First, testimony from a witness in the building independently pointed to the pre-murder theft of the cards, by indicating that several minutes passed between her seeing Mr. Willingham walk by in the direction of the washroom and her hearing the noise of the ensuing attack. Second] regardless of the whole credit card scenario, the sheer brutality of the attack, espécially the forceful kick to the head with which it concluded, weighed heavily in favor of a finding of intent to kill. Under the circumstances, the district court’s determination of harmless error was correct.
III. Admission of Videotaped Statement Given at the Crime Scene
Mr. Willingham objects to admission of the videotaped statement he gave at the *928crime scene, asserting that this “reenactment of the assault was so prejudicial, demeaning and cumulative that [he] was denied a fair trial, due process of law and a reliable sentencing proceeding.” Aplt. Br. at 63. On his direct appeal, the OCCA held the videotape was merely “a walk through of the crime scene with [Mr. Willingham] telling his version of the events,” and, as such, did not involve any identifiable error. Willingham, 947 P.2d at 1083-84. When Mr. Willingham resumed his objection on habeas, the district court noted that he did not advance any specific reasons why the videotape was inadmissible or identify what particular material contained therein could give rise to actionable prejudice. Thus, the district court summarily denied relief because Mr. Willingham had failed, as a threshold matter, to develop an argument sufficient for federal review.
Mr. Willingham’s claim fails for both reasons identified above. On appeal, he makes no attempt to shore up the basic argumentative deficiencies noted by the district court. On the contrary, his appellate briefing is essentially a verbatim copy of the conclusory allegations presented in his habeas petition. In any event, upon review of the videotaped statement, we agree with the OCCA’s description of its content; Mr. Willingham’s attempt to characterize it as a provocative reenactment of the murder is sheer hyperbole.
IV. Admission of Photographs of the Victim
Mr. Willingham claims that the trial court improperly admitted twenty-two photographs of Mrs. Van Wey’s body, which he contends were unduly prejudicial to the defense at both stages of trial. Where no particularized constitutional guarantees are directly implicated, such an evidentiary objection is cognizable on ha-beas only if the alleged error was “so grossly prejudicial that it fatally infected the trial and denied the fundamental fairness that is the essence of due process.” Fox v. Ward, 200 F.3d 1286, 1296 (10th Cir.) (quotation omitted), cert. denied, 531 U.S. 938, 121 S.Ct. 329, 148 L.Ed.2d 264 (2000). With this federal standard in mind, we conclude that the OCCA’s resolution of this matter was not unreasonable and, therefore, Mr. Willingham is not entitled to relief under § 2254(d). See Thomas v. Gibson, 218 F.3d 1213, 1225 (10th Cir.2000).
On Mr. Willingham’s direct appeal, the OCCA explained that “[t]he test for admissibility of photographs is not whether they are gruesome or inflammatory, but whether their probative value is substantially outweighed by the danger of unfair prejudice,” and held that the victim photographs were properly admitted at the guilt phase for their relevance to the critical element of intent to kill and at the penalty phase for their relevance to the serious physical abuse requirement of the HAC aggravator. Willingham, 947 P.2d at 1083 (also holding photographs depicted sufficiently different aspects of victim’s injuries to undercut any challenge on ground they were cumulative). The district court agreed that the photographs were properly admitted for these important purposes, and held that Mr. Willingham therefore could not demonstrate a due process violation warranting habeas relief.
Mr. Willingham’s appellate argument on this issue fails to come to grips with the primary basis for the rulings of the district court and OCCA. He simply repeats his charge that the photographs are gruesome, without addressing their obvious facial relevance to critical elements of the State’s case at both stages of trial. We note one additional point, for clarification. When a victim dies or loses consciousness *929early on in an assault, photographs of all of her injuries might involve irrelevant and/or unduly prejudicial material at the penalty phase, since the HAC aggravator focuses on the conscious suffering of the victim. Cf. Powell v. State, 906 P.2d 765, 780 (Okla.Crim.App.1995) (holding admission of victim photographs during penalty phase “came very close” to reversible error for just this reason). Here, however, there is no such concern; Mr. Willingham’s own testimony described Mrs. Van Wey as conscious and struggling to defend herself throughout the fatal beating.
