
588 F.3d 1185 (2009)
Jason Farrell McGEHEE, Appellee,
v.
Larry NORRIS, Director, Arkansas Department of Correction, Appellant.
Jason Farrell McGehee, Appellant,
v.
Larry Norris, Director, Arkansas Department of Correction, Appellee.
Nos. 08-1182, 08-1513.
United States Court of Appeals, Eighth Circuit.
Submitted May 14, 2009.
Filed December 16, 2009.
*1187 Pamela Rumpz, AAG, argued, Little Rock, AR, Teena L. Watkins, Darnisa Johnson, Kelly Hill, Lauren Heil, Little Rock, AR, on the brief, for appellant/cross-appellee.
Julie Brain, AFPD, argued, Little Rock, AR, Josh Lee, Deborah Czuba, Jeffrey M. Rosenzweig, Little Rock, AR, on the brief, for appellee/cross-appellant.
Before WOLLMAN, JOHN R. GIBSON, and MURPHY, Circuit Judges.
WOLLMAN, Circuit Judge.
In 1998, an Arkansas jury found Jason Farrell McGehee guilty of the capital murder of John Melbourne and sentenced him to death. The Supreme Court of Arkansas affirmed the conviction and sentence. After exhausting his avenues for state relief, McGehee filed a petition for a writ of habeas corpus in the United States District Court for the Eastern District of Arkansas, challenging his sentence on five separate grounds. The district court granted the writ on the ground that the state trial court improperly excluded relevant mitigating evidence during the sentencing phase of McGehee's trial. The State of Arkansas appeals the grant of the writ, and McGehee cross-appeals the dismissal of his other claims. We reverse the grant of habeas relief and affirm the district court's dismissal of the remaining claims.

I. Factual and Procedural Background

A. The Crime
During the summer of 1996, McGehee, then twenty years old, was the leader of a group of teens and young adults who resided in an abandoned house at 1123 North Spring Street in Harrison, Arkansas. The group, which included McGehee, Melbourne, Benjamin McFarland, Christopher Epps, Candace Campbell, and Robert Diemert, used stolen and forged checks to finance the purchase of food, alcohol, and illegal drugs. Melbourne, fifteen, was the youngest of these individuals.
On August 19, 1996, McGehee sent Melbourne to obtain cash with a stolen check. Melbourne's efforts to pass the bad check aroused the suspicion of a local storekeeper, who contacted the police. When the police questioned Melbourne about his activities, he disclosed that there was stolen property at the house on Spring Street. The police went to the residence to investigate but eventually left when no one answered the door. McGehee, McFarland, Campbell, and Epps had been hiding inside and concluded that Melbourne had "snitched" to the police. They determined *1188 that they would beat up Melbourne to teach him a lesson, and McFarland and Epps left to find him and bring him back to the house.
When Melbourne arrived, McGehee confronted him, demanding to know why he had talked to the police. Shortly thereafter, the group initiated a torturous beating. Melbourne was stripped naked, punched, kicked, and burned with a candle. There was also evidence that Lysol was sprayed in his face. The beating continued for more than an hour, with McGehee delivering most of the blows. Although Melbourne initially attempted to escape the onslaught, he eventually became so weak that he ceased to resist. In Campbell's words, "[H]e looked like he was really tired and exhausted. He was real weak at that point.... He had give up [sic] fighting."
At some point, McGehee decided that the group needed to leave the house because he feared the police would return to arrest him. McGehee decided to travel to his uncle's vacant farmhouse in Omaha, Arkansas, and then head to the state of Utah, where he had family. McGehee allowed Melbourne to put his clothes on, following which he was bound and placed in a car. During the trip to Omaha, there was testimony that McGehee asked Melbourne, "how does it feel to know you are going to die?" When they arrived, Melbourne was again stripped and beaten. McGehee punched and kicked Melbourne; threw a box fan at him; struck him repeatedly with a wooden axe handle; and threatened him with a knife to his throat. The other members of the group all participated in the beating to varying degrees. Campbell kicked Melbourne in the groin and burned his genitals with a candle. When Melbourne tried to get away, McGehee and McFarland dragged him back.
After about an hour, the group took a break from the assault, at which time McGehee suggested that they needed to get rid of Melbourne. McGehee, McFarland, and Epps then took Melbourne, bound and naked, into the woods, where Melbourne made a final plea for his life. The three took turns strangling him to death, with McGehee putting his foot on Melbourne's throat as he gasped for air. McGehee, McFarland, and Epps appeared to be laughing as they emerged from the woods.

B. McGehee's Trial
Prior to his trial, McGehee underwent a forensic evaluation at the Arkansas State Hospital. The evaluation indicated that McGehee was of average intelligence, not mentally ill at the time of the offense, and competent to stand trial. McGehee subsequently filed a motion for funds to obtain psychiatric assistance, arguing that he needed expert assistance for both the guilt and penalty phases of his trial. Specifically, his counsel contended that McGehee might have potentially suffered adverse effects from his father's exposure to the chemical Agent Orange in Vietnam. The state stipulated that McGehee's father had been exposed to the chemical, but opposed the motion on the ground that there was an insufficient scientific basis to show that any inheritable defects would be relevant to mitigation. The court denied McGehee's motion, stating that "[i]f you can present anything to [the] Court as to whom can do this and if they can do it promptly and information and material on why this is going to [be] mitigating, but I just cannot regard this as very substantial."
