BENAVIDES, Circuit Judge:

Petitioner Jeffrey Eugene Tucker (Tucker), convicted of capital murder in Texas and sentenced to death, appeals the denial of federal habeas relief. He raises several issues, including ineffective assistance of counsel, presentation of false testimony by the State, and evidentiary error. We affirm.

I. Factual and Procedural History

On July 10, 1988, Tucker noticed a newspaper advertisement listing a late model pickup truck and travel trailer for sale. Wilton Humphreys (Humphreys) and his wife had placed the advertisement. Tucker called and made inquiries to Mrs. Humphreys with respect to the truck and trailer. The next morning, Tucker stole two checks from his brother and used the proceeds to purchase a .38 caliber gun and ammunition from a pawn shop.

Tucker placed another telephone call to the Humphreys and arranged to meet them at their home in Granbury, Texas. Tucker identified himself to the Humphreys as J.D. Travis. It is undisputed that Tucker drove to the Humphreys' home with the intent to rob them of their truck. Sometime during his drive to their home, he stopped and fired the gun. After taking a test drive with Humphreys as a passenger, Tucker drove to town, ostensibly to finalize the sale at a local bank.

According to Tucker's confession, upon arriving at the bank parking lot, he retrieved his firearm and aimed it at Humphreys. Tucker informed Humphreys that he was "taking the truck and trailer and . . . would let him out eventually down the road when [he] felt it was a reasonable place to let him out. . . ." After driving approximately twenty miles, Tucker pulled over on a country road, exited the vehicle, and instructed Humphreys to do the same. Tucker then observed Humphreys re-enter the vehicle through the passenger side door. While Humphreys was attempting to shut the driver's side door, Tucker wrested it open and shot Humphreys in the face and chest. After shooting Humphreys, Tucker pulled him from the cab of the truck and drove away, running over Humphreys' legs.

Three days after killing Humphreys, Tucker was apprehended in the stolen truck after a high speed chase in New Mexico. Tucker confessed both orally and in writing to shooting Humphreys. In the confessions, he asserted that although he had intended to steal the truck, he had not intended to shoot Humphreys.

The physical evidence tends to corroborate much of Tucker's confession. A portion of the inside door handle from the driver's side of the truck was recovered at the crime scene. The medical examiner testified that Humphreys had been shot three times (once in the face and twice in the chest area, the latter two were fatal gunshot wounds). Humphreys' legs were broken, and there were tire tracks on his trousers. However, the medical examiner testified that Humphreys had received a blunt force trauma to the back of his head before the fatal gunshot wounds. Tucker's story does not account for this wound.

In October of 1989, Tucker was convicted of capital murder in Parker County, Texas. The jury answered the two special issues affirmatively, and pursuant to Texas law the trial court assessed punishment of death by lethal injection. The Court of Criminal appeals affirmed his conviction and sentence in an unpublished opinion on June 9, 1993. Tucker filed an application for state habeas relief in April of 1997, and the state trial court issued findings of fact and conclusions of law recommending that relief be denied. The Texas Court of Criminal Appeals denied relief based on those findings and conclusions.

On November 3, 1998, Tucker filed a petition for habeas corpus in federal district court, which commenced the instant proceedings. He filed an amended petition on January 4, 1999. In September, the district court denied his petition in an unpublished opinion and granted his motion for a certificate of appealability. Tucker now appeals.

II. Analysis

A. WHETHER AEDPA VIOLATES ARTICLE III

Tucker argues that the Antiterrorism and Effective Death Penalty Act (AEDPA) violates Article III. More specifically, he argues that, as interpreted by this Court in Drinkard v. Johnson, 97 F.3d 751, 769 (5th Cir. 1996), the AEDPA standards violate Article III by forcing federal judges to defer to a state court's view with respect to federal constitutional rights. In Drinkard, this Court held "that an application of law to facts is unreasonable only when it can be said that reasonable jurists considering the question would be of one view that the state court ruling was incorrect." 97 F.3d at 769. Tucker complains of this formulation of the "unreasonable application" rule.

Since the filing of Tucker's opening brief, the Supreme Court has addressed his concerns. See Williams v. Taylor, 529 U.S. 362, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000). In Williams, the Supreme Court explained that when making the "unreasonable application" determination, federal courts should inquire whether the state court's application of clearly established federal law was objectively unreasonable. 120 S.Ct. at 1521. The Court specifically noted that, in Drinkard, we apparently had applied the reasonable jurist standard in a subjective manner. Id. at 1522.