V. Reasonable Doubt Instruction
In Cage v. Louisiana, 498 U.S. 39, 111 S.Ct. 328, 112 L.Ed.2d 339 (1990), and Estelle v. McGuire, 502 U.S. 62, 112 S.Ct. 475, 116 L.Ed.2d 385 (1991), the Supreme Court held that “a jury instruction is unconstitutional if there is a reasonable likelihood that the jury understood the instruction to allow conviction without proof beyond a reasonable doubt.” Tyler v. Cain, 533 U.S. 656, 121 S.Ct. 2478, 2480 & n. 1, 150 L.Ed.2d 632 (2001). Invoking this body of law, Mr. Willingham objects to the reasonable doubt instruction given at his trial, which stated in part:
“[I]f you find and believe beyond a reasonable doubt under the law and the evidence herein that the said defendant did commit the offense of murder in the first degree as charged in the complaint and information herein, you will find the defendant guilty of said offense and so state by your verdict. However, if you fail to find and believe the defendant guilty or if you entertain a reasonable doubt as to his guilt, then in either case you should return a verdict of not guilty.”
Trial Tr. Vol. III at 150-51 (emphasis added). He argues that replacement of the clearly mandatory “will,” used where the instruction relates the lack of reasonable doubt to a guilty verdict, with the allegedly more permissive “should,” used where the instruction relates the presence of reasonable doubt to a not guilty verdict, allowed the jury some discretion to convict even if they harbored a reasonable doubt about his guilt.
Rejecting this claim, the OCCA explained “[t]he term ‘should,’ when used as it was used by the trial court, is defined as expressing an obligation or duty. Should is never placed on the level with ‘may,’ which is clearly permissive.” Willingham, 947 P.2d at 1082. Indeed, the Supreme Court has never indicated that the mandatory force inherent in the term “should” is insufficient to properly guide a jury’s application of the reasonable doubt standard. Moreover, we note that the trial court referred to reasonable doubt at several other points in its charge, repeatedly directing that a not guilty verdict “must” follow if the jury harbored a reasonable doubt about the defendant’s innocence. The OCCA’s conclusion that the instructions, read as a whole, adequately stated “the jury’s duty to determine if the State has proven its ease beyond a reasonable doubt,” id. at 1083, was neither “contrary to” nor “an unreasonable application of’ the clearly established law summarized in Tyler. Accordingly, habeas relief on this claim is foreclosed by § 2254(d)(1).
VI. Evidence Supporting HAC Aggravator
Mr. Willingham challenges the sufficiency of the' evidence supporting the HAC aggravator. The controlling constitutional test is whether any rational trier of fact could have found the aggravator beyond a reasonable doubt. Hale, 227 F.3d at 1334-35. This court has not decided, for AEDP1A purposes, whether such issues of evidentiary sufficiency are legal *930and hence governed by § 2254(d)(1), or factual and hence governed by §§ 2254(d)(2), (e)(1); in any event, however, the critical question is “whether the OCCA’s decision [affirming the HAC finding] was reasonable.” McCracken v. Gibson, 268 F.3d 970, 981 (10th Cir.2001). In our view, it clearly was.
The OCCA summarized the evidence supporting the HAC aggravator as follows:
Appellant’s own testimony reveals that he punched Mrs. Van Wey in the face at least three times, then he slammed her head into the wall causing her to fall to the ground on her back. Mrs. Van Wey was still conscious at that point because she was able to roll over and rise to her hands and knees before being kicked in the face by Appellant. Circumstantially, it was at that point that she lost consciousness and aspirated her own blood which caused her death. Certainly this evidence supports a finding that Mrs. Van Wey was subjected to serious physical abuse ....
Along with Appellant’s testimony, the medical examiner testified that there were at least four violent blows to the victim’s head. This evidence combined with Appellant’s testimony can lead one to conclude that some of these blows occurred prior to the loss of consciousness. Circumstantial evidence and common sense would lead a reasonable jury to believe that this killing was successfully designed to inflict a high degree of pain on the victim. Therefore, there was sufficient evidence to show that the murder was especially heinous, atrocious or cruel.
Willingham, 947 P.2d at 1085.
Mr. Willingham does not take issue with the factual accuracy of that summary, which the trial record clearly bears out. Rather, he contends “Mrs. Van Wey was beaten to unconsciousness so quickly that she suffered little longer than had [he] walked in and shot her.” Aplt. Br. at 66. He does not cite any authority, and we know of none, to support his cavalier equation of the extended, brutal beating suffered by Mrs. Van Wey with a single, mercifully swift gunshot. The district court correctly rejected this contention as wholly without merit.