The jury found McGehee guilty of capital murder and kidnapping. At the sentencing phase of the trial, John Melbourne, Sr., testified about the impact of his son's death, stating that since the murder he had been battling depression and unable to work or sleep. He testified that the trauma *1189 had caused him and his wife to divorce and that his remaining children struggled with the loss of their brother.
By way of mitigation, McGehee introduced, among other things, evidence of his difficult life, dysfunctional family, and parental abandonment. The court ruled that McGehee could not introduce evidence that two of his co-defendants were convicted of capital murder and kidnapping and did not receive the death penalty.
Five witnesses testified on McGehee's behalf. LaRee Peacock, McGehee's maternal grandmother, testified that McGehee did not have a good relationship with his father because his parents had divorced when McGehee was young. Peacock testified that McGehee got along well with his mother until a period when she became religious and immediately expected him to do the same. Peacock testified that McGehee was not physically abused as a child, but she stated that he suffered mental abuse because his mother would, for example, get angry and refuse to feed McGehee and his sister dinner if they did not go to church. Peacock testified that McGehee's mother took him to a counselor who recommended that she discipline McGehee by withholding something of which he was very fond. Accordingly, his mother took away his dog and withheld other items when she became angry. Eventually, the narrative focus of Peacock's testimony drew an objection from the state:
McGehee's Counsel: Did [McGehee's Mother] Robin neglect those children? Peacock: Well, they were clothed. And like I say, if they didn't go to church, she would be upset. And one time we had gone out there for lunch and I can't remember what [McGehee's sister] Kimber had done, but she made her eat on the basement steps and she sat down there crying and it actually spoiled my lunch because I didn't feel like eating. I just, I just lost my appetite. Another time
Prosecutor: Your Honor, I'm goingI apologize for interrupting but I'm going to object at this time. I don't think the purpose is just to relay [sic] incident after incident. The questions are directed and are going to one of the mitigating factors and I think that's appropriate but this [is inappropriate].
Linda Christensen, McGehee's aunt, was the final defense witness. She testified that the relationship between McGehee's parents was dysfunctional and that there was a good deal of mental cruelty in their household. Christensen testified that McGehee did not have a relationship with his father's family and he did not meet his paternal grandparents until he was ten years old. She stated that McGehee and his mother "idolized each other" but that things changed when McGehee started getting into trouble. She also testified that at some point McGehee's mother became fanatically religious and unusually strict, stating that "[s]ometimes for punishment, she would make them read the scriptures, sometimes [for] an hour, which only made the kids rebel." Like Peacock, Christensen's testimony relied heavily on anecdotes and eventually drew an objection:
McGehee's Counsel: To make it more relevant, the prosecutor has been lenient here, can you tell me a little bit about any punishments outside that Jason would suffer?
Christensen: That Jason would suffer, yes. Jason wasn't keeping a curfew. He was staying out later than his mother wanted and they never believed in locking the house before but when Jason came home, the house was locked. The house was locked and there were wooden dowels placed inside the windows and chunks of wood and books and just *1190 about anything she could find to put into the windows so he couldn't slide the windows open.
McGehee's Counsel: He couldn't get back in the house?
Christensen: He couldn't get back in the house and she said Jason knows how to knock. He should have come home when I told him to and if he wants in the house, he can knock. And so Jason slept in the dog run, in a small square dog run with his dog, Speckles. It didn't have a roof and it was pretty cold because where we come from, it can freeze up until June, and this was the first part of April.
McGehee's Counsel: How long did this go on?
Christensen: Probably about seven to ten days. McGehee's Counsel: He just didn't get to come in?
Christensen: No. He didn't get to come in. She said if he wants to come in, he can knock. So I took him up food, took him up sandwiches. And he was living on [C-rations]. He found some [C-rations] and stuff. And I gave him some tissue papers and he was going to the bathroom outside and he got into the cellar and he got some bottled tomatoes. He dug holes in the dirt. He's [sic] stand his bottles of tomatoes up. When we went up there, he had eatenhe was eating bottled tomatoes and we were afraid he would get poisoned, get botulism. And he was living out there with his dog. There was no cover on this dog run.
McGehee's Counsel: I'm not going to ask a lot about dogs but apparently some of your family is weird about how they handle their animals?
Christensen: Yes.
McGehee's Counsel: Can you just elaborate on that? What happened to his dogs even when he was a small child?
Christensen: When he was a baby, he had a Doberman Pincher
At that point, the prosecutor objected on the ground that the testimony was "very, very far afield from anything that's relevant to the mitigating circumstances that I know about." McGehee's counsel did not explain how the incident was relevant to McGehee's sentence, simply stating that "[t]he jury needs to know the background of why this man did what he did." The trial judge sustained the objection on the ground that he could not see the relevance of "[s]omething years and years ago involving a dog."
Later, the court sustained a similar objection to Christensen's testimony about abuse that McGehee's sister suffered at the hands of their stepfather:
Christensen: [McGehee] was supposed to discipline his sister, Kimber. My sister let Jason do that a lot. [McGehee's stepfather] Wayne wasn't allowed to discipline her. She'd say, no, don't discipline my kids, but when they got out of hand, she would tell Wayne, when they got older, she would say aren't you going to do something with these kids. And so, you know, Jason had problems fighting on and off growing up, but Wayne beat Kimber up and Family Services were called in. She had big bruises on the back of her legs that they took pictures of.