The Supreme Court thus has clarified how the challenged language of the AEDPA should be interpreted. Of course, as instructed by the Supreme Court, when making the "unreasonable application" inquiry under the AEDPA, we will determine whether the state court's application of clearly established federal law was objectively unreasonable. We now apply the AEDPA inquiry to each of his claims.

B. INEFFECTIVE ASSISTANCE OF COUNSEL AT SENTENCING

Tucker raises a broad claim of ineffective assistance during the punishment phase. He argues that the district court erred in concluding that he had not shown prejudice as a result of counsel's deficient performance in failing to investigate or present vital mitigating evidence with respect to the abuse he suffered as a child. In Williams v. Taylor, the Supreme Court recently reaffirmed the familiar two-prong test:

First, the defendant must show that counsel's performance was deficient. This requires showing that counsel made errors so serious that counsel was not functioning as the "counsel" guaranteed the defendant by the Sixth Amendment. Second, the defendant must show that the deficient performance prejudiced the defense. This requires showing that counsel's errors were so serious as to deprive the defendant of a fair trial, a trial whose result is reliable.

120 S.Ct. at 1511 (quoting Strickland v. Washington, 466 U.S. 668, 687, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984)). To demonstrate that counsel was ineffective, a petitioner must establish that counsel's representation fell below an objective standard of reasonableness. See id. To show prejudice, he must show that there is a reasonable probability that, but for counsel's error, the result of the proceeding would have been different. See id. at 1511-12. We will assume that counsel's performance with respect to this claim was deficient and determine whether Tucker has shown prejudice as a result.

Tucker asserts that had counsel conducted an adequate investigation into his personal background they would have discovered that he suffers from organic brain impairment, was severely sexually, physically, and emotionally abused as a child, and ultimately became addicted to cocaine.

The State counters that the evidence Tucker asserts should have been introduced is both mitigating and aggravating and therefore does not establish prejudice. In Williams v. Taylor, however, the Supreme Court recognized that not all of the additional evidence need be favorable to the petitioner. 120 S.Ct. at 1514. The Court explained that while the newly proffered evidence "may not have overcome a finding of future dangerousness, the graphic description of Williams' childhood, filled with abuse and privation, or the reality that he was borderline mentally retarded, might well have influenced the jury's appraisal of his moral culpability." 120 S.Ct. at 1515 (internal quotation marks and citation omitted). Further, "[m]itigating evidence unrelated to dangerousness may alter the jury's selection of penalty, even if it does not undermine or rebut the prosecution's death-eligibility case." Id. at 1516. Had counsel presented and explained the newly proffered mitigating evidence to Williams' jury, there was a reasonable probability that the result of the sentencing hearing would have been different. See id. Thus, the Supreme Court concluded that the state court's rejection of Williams' claim was contrary to, or involved an unreasonable application of, clearly established federal law. See id.

In the case at bar, the district court found that counsel presented evidence of Tucker's "neglectful, absent father and the dysfunctional home life he had with his mother, his isolation and low self-esteem; his substance abuse problems; his stays in residential treatment programs at both Buckner and the Wichita Falls state hospital; and his relatively limited exposure to male role models." The court denied relief, concluding that "[t]he additional evidence Tucker now asserts should have been presented would have had little mitigating effect, whether considered alone or in conjunction with the evidence already in the jury's possession, and fails to meet the second prong of Strickland." Therefore, the court concluded that Tucker had "not demonstrated that the state court's rejection of his claim of ineffective assistance of counsel was unreasonable."

After reviewing the record, we are convinced that Williams v. Taylor is distinguishable from Tucker's case in that there apparently was no evidence offered by counsel with respect to the mistreatment, abuse, and neglect of Williams' "nightmarish" childhood. In contrast, Tucker's trial counsel did elicit mitigating evidence from several family members with respect to his upbringing.

Essentially, Tucker's argument is that counsel should have put on a stronger case in mitigation of the death penalty. We do not profess to be unmoved by the dreadful circumstances of Tucker's childhood, and we understand the relevance of such evidence to the jury's determination of Tucker's moral culpability at the time he committed the murder. Nevertheless, we are persuaded that, although counsel could have presented additional mitigating evidence, the evidence before the jury illustrated the bleakness of Tucker's home life. Indeed, a reading of the cold trial record demonstrates Tucker was raised in an environment of rejection and neglect.