He also insists this case is controlled by Thomas v. Gibson, 218 F.3d 1213, which invalidated a HAC finding that had been based solely on evidence of multiple blows and the inference “that a murderer would [not] continue striking a murder victim if the first landed blow rendered the victim unconscious.” Id. at 1228. Thomas is in-apposite. In that case there was “no evidence that a struggle had taken place, that [the victim] had defensive wounds, or that [the defendant] had any wounds on his body consistent with a struggle when he was arrested shortly after the murder.” Id. Moreover, a witness “close enough to observe many details ... did not testify to hearing any noises, voices, or screams.” Id. Here, in contrast, we have Mr. Willingham’s own description of Mrs. Van Wey’s conscious struggle until the final violent blow was landed, which is consistent with the injuries inflicted and further corroborated by the fresh scratch on Mr. Willingham’s neck at the time of his arrest. We also have testimony from a witness who heard banging noises and a scream coming from the direction of the women’s washroom at the time in question. Clearly, the kind of inference questioned in Thomas was not needed by the OCCA to affirm the HAC finding in this case.
VII. Victim Impact Evidence
Mr. Willingham claims that victim impact evidence presented at the penalty phase was unduly emotional, impermissibly contradicted substantive evidence of the *931circumstances of the murder, and included improper “opinions about the crime, the defendant, and the appropriate sentence.”5 Hain v. Gibson, 287 F.3d 1224, 1238 (10th Cir.2002) (quotation omitted). On direct appeal, the OCCA (1) summarized the evidence and acknowledged some of it was indeed improper, see Willingham, 947 P.2d at 1085-86, 1088, (2) noted the absence of a trial objection, but stated it would consider the matter “under [its] statutorily mandated sentence review to determine whether the statements caused [Mr. Willingham] to be sentenced to death for improper reasons,” id. at 1086, and (3) ultimately concluded that “even absent the improper victim impact evidence, the result would have been the same,” id. at 1088-89. The district court followed essentially the same approach, noting the improper testimony but denying relief in light of the overwhelming evidence of guilt in the first stage and of aggravation in the penalty phase. We agree with both the OCCA and the district court, though it is important to clarify the harmless error standard underlying our conclusion that habeas relief is not warranted here.
While the OCCA appears to have applied a species of harmless error analysis, denying relief for recognized error due to lack of prejudice, there is no indication that it employed the “harmless beyond a reasonable doubt” standard of Chapman v. California, 386 U.S. at 24, 87 S.Ct. 824. Consequently, we consider the question of harmless error de novo under the general standard established for habeas cases in Brecht v. Abrahamson, 507 U.S. 619, 113 S.Ct. 1710, 123 L.Ed.2d 353, asking whether the objectionable victim impact evidence “had substantial and injurious effect or influence in determining the jury’s [death penalty] verdict,” id. at 637, 113 S.Ct. 1710 (quotation omitted). See Sallahdin v. Gibson, 275 F.3d 1211, 1230 (10th Cir.2002); Hale, 227 F.3d at 1324-25; Herrera, 225 F.3d at 1179.
Several factors convince us that the victim impact evidence in question had no such effect or influence. The jury properly found that the brutal, demeaning attack on Mrs. Van Wey was especially heinous, atrocious or cruel--a finding effectively compelled by Mr. Willingham’s own description of the'crime quite' apart from the few speculative embellishments in the victim impact testimony. Mr. Willingham was admittedly responsible for the attack, which, moreover, the jury had already found during the guilt phase was carried out with a fatal intent, thus rejecting his primary extenuating plea that he never meant to inflict serious harm. Finally, the “provocation” cited for the attack, that Mrs. Van Wey was rude to him when he persisted in clearly unwanted sales advances, was so ludicrously disproportionate, and temporally remote, to his violent response that any indirect refutation (or substantiation) on the point could hardly have mattered to the jury. Under the circumstances, we are confident that the improper aspects of the victim impact evidence did not play any substantial role in the jury’s assessment of the death penalty in this case. See Hain, 287 F.3d at 1239-40 (holding admission of comparable victim *932impact evidence harmless for similar reasons).