Prosecutor: Your Honor, at this point we're talking about somebody who isn't even the defendant, and I really think we're way far afield from directional testimony. I would ask that we focus on what we're here to do.
McGehee's Counsel: My position is I'm here to try to save his life and if it helps this jury with the background, that's why I'm asking.
The Court: Well, I'm going to sustain the State's objection.
*1191 After the jury had retired to deliberate on the sentence, McGehee's counsel sought to make a record about what Christensen would have testified to in the absence of the state's objection:
McGehee's Counsel: I was just trying to show a pattern as to how violent a family they were because the dogs' throats are slit and they were blaming Jason for being the, not the one that did it but that because he wanted a new puppy, God had these animals killed and I just was trying to show once again the pattern of violence in the family that helped got [sic] him where he was. And that's what I wanted to bring up. That's all I have, Judge.
...
The Court: Well, they haven't really charted, ever since we bifurcated proceedings not only in capital cases but in other cases, it's still uncharted. To what extent, the Court just allows an endless sequence of [anecdotes] to be presented by the defense. There has to be some limits placed on it.... I don't know, maybe to some extent it's just wide open and it's just how much time we're going to take and how many different [anecdotes] we get to listen to about an individual's history. But some presumably isolated act of cruelty to animals that happened years and years ago, I'm still not convinced has any particular relevance....
The jury unanimously found that the state had proved two aggravating circumstances beyond a reasonable doubt: (1) that the murder was committed for the purpose of avoiding or preventing arrest and (2) that the murder was committed in an especially cruel or depraved manner. The verdict forms also indicated a non-unanimous finding that McGehee probably came from a dysfunctional family. The jury found that the aggravating circumstances outweighed beyond a reasonable doubt any mitigating circumstances and justified a sentence of death.

C. Direct Appeal and State Post-Conviction Proceedings
On appeal to the Arkansas Supreme Court, McGehee argued that the trial court erred in excluding evidence that McFarland and Epps had received life sentences and in sustaining the state's various objections to mitigation testimony. The Arkansas Supreme Court rejected McGehee's contention that his co-defendants' sentences were relevant, stating that "[McGehee] cites no authority or convincing argument in support of his theory, and we are not aware of any." McGehee v. State, 338 Ark. 152, 992 S.W.2d 110, 123 (1999) (McGehee I).
The court similarly rejected McGehee's contention that the trial court had erred in sustaining the state's objections to parts of Christensen's testimony. With respect to Christensen's statement about what had happened to McGehee's dogs when he was a child, the court held that the trial judge had not erred because "it was not clear where defense counsel was going with the testimony." Id. at 124. The court further stated that the anecdote was irrelevant to McGehee's punishment, "in light of the fact that the testimony merely described the family's attitude about the death of their dogs, an event that occurred when [McGehee] was just a baby." Id. Moreover, the court concluded that the trial judge had not erred in sustaining the state's objection to Christensen's testimony about the abuse McGehee's sister suffered because it was "not clear from [McGehee's] brief how this evidence would [have been] relevant to the issue of his punishment." Id. Alternatively, the court held that the argument was moot, because "[a]lthough the State objected to the testimony and the trial court sustained the *1192 objection, the jury was never admonished not to consider the evidence." Id. at 125. Finally, pursuant to Rule 4-3(h) of the Arkansas Supreme Court Rules, the court reviewed the record for adverse rulings to which McGehee had objected at trial but not raised on appeal. Finding no reversible error, the court affirmed McGehee's conviction and sentence. Id.
McGehee filed a petition for state post-conviction relief, arguing that his trial counsel was ineffective for, among other things, failing to challenge the constitutionality of his sentence on the ground that his co-defendants received lesser sentences and for abandoning any challenge to the victim impact testimony. The trial court denied the petition, and the Arkansas Supreme Court subsequently affirmed, holding that proportionality review of death sentences was not required and that the admission of victim impact testimony was not unconstitutional. McGehee v. State, 348 Ark. 395, 72 S.W.3d 867, 878-79 (2002) (McGehee II).

D. Federal Habeas Proceedings
McGehee filed a petition for a writ of habeas corpus in the United States District Court for the Eastern District of Arkansas, challenging only his sentence of death. McGehee argued that his constitutional rights were violated by (1) the trial court's refusal to grant a continuance or provide funds for additional psychiatric evaluation; (2) the trial court's exclusion of relevant mitigating evidence; (3) the disproportionate penalty that he received compared to his co-defendants; and (4) the use of victim impact testimony during his sentencing. McGehee also asserted that his sentence should be vacated because three of the state's witnesses had recanted their testimony in ways that mitigated McGehee's role in the offense.
In conjunction with his claim that he was improperly denied psychiatric assistance, McGehee's petition relied upon new evidence, never presented in state court, about the psychological trauma that he allegedly endured during childhood. The evidence included declarations from some of McGehee's mitigation witnesses. Linda Christensen's declaration stated that when McGehee was a toddler his father cut the throats of the two family dogs. The declaration also described the following incident:
[McGehee's stepfather] Wayne had gotten mad. He was mad at Jason and Kimber and I don't know if he took it out on [Jason's dog] Dusty. Dusty and their other dog, King, were fighting over food that night when they got home. They were all down in the basement. Wayne got mad. He got up and kicked Dusty in the side with his cowboy boots as hard as he could. Dusty started bleeding out his rectum. He lay and suffered and the kids had to watch him die slowly. He was bleeding internally. By about 5:00 a.m. the next morning, Dusty was dead. I really believe part of Jason died with him. That was the turning point. Jason was never the same after that.