Notwithstanding Tucker's assertions to the contrary, defense counsel did present a sympathetic picture of Tucker's life to the jury. As the district court stated, the evidence revealed to the jury that Tucker was emotionally abused and neglected as a child and that he had a problem with illegal drugs.

At the punishment phase, Tucker's aunt testified that her sister, Cecelia, did not want to give birth to Tucker and that Tucker's maternal grandfather "forced" Tucker's father to marry Cecelia, who was only sixteen years old at the time. His aunt further testified that Tucker's mother admitted that "she didn't love him, never wanted him."

Tucker's parents divorced and remarried and then divorced again approximately a year after Tucker's brother was born. The testimony indicated that Tucker's home environment was very dysfunctional. His mother had problems with respect to her sexual orientation, and relatives testified that she would dress Tucker in girl's clothing.

Tucker's relatives described him as insecure, "love-starved," and "very sick" with "deep-seated problems." Several witnesses related that Tucker's father was "never around" during his childhood and was "not supportive."

The jury was made aware that his mother sent him to a "state home" in Wichita Falls, and on another occasion, Tucker was admitted to the residential program at Buckner's Children's Home. Most disturbing, Tucker, as an adolescent, contacted the state authorities and successfully requested that he be removed (at least temporarily) from the custody of his mother.

Tucker asserts the jury should have been informed that at one point during his childhood his behavior had improved due to certain medication that had been prescribed. Despite this improvement, his mother failed to refill the prescription. Such evidence, he argues, would have demonstrated that he was "treatable" but his family did not care enough to follow through with the treatment.

Notwithstanding Tucker's assertion otherwise, his mother did testify that at one time she perceived a particular treatment was helping Tucker, but the treatment was discontinued because she could not afford it. As such, the jury did have before it some indication that Tucker was "treatable."

Although Tucker now presents additional mitigating evidence, including evidence of physical and sexual abuse, we believe the evidence at trial — especially the testimony that Tucker was able to have himself removed from the custody of his mother — spoke volumes to the jury with respect to how intolerable his home environment was both subjectively (to Tucker) and objectively (to the authorities). Further, some of the newly proffered evidence arguably would have been aggravating as opposed to mitigating. For instance, a psychologist who examined Tucker wrote that there was a "psychological time bomb" in Tucker that "detonated" at the time of the murder.

We are mindful that we must give proper consideration to the "quality and volume of the additional mitigating evidence." Neal v. Puckett, 239 F.3d 683, 694 (5th Cir. 2001). Further, as we previously have recognized, this inquiry is very difficult. Id. Nevertheless, we remain unconvinced that the state court's conclusion (Tucker was unable to show that, if the newly proffered evidence had been presented and explained by counsel, there is a reasonable probability that the result of the sentencing phase would have been different) was erroneous.

Even assuming arguendo that the state court's conclusion was erroneous, applying the previously set forth deferential AEDPA standard, we believe we are constrained to hold that the state court's conclusion was not contrary to, or an unreasonable application of, established federal law. See id. at 694-97 (holding that although the state court's decision was erroneous, because it did not involve an unreasonable application of Strickland, the AEDPA requires that the habeas petition must be denied). We must therefore deny relief on this claim.

C. INEFFECTIVE ASSISTANCE CLAIM WITH RESPECT TO EVIDENCE OF PRIOR ASSAULT

During the punishment phase, the State introduced evidence of Tucker's prior conviction for the aggravated assault of his cellmate, Louis Savant. Tucker asserts that the district court neglected to address his claim that counsel rendered ineffective assistance by failing to develop and present available evidence to rebut (or at least mitigate against) the State's characterization of this assault. After reviewing the record, we question whether Tucker adequately apprised the district court of this particular claim until after the State had responded to his amended habeas petition. Under these circumstances, we do not believe Tucker has shown that the district court abused its discretion by essentially denying him the opportunity to add another ground of ineffective assistance of counsel after the State had replied to his amended petition. Cf. Briddle v. Scott, 63 F.3d 364, 379 (5th Cir. 1993) (explaining that decision to grant or deny motion to amend after an answer is reviewed for abuse of discretion).

Assuming arguendo that Tucker adequately apprised the district court of this claim, he requests that we remand it for further proceedings. Relying on King v. McCotter, 795 F.2d 517, 518 (5th Cir. 1986), Tucker asserts that in capital cases