VIII. Prosecutorial Misconduct
Mr. Willingham claims several remarks made by the prosecutor to the jury were improper and entitle him to relief under the “fundamental fairness” standard that generally governs such claims on habeas. See Neill v. Gibson, 278 F.3d 1044, 1058 (10th Cir.2001), petition for cert. filed, (U.S. May 6, 2002) (No. 01-10121). The OCCA concluded none of the remarks rose to the level of actionable prosecutorial misconduct. See Willingham, 947 P.2d at 1084. In denying habeas relief, the district court (1) set out the allegedly objectionable remarks; (2) noted the conclusory nature of Mr. Willingham's objection to them, but nevertheless evaluated their impact in light of the record as a whole, including the strength of the State’s case on guilt and aggravation; (3) concluded none of the remarks, individually and/or cumulatively, deprived Mr. Willingham of a fundamentally fair trial; and (4) upheld the OCCA’s decision denying relief on this claim pursuant to § 2254(d).
On appeal, Mr. Willingham does not really address the district court’s opinion, much less attempt to identify specifically any error in its rationale. In fact, his appellate briefing does little more than restate, essentially verbatim, the allegations originally set out in his habeas petition. In any event, we have reviewed the comments and the trial record, which lead us to the same conclusion reached by the district court.
Mr. Willingham objects to the prosecutor’s personal “prayer” for a first degree murder verdict during closing argument in the guilt phase:
The evidence is overwhelming. There’s only one verdict, and I pray you’re strong enough, ... however long it takes, set in there, talk this case over, discuss this case, but I pray there be only one verdict, and that’s guilty of murder in the first degree.
Trial Tr. Vol. III at 180. He also objects to the following exhortatory remarks by the prosecutor during closing argument in the penalty phase:
I’d like to put this, if I may, in perspective. Most of you, if you had a stray dog that had its head busted up, the dog is dying, the dog is wallering down trying to get up, most human beings could not kick that stray dog in the face hard enough to break a nose, shove it back into the eyelids, knock out teeth, split lips and watch that dog gurgle and die, or turn around and walk off while it was in the throes of death. Most people cannot do that. That should tell you something about a human being that has the ability to do that to an old woman and walk out.
How many of you will ever be able to get this vision of that bathroom and this woman’s face out of your mind. It’s going to haunt you for months. It’s going to change every one of you to some degree that’s been affected with this case. You can’t help it if you’re a normal human being.
I want to get back to this ... life without parole, make him think about it day in and day out. I submit to you this man wouldn’t think about it past the day of his judgment and sentence. Correlate the two for you, if I may; [Mrs.] Van Wey is not ever going to see another Christmas. Life without parole, he’s going to see them year after year after year ... [Mrs.] Van Wey will never *933celebrate another birthday. Life without parole, he’ll celebrate it every year.
Every one of you told me that you could give the death penalty. A number of you told me that you would not take the easy way out. Now the easy way out is to say I just can’t do this or it’s too great, I don’t want to have to deal with this. Let’s just do life without parole and go to the house. That’s the easy way out in this case.
[T]he evidence in this case is overwhelming — overwhelming. I pray you be strong. I pray you members of the jury be strong. There’s only one verdict. Anything less will be the second travesty in this case.
Trial Tr. Vol. IV at 116-117, 128-131.
Comparable — indeed, substantially more inflammatory — remarks have not warranted habeas relief under the fundamental fairness standard in prior cases before the Supreme Court and this circuit. See, e.g., Darden v. Wainwright, 477 U.S. 168, 178-83, 106 S.Ct. 2464, 91 L.Ed.2d 144 (1986); Pickens v. Gibson, 206 F.3d 988, 1000 (2000); Hopkinson v. Shillinger, 866 F.2d 1185, 1205-11 (10th Cir.1989), overruled on other grounds as recognized by Davis v. Maynard, 911 F.2d 415, 417 (10th Cir.1990). Further, the obvious strength of the State’s evidence at both phases of trial undercuts Mr. Willingham’s claim that the few remarks noted above played any significant role in the proceedings. In sum, “we cannot conclude that these remarks, alone or considered together, rendered [Mr. Willingham’s] trial fundamentally unfair. The [OCCA’s] decision denying ... relief on these claims was, therefore, not unreasonable.” Pickens, 206 F.3d at 1000 (quotation omitted).