McGehee did not refer to this account in his argument concerning the trial court's exclusion of mitigating evidence, contending instead that the Arkansas Supreme Court had acted unreasonably in affirming the trial court on the record that was before it at the time.
In its response to the petition, the state argued that McGehee's psychiatric assistance and witness recantation claims were defaulted and that the Arkansas Supreme Court's affirmance of the trial court's rulings on mitigation evidence "was not an unreasonable application of the law to the facts of this case." J.A. 256. The state argued that an evidentiary hearing was unnecessary, stating that "[t]he AEDPA *1193 also significantly restricts the instances in which a federal habeas petitioner may obtain an evidentiary hearing and precludes such a petitioner from presenting any evidence, testimonial, or otherwise, until he has made the showing required by 28 U.S.C. § 2254." Id. at 262, 992 S.W.2d 110.
The district court granted the writ on the basis of the trial court's exclusion of mitigating evidence and rejected the remainder of McGehee's claims. In analyzing the mitigation claim, the court relied heavily on the new evidence, stating that "McGehee's petition provides a declaration from Linda Christensen and the testimony she would have provided regarding the family's treatment of animals if she were permitted to continue with her testimony at the sentencing." The court stated that it was "particularly concerned by two different stories related to the treatment of animals by McGehee's family while in the presence of McGehee as a baby and as an adolescent." The court, however, did not consider whether McGehee had overcome § 2254's restrictions on the consideration of evidence not presented in state court.
The court set aside McGehee's death sentence and ordered the state to grant a new penalty-phase trial or to change McGehee's sentence to life in prison without parole. As recounted above, the state appeals the court's ruling on the mitigation claim, and McGehee cross-appeals the denial of his other claims.

II. Analysis
We review the district court's conclusions of law de novo and its factual findings for clear error. Hunt v. Houston, 563 F.3d 695, 702 (8th Cir.2009). Under the Antiterrorism and Effective Death Penalty Act (AEDPA), if the issues raised in a petition for habeas corpus were adjudicated on the merits in state court, the petition must be denied unless the relevant state court decision was either "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), or "based on an unreasonable determination of the facts in light of the evidence presented in the State court proceeding." Id. § 2254(d)(2). "An incorrect decision is not necessarily unreasonable, and we may not grant a writ of habeas corpus unless the state court decision is both wrong and unreasonable." Palmer v. Clarke, 408 F.3d 423, 429 (8th Cir.2005).

A. Exclusion of Mitigating Evidence
We begin by addressing the state's argument that the district court erred in granting habeas relief based on the exclusion of mitigation testimony. McGehee argues that the Arkansas Supreme Court wrongfully affirmed the trial judge's decision to sustain objections to Christensen's testimony about the mistreatment of family dogs and the abuse of McGehee's sister.[1]

1. The District Court's Consideration of New Evidence
As a threshold issue, the parties disagree about the evidence that we may consider in evaluating this claim. The state contends that the district court erred in considering Christensen's declaration about what her testimony would have been if the trial judge had not sustained the state's objection. McGehee responds that the state waived any objection to the new evidence because it did not specifically raise the issue until it filed its reply brief in the present appeal. He asserts that the *1194 state "never once contended below that the district court was required to disregard the exhibits attached to [his] Petition."
We disagree with McGehee's characterization of the state's arguments and conclude that the district court erred in considering evidence never presented in state court. The new evidence in McGehee's district court petition was not presented in conjunction with his argument that mitigation testimony was improperly excluded; instead, he relied on the new evidence to support his claim that he was improperly denied psychiatric assistance. He first incorporated the new evidence as a part of his mitigation claim in his brief filed in opposition to the state's appeal from the grant of habeas relief. The state's response to McGehee's petition did not address the merits of the psychiatric assistance claim because it was the state's position that the claim was procedurally defaulted. But the state did assert that the AEDPA precludes a petitioner "from presenting any evidence, testimonial, or otherwise, until he has made the showing required by 28 U.S.C. § 2254." J.A. 262.
Moreover, nothing in the state's filings in the district court or before us could be construed as a concession to the consideration of new evidence. The state did not cite to the additional evidence, treating it as irrelevant. In the facts section of its opening brief, the state discussed only the evidence that was before the Arkansas Supreme Court, and most of its argument was devoted to establishing that "the Arkansas Supreme Court's affirmance of the trial court's rulings was not an unreasonable application of the law to the facts of this case." The state also made numerous references to § 2254(d), which requires federal courts to assess state court decisions "in light of the record the [state] court had before it." Holland v. Jackson, 542 U.S. 649, 652, 124 S.Ct. 2736, 159 L.Ed.2d 683 (2004).