IX. Ineffective Assistance of Counsel
None of Mr. Willingham’s allegations of ineffective assistance were raised on direct appeal. On state post-conviction, the OCCA held those relating to trial were procedurally defaulted and those relating to appeal failed for lack of facts to support a finding of deficient performance. Willingham v. State, No. PC-97-389 (Okla. Crim.App. March 19, 1998). The district court approached the matter as follows. First, it upheld the OCCA’s denial of the appellate ineffectiveness claim as reasonable under § 2254(d). Second, it held that all of the trial ineffectiveness allegations, except those relating to counsel’s failure to develop mental health and related mitigation evidence, could have been pursued on direct appeal by separate counsel and, thus, were properly barred under English v. Cody, 146 F.3d 1257, 1263 (10th Cir.1998). Finally, it reviewed the claim relating to the mental health and mitigation evidence under Strickland v. Washington, 466 U.S. 668, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984), and held that (1) the failure to obtain treatment records which counsel had been told did not exist was not deficient performance, and (2) the failure to call certain witnesses in mitigation, even if deficient, was not prejudicial.
Despite the significance of the district court’s procedural bar holding, on appeal Mr. Willingham does not mention, let alone meaningfully challenge, the court’s analysis in that regard. Rather, his appellate brief simply recites his numerous complaints about counsel, many in very eonclu-sory fashion, as if there had been no procedural bar ruling undercutting most of them. We shall focus on the primary claim decided on the merits by the district court, regarding the mental health and mitigation evidence Mr. Willingham insists his counsel should have developed and pre*934sented at trial. For procedural and substantive reasons, none of his other allegations warrant specific comment.6
Mr. Willingham cites three types of evidence in this regard: 'records of his treatment for depression as a child; potential expert testimony regarding the psychological consequences of his abusive upbringing; and lay testimony further describing his troubled childhood. As for the treatment records, the district court properly held two points undercut Mr. Willingham’s claim. First, he admitted that his counsel requested such records but were informed they did not exist. Second, he did not suggest what counsel could have done differently to- obtain the records nor did he indicate what was contained in the records which could have altered the outcome of his trial. Mr. Willingham’s cursory discussion of the matter on appeal does not in any way undermine the district court’s analysis.
Mr. Willingham complains about two different categories of potential expert testimony. The first involves certain experts who did not evaluate Mr. Willingham until their recruitment by post-conviction counsel. His allegations of ineffective assistance in this regard are explicitly derivative of his complaint about counsel’s failure to obtain his childhood treatment records — i.e., he argues that competent counsel would have obtained such evaluations if “[t]imely edified by” the treatment records. Aplt. Br. at 38. Because, as just explained, counsel lacked those records through no fault of their own, the district court reasonably rejected this aspect of Mr. Willingham’s claim on the ground that he had not suggested any viable basis for concluding that counsel should have sought out the additional psychological evaluations.
Mr. Willingham also asserts that counsel were ineffective for failing to call Phillip J. Murphy, Ph.D., to testify. Doctor Murphy had interviewed Mr. Willingham prior to trial and concluded “he was not typically a continuing threat to society, especially in prison where there is a typical absence of older females who are most likely to trigger his unresolved anger with his mother.” PosWConviction App. Vol. 3, Psychological Report by Dr. Murphy at 2 (report prepared for post-conviction proceeding but reciting pre-trial finding). Because the continuing threat aggravator was ultimately rejected by the jury in any event, the district court held Mr. Willingham could not show any prejudice in that respect. As for counsel’s failure to call Dr. Murphy for more general mitigation purposes, the district court held counsel could reasonably have concluded that his testimony would not have been especially significant, or even favorable, to the defense. We have reviewed Dr. Murphy’s report, and agree with that assessment. Moreover, as the report indicates, and Mr. Willingham acknowledges in his appellate brief, Dr. Murphy’s opinions about Mr. Willingham’s post-traumatic stress disorder and his love-hate relationship with his mother were dependent upon Dr. Murphy’s review of the same treatment records discussed above, which were not available to counsel.
Finally, Mr. Willingham argues that counsel should have called additional lay witnesses to testify about his abusive upbringing by his mother. The district court *935disposed of this aspect of his claim on Strickland’s prejudice prong. The court noted that Mr. Willingham’s mother testified for the defense regarding the deplorable conditions under which he was raised, including their poverty and his exposure to the abusive, drug-dependent men she dated. She also admitted she was verbally and physically abusive to him, and would neglect him while she stayed out all night at the bars. Since the other witnesses could have done little to add to the substance of what Mr. Willingham’s mother had said, the district court concluded, correctly in our view, that no reasonable probability existed that their testimony would have changed the outcome of the sentencing proceedings. See generally Strickland, 466 U.S. at 695, 104 S.Ct. 2052.