McGehee's contention that the state waived its objection to the new evidence is therefore untenable. See Williams v. Norris, 576 F.3d 850, 860 (8th Cir.2009) (holding that the state did not waive its objection to an evidentiary hearing where its motion included a general statement that "incorporated the fundamental purpose behind the restrictions on evidentiary hearings in § 2254(e)(2)"); cf. Miller-El v. Dretke, 545 U.S. 231, 257 n. 15, 125 S.Ct. 2317, 162 L.Ed.2d 196 (2005) (discussing, without deciding, whether the state may have waived its objection to consideration of new evidence where it (1) proposed that the court consider the material, (2) failed to reference the AEDPA provision limiting consideration of new evidence, and (3) relied on the evidence to support its argument); Richey v. Bradshaw, 498 F.3d 344, 351-52 (6th Cir.2007) (holding that the state waived its objection to the court's reliance on new evidence where (1) the state urged the district court to consider the evidence, (2) the district court found the petitioner had been diligent in attempting to develop the evidence in state court, and (3) the state did not challenge the district court's ruling on appeal).
Under § 2254(e)(2), a habeas petitioner is generally barred from receiving an evidentiary hearing unless he has been diligent in attempting to develop the factual basis of his claim in state court. Michael Williams v. Taylor, 529 U.S. 420, 440, 120 S.Ct. 1479, 146 L.Ed.2d 435 (2000). "Those same restrictions apply a fortiori when a prisoner seeks relief based on new evidence without an evidentiary hearing." Holland, 542 U.S. at 653, 124 S.Ct. 2736. McGehee did not argue in the district court, and he does not argue here, that the new evidence in Christensen's declaration satisfies the diligence requirements or any exception to § 2254(e)(2). Our review of the record satisfies us that *1195 there was "no state court ruling or other state-created impediment" that prevented McGehee from developing the facts surrounding Christensen's testimony. Williams, 576 F.3d at 862. McGehee's counsel had the opportunity to make a proffer of evidence in the trial court, and the trial judge even suggested that the witness could make the proffer herself. McGehee has long been aware of the significance of Christensen's testimony because it formed the basis of one of his arguments on direct appeal. Nevertheless, McGehee did not develop the additional facts that he sought to introduce in the district court. The state court record makes it clear that McGehee failed as a matter of law to meet the mandatory restrictions on the admission of new evidence in a habeas proceeding. Accordingly, we focus our analysis on the evidence that was available to the Arkansas Supreme Court. See Id. at 862-63.

2. The Arkansas Supreme Court's Decision
In Lockett v. Ohio, 438 U.S. 586, 98 S.Ct. 2954, 57 L.Ed.2d 973 (1978), the Supreme Court held that the Eighth and Fourteenth Amendments require that the sentencer in a capital case "not be precluded from considering, as a mitigating factor, any aspect of a defendant's character or record and any of the circumstances of the offense that the defendant proffers as a basis for a sentence less than death." Id. at 604, 98 S.Ct. 2954. The Court later explained "the corollary rule that the sentencer may not refuse to consider or be precluded from considering `any relevant mitigating evidence.'" Skipper v. South Carolina, 476 U.S. 1, 4, 106 S.Ct. 1669, 90 L.Ed.2d 1 (1986) (quoting Eddings v. Oklahoma, 455 U.S. 104, 114, 102 S.Ct. 869, 71 L.Ed.2d 1 (1982)). The Court has used broad language to describe the relevance standard, observing that the meaning of relevance in the mitigation context is not unlike the meaning of relevance in other contexts; it is "evidence which tends logically to prove or disprove some fact or circumstance which a fact-finder could reasonably deem to have mitigating value." Tennard v. Dretke, 542 U.S. 274, 284, 124 S.Ct. 2562, 159 L.Ed.2d 384 (2004) (quoting McKoy v. North Carolina, 494 U.S. 433, 440, 110 S.Ct. 1227, 108 L.Ed.2d 369 (1990)). The precise application of that broad language, however, is not always clear, and we have acknowledged that there is "little guidance on what constitutes relevance for Lockett purposes." Sweet v. Delo, 125 F.3d 1144, 1158 (8th Cir.1997).
The Lockett line of cases has focused on the categorical exclusion of certain types of mitigating evidence. See Sweet, 125 F.3d at 1158 (collecting cases). This case, however, involves a somewhat different issue: namely, the extent to which a trial judge may, when there are no categorical limitations on mitigation evidence, exclude testimony because of its apparent lack of probative value. The Supreme Court has addressed this issue only indirectly. In Skipper, the Court held that evidence of a defendant's positive adjustment to pre-trial incarceration could not be categorically excluded from the sentencing decision, but it also stated that not "all facets of the defendant's ability to adjust to prison life must be treated as relevant and potentially mitigating." 476 U.S. at 7 n. 2, 106 S.Ct. 1669. As one example, the Court suggested that the frequency of the defendant's showers would be irrelevant. Id. Similarly, in Tennard the Court stated that it had "never denied that gravity has a place in the relevance analysis, insofar as evidence of a trivial feature of the defendant's character or the circumstances of the crime is unlikely to have any tendency to mitigate the defendant's culpability." 542 U.S. at 286, 124 S.Ct. 2562.
*1196 Evaluated against this precedent, the Arkansas Supreme Court's rejection of McGehee's mitigation arguments was not unreasonable or contrary to clearly established law. McGehee introduced five mitigation witnesses to establish that he had a dysfunctional family, very poor relationships with his father and stepfather, and a mother who behaved erratically and struggled to manage her children. Much of the testimony was discursive, anecdotal, and open-ended. At the time the prosecutor made his first objection to Christensen's testimony, Christensen had just recounted a lengthy anecdote of arguably no mitigating value. Christensen had testified that as an adolescent, McGehee refused to keep his mother's curfew and that a battle of wills ensued. McGehee's mother locked the doors after McGehee failed to come home one evening. Rather than asking his mother for permission to enter the house, McGehee apparently chose to sleep outside with his dog, subsisting on bottled tomatoes and sandwiches delivered by his aunt.
McGehee's counsel then asked Christensen to discuss what happened to McGehee's dogs "when he was a small child," and Christensen answered, "[w]hen he was a baby, he had a Doberman Pincher." At that point, the prosecutor objected on the ground that the testimony was irrelevant. McGehee's counsel did not explain the substance of the testimony or how the jury could find a story about McGehee's dogs relevant to his sentence. In upholding the trial judge's decision, the Arkansas Supreme Court accurately observed that "it was not clear where defense counsel was going with the testimony." McGehee I, 992 S.W.2d at 124.
Later, after the jury had retired to deliberate, McGehee's counsel proffered additional information about Christensen's testimony. He stated that he wanted to show that the family was violent because the dogs' throats had been slit and McGehee's parents had told him it was because he wanted a new puppy. McGehee's counsel did not request that the jury be returned to the courtroom to hear that additional evidence, and McGehee has cited no authority that should have compelled the trial judge to take that step sua sponte.
Moreover, even after the proffer, the relevance of that testimonyif understood as a question about the gravity of the evidence and its likelihood of influencing the sentencing decisionis debatable. The death of a pet can be a traumatic experience for a child, and the story of parental cruelty may have contributed to the picture of family dysfunction. But to the extent that the testimony was offered to show a pattern of physical violence, it was contradicted by other evidence. McGehee's grandmother testified that McGehee was not physically abused or neglected as a child. Christensen never stated that McGehee suffered physical abuse, and McGehee's counsel did not allege any such abuse as a mitigating circumstance. Accordingly, the trial judge's statement that the incident was an "isolated act of cruelty to animals that happened years and years ago" appears to have been a fair characterization. We cannot say that the Arkansas Supreme Court's decision affirming the trial judge's ruling was unreasonable.
Nor was it unreasonable for the Arkansas Supreme Court to conclude that McGehee was not prejudiced by the trial judge's decision to sustain an objection to Christensen's testimony about the abuse of McGehee's sister, Kimber. Christensen testified that McGehee's stepfather was not allowed to discipline Kimber and that he had once beat her to the point that she had bruises on the back of her legs, prompting a visit from Family Services. The prosecutor objected on the basis that the witness was "talking about somebody *1197 who isn't even the defendant, [and straying] way far afield from directional testimony." The trial judge sustained the objection, but did not admonish the jury not to consider that evidence.
McGehee argues that the jury was unable to consider the evidence because it could have interpreted the judge's decision to sustain the objection as an admonition to disregard Christensen's testimony. He contends that this is so because the jury was earlier instructed to follow all of the judge's evidentiary rulings. The evidentiary instruction to which McGehee points, however, was given during the guilt phase of McGehee's trial. The jury did not receive a similar instruction before its sentencing deliberation. To the contrary, the jury was instructed that it could consider anything, in its discretion, that it found to be a mitigating circumstance. During his closing argument in the penalty phase, McGehee's counsel highlighted the fact that the jury could consider mitigating circumstances ignored by the lawyers or the court. McGehee's reliance on Penry v. Lynaugh, 492 U.S. 302, 109 S.Ct. 2934, 106 L.Ed.2d 256 (1989), in which the Court granted habeas relief because of the absence of such juror discretion, is therefore misplaced.
Even if there were any error in the exclusion of Christensen's testimony, it was harmless.[2]See Sweet, 125 F.3d at 1158-59 (concluding that Lockett errors may be held harmless). Although McGehee's childhood was apparently difficult, the excluded evidence does not begin to approach the significance of the evidence in other notable cases in which the absence of mitigation testimony has been held prejudicial. See, e.g., Rompilla v. Beard, 545 U.S. 374, 391-92, 125 S.Ct. 2456, 162 L.Ed.2d 360 (2005) (petitioner's parents were violent alcoholics, and he was beaten regularly, locked inside an excrement-filled dog pen, and not allowed to visit other children); Wiggins v. Smith, 539 U.S. 510, 517, 123 S.Ct. 2527, 156 L.Ed.2d 471 (2003) (petitioner was left home alone for days, forcing him to beg for food and eat paint chips and garbage, and he was physically and sexually abused by his mother and foster parents); Terry Williams v. Taylor, 529 U.S. 362, 395-96, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000) (petitioner had a "nightmarish childhood," during which he was forced to live in unimaginable squalor and severely and repeatedly beaten by his father).