X. Cumulative Error
The OCCA rejected a cumulative error claim on Mr. Willingham’s direct appeal on the basis that “hav[ing] found no single error requiring reversal, we cannot find that the proceedings, as a whole, were unfair.” Willingham, 947 P.2d at 1088. This rationale, taken on its face, would render the cumulative error inquiry meaningless, since it indicates that cumulative error may be predicated only upon individual error already requiring reversal. Instead, the proper inquiry “aggregates all the errors that individually might be harmless [and therefore insufficient to require reversal], and it analyzes whether then-cumulative effect on the outcome of the trial is such that collectively they can no longer be determined to be harmless.” United States v. Wood, 207 F.3d 1222, 1237 (10th Cir.2000) (quotation omitted). We therefore consider Mr. Willingham’s cumulative error claim de novo, applying the controlling federal standard. See Herrera, 225 F.3d at 1179. The crux of our review is “whether the defendant’s substantial rights were affected.” Wood, 207 F.3d at 1237 (quotation omitted).
As indicated at various points throughout this opinion, the strength of the State’s case on both guilt and aggravation effectively undercuts Mr. Willingham’s assertion of actionable prejudice in connection with the few errors which may have occurred during the proceedings. Now, “[considering [any such] errors in the aggregate, we conclude upon review of the entire record that the cumulative [effect] is harmless” as well. United States v. Becker, 230 F.3d 1224, 1233 (10th Cir.2000), cert. denied, 532 U.S. 1000, 121 S.Ct. 1666, 149 L.Ed.2d 647 (2001); see also Moore v. Gibson, 195 F.3d 1152, 1175 (10th Cir.1999).
Accordingly, the judgment of the district court is AFFIRMED.
. We note Mr. Willingham indiscriminately briefed all of the issues originally asserted in his habeas petition, appending a summary request for a COA at the end of his discussion of the five uncertified claims. Appellate review of these matters has been waived. Romano v. Gibson, 278 F.3d 1145, 1155 (10th Cir.2002); Cannon v. Gibson, 259 F.3d 1253, 1259 n. 3 (10th Cir.2001), cert. denied, - U.S. -, 122 S.Ct. 1966, 152 L.Ed.2d 1026 (2002).
. See generally Miranda v. Arizona, 384 U.S. 436, 86 S.Ct. 1602, 16 L.Ed.2d 694 (1966).
. While "the Constitution’s Ex Post Facto Clause figures prominently in [Mr. Willing-ham's] argument,” strictly speaking the "limitations on ex post facto judicial decisionmak-ing” derive from the Due Process Clause, which does not incorporate wholesale all the restrictions directly imposed on legislative action by the former provision. Rogers v. Tennessee, 532 U.S. 451, 456-61, 121 S.Ct. 1693, 149 L.Ed.2d 697 (2001).
. The district court used the "harmless beyond a reasonable doubt” standard of Chapman v. California, 386 U.S. 18, 24, 87 S.Ct. 824, 17 L.Ed.2d 705 (1967), instead of the “substantial and injurious effect or influence” habeas standard from Brecht v. Abrahamson, 507 U.S. 619, 637, 113 S.Ct. 1710, 123 L.Ed.2d 353 (1993) (quotation omitted) which we have held still controls in post-AEDPlA cases where, as here, there is no state court Chapman determination to defer to under § 2254(d). See Hale v. Gibson, 227 F.3d 1298, 1324-25 (10th Cir.2000); cert. denied, 533 U.S. 957, 121 S.Ct. 2608, 150 L.Ed.2d 764 (2001); see also Herrera v. Lemaster, 225 F.3d 1176,. 1179 & n. 3 (10th Cir.2000), reopened & reh'g granted en banc (Feb. 28, 2002). However, our conclusion on harmless error does not turn on which of these standards applies.
. Mrs. Van Wey's family described her as a loving wife, caring mother and generous person, properly indicating the human loss caused by her death. But some family members injected speculative, inflammatory details about the crime and the commensurate retribution it demanded — one daughter suggested that Mr. Willingham be confined in a small area, beaten, and made “to crawl [to] try to get away,” “beg for his life” and “choke on his own blood.” Spme also contradicted trial evidence regarding the asserted provocation for the crime, denying that Mrs. Van Wey was capable of the rude vulgarity Mr. Willing-ham attributed to her. All three children asked the jury to impose a death sentence.
. Mr. Willingham has also summarily asserted ineffective assistance of counsel in connection with many of the substantive claims addressed throughout this opinion. As we have rejected these other matters on the merits, separate consideration of the associated ineffective assistance claims is unnecessary.'