As noted above, McGehee had the opportunity to provide evidence of the dysfunctional family and poor parenting that influenced his life choices. The mitigation testimony was somewhat conflicting, however, in that it showed that McGehee was not physically abused and that he had at least some family members and friends who cared for him during his childhood and early teenage years. Additional testimony about the death of McGehee's dogs would not have significantly altered the jury's picture of McGehee's upbringing, and it would not have been likely to influence the sentencing decision. More precisely, we conclude that the Supreme Court's recent observation in a death penalty case is particularly apt here: "Additional evidence on [this point] would have offered an insignificant benefit, if any at all." Wong v. Belmontes, ___ U.S. ___, 130 S.Ct. 383, 388, ___ L.Ed.2d ___ (2009) (per curiam); cf. Grayson v. Thompson, 257 F.3d 1194, 1227-28 (11th Cir.2001) (holding that petitioner was not prejudiced *1198 by the absence of mitigation evidence, in part, because "[a]lthough the graphic picture of [petitioner's] home life ... was not presented at trial, the judge did not wholly disregard [petitioner's] unfortunate background in sentencing him to death").
The absence of any prejudice is particularly apparent given the horrific nature of the crime. See Sweet, 125 F.3d at 1158 (considering the nature of the crime as one element in determining harmlessness). The evidence at trial showed that McGehee was the ringleader of a torture murder and that his weaker, younger victim was brutalized because he told the truth when confronted by the police. McGehee inflicted most of the blows during the several hours in which Melbourne was tortured, and he exhibited no hesitation or remorse, apparently laughing just after he had left Melbourne's naked body lying in the woods. In the context of ineffective assistance of counsel claims, at least one of our sister circuits has stated that in death penalty cases involving a carefully planned murder, torture, rape, or kidnapping, "the aggravating circumstances of the crime outweigh any prejudice caused when a lawyer fails to present mitigating evidence." Payne v. Allen, 539 F.3d 1297, 1318 (11th Cir.2008) (quoting Dobbs v. Turpin, 142 F.3d 1383, 1390 (11th Cir.1998)). McGehee's crime involved both torture and kidnapping, compounded in its cruelty by McGehee's mocking, taunting statement, "how does it feel to know you are going to die?" In light of the entire record, therefore, we cannot say that the excluded evidence had a substantial and injurious effect on the jury's sentencing decision. See Fry v. Pliler, 551 U.S. 112, 121-22, 127 S.Ct. 2321, 168 L.Ed.2d 16 (2007) (standard for reviewing harmlessness in § 2254 proceedings). Accordingly, the district court erred in granting McGehee's habeas petition on this claim.

B. Denial of a Continuance and Funds for Psychiatric Assistance
We turn next to McGehee's contention that the district court erred in denying him habeas relief on his psychiatric assistance claim.[3] As recounted above, McGehee requested a continuance and psychiatric assistance to determine whether he suffered detrimental effects from his father's exposure to Agent Orange in Vietnam. The trial judge denied the request, noting that McGehee had already been granted a psychiatric evaluation and that the significance of his father's chemical exposure was doubtful.
Under Ake v. Oklahoma, 470 U.S. 68, 105 S.Ct. 1087, 84 L.Ed.2d 53 (1985), a defendant's threshold showing that his mental state at the time of the offense is likely to be a significant factor at trial requires the state to provide access to a psychiatrist's assistance if the defendant cannot otherwise afford to pay for his own expert. Id. at 74, 105 S.Ct. 1087. The entitlement to an Ake expert may extend to the penalty phase of a trial, and to the extent that the district court's opinion suggested otherwise, it was incorrect. See id. at 83, 105 S.Ct. 1087; Starr, 23 F.3d at 1288 ("Ake also explains that, when appropriate, the right to expert assistance extends *1199 to the sentencing phase of capital proceedings.").
McGehee was not entitled to an Ake expert, however, because he did not satisfy the initial showing that his mental state was likely to be a significant factor at trial. Ake and the other cases on which McGehee relies all involved elements not present herea readily observable mental impairment or the prosecution's use of a psychiatric expert to establish guilt or aggravating factors at sentencing. See Ake, 470 U.S. at 71-73, 105 S.Ct. 1087; see also Tuggle v. Netherland, 516 U.S. 10, 11, 116 S.Ct. 283, 133 L.Ed.2d 251 (1995) (per curiam) (government "presented unrebutted psychiatric testimony" concerning the defendant's future dangerousness); Boliek v. Bowersox, 96 F.3d 1070, 1074 (8th Cir. 1996) (petitioner was "an indigent capital defendant with a long history of mental-health problems"); Starr, 23 F.3d at 1288-89 (petitioner had been diagnosed as mildly to moderately retarded); cf. Branscomb v. Norris, 47 F.3d 258, 262 (8th Cir.1995) (rejecting an Ake claim because the petitioner failed to produce evidence of mental incapacity).
The language in McGehee's motion for a continuance belies the contention that he satisfied Ake's requisite showing. McGehee asserted that he needed expert assistance to explore "the potential inheritance" of chemical defects attributable to Agent Orange. Although the state was willing to stipulate that McGehee's father had been exposed to Agent Orange, McGehee offered no evidence that any such exposure had affected his own mental state, and his counsel could only speculate about what tests needed to be performed and what they might show. Moreover, the state did not rely on any psychiatric experts in the guilt or penalty phases of McGehee's trial. Ake requires more than the mere possibility that an expert might be of some assistance to a defendant's case. Little v. Armontrout, 835 F.2d 1240, 1244 (8th Cir. 1987) (en banc). "Rather, the defendant must show a reasonable probability that an expert would aid in his defense, and that denial of expert assistance would result in an unfair trial." Id. McGehee did not make this showing, and the district court thus properly denied relief on this claim.

C. Proportionality Review and Victim Impact Testimony
McGehee's next two claims, that his sentence was disproportionate to that of his co-defendants and that the state relied on unconstitutional victim impact testimony, are foreclosed by our precedent and the AEDPA. McGehee argues that his death sentence violated the Eighth Amendment because two of his co-defendants, who he contends were equally culpable, received life sentences. As McGehee concedes, however, in Pulley v. Harris, the Supreme Court held that the Constitution does not require courts to consider whether a punishment is "disproportionate to the punishment imposed on others convicted of the same crime." 465 U.S. 37, 43, 104 S.Ct. 871, 79 L.Ed.2d 29 (1984); see also Kane v. Garcia Espitia, 546 U.S. 9, 10-11, 126 S.Ct. 407, 163 L.Ed.2d 10 (2005) (per curiam) (instructing that a right cannot be clearly established for purposes of the AEDPA when the right at issue has not been articulated by the Supreme Court); Middleton v. Roper, 498 F.3d 812, 821 (8th Cir.2007). McGehee also contends that the victim impact testimony at his sentencing violated the constitutional prohibition on arbitrariness in death penalty proceedings because the jury was not provided a framework for evaluating the evidence in its sentencing decision. We rejected an identical challenge to the Arkansas capital sentencing scheme in Johnson v. Norris, 537 F.3d 840, 850-52 (8th Cir.2008), cert. denied, ___ U.S. ___, 129 S.Ct. 1334, 173 *1200 L.Ed.2d 605 (2009), and absent en banc review, we are not at liberty to revisit that decision.

D. Denial of an Evidentiary Hearing
Finally, McGehee argues that the district court erred in denying his motion for an evidentiary hearing. He contends that he is entitled to a hearing because declarations from three co-defendants who testified at his trialCampbell, Diemert, and Eppsestablish that they committed perjury and that the state knowingly used fabricated testimony. McGehee further argues that the amended testimony would make him ineligible for the death penalty because he did not personally inflict the fatal wounds and did not act with reckless indifference to human life. See Tison v. Arizona, 481 U.S. 137, 158, 107 S.Ct. 1676, 95 L.Ed.2d 127 (1987).
Where § 2254(e)(2) does not otherwise bar an evidentiary hearing, "the decision to grant such a hearing rests in the discretion of the district court." Schriro v. Landrigan, 550 U.S. 465, 468, 127 S.Ct. 1933, 167 L.Ed.2d 836 (2007). In making its determination, the district court must consider whether a hearing "could enable an applicant to prove the petition's factual allegations, which, if true, would entitle the applicant to federal habeas relief." Id. at 474, 127 S.Ct. 1933.
The district court properly concluded that, even if accepted as true, the statements of McGehee's co-defendants would not entitle him to habeas relief. As the district court recognized, the statements "do not do much more than recount the events that were testified to at the trial." In their declarations, Campbell, Diemert, and Epps stated that when they testified, they were immature, afraid of punishment, and eager to curry favor with the prosecutor. They also claimed that they exaggerated McGehee's role in the attack. Campbell, for example, explained that when she testified that McGehee delivered most of the blows, she was referring only to "the specific time we were discussing," and "never meant to imply that Jason did most of the hitting overall." J.A. 206. Similarly, Epps stated that McGehee did not take part in strangling Melbourne and did not laugh as he walked out of the woods. Individually and collectively, the declarations indicate that McGehee was more of an equal participant in the murder, rather than the ringleader.
The declarations, however, do not show that the state knowingly used perjured testimony, and they fail to establish that McGehee did not act with reckless indifference to human life. There is no dispute that McGehee was a significant participant in two merciless beatings and was one of the three individuals who took Melbourne into the woods to die. Accordingly, the district court did not abuse its discretion in denying McGehee an evidentiary hearing on this claim. See Tison, 481 U.S. at 158, 107 S.Ct. 1676 (holding that major participation in a felony, combined with reckless indifference to human life, establishes the requisite culpability for capital murder).

III. Conclusion
The judgment is reversed, and the case is remanded with directions to dismiss the petition.
NOTES
[1]  McGehee also argues that he should have been permitted to present the sentencing jury with evidence of the life sentences of his co-defendants. As he concedes, however, we rejected an identical argument in Simpson v. Norris, 490 F.3d 1029, 1033 (8th Cir.2007).
[2]  Although McGehee contends that the state waived its harmless error argument by failing to raise it in the district court, we have the discretion to overlook a waiver and will do so when, as here, the record is straightforward and the finding of harmlessness is beyond reasonable dispute. See Lufkins v. Leapley, 965 F.2d 1477, 1482 (8th Cir.1992).
[3]  The state originally maintained that this claim was procedurally defaulted because McGehee failed to raise it in state court. In Starr v. Lockhart, 23 F.3d 1280, 1287 (8th Cir. 1994), we held that the Arkansas Supreme Court's automatic review under Rule 4-3(h) preserves a petitioner's Ake claim, avoiding procedural default even when the argument was not raised in state proceedings. Our recent decision in Williams, however, cast doubt on Starr's continued application post-AEDPA. Williams, 576 F.3d at 865. Because we conclude that McGehee's Ake argument fails on the merits, we need not decide whether the Starr analysis applies in this case. See 28 U.S.C. § 2254(b)(2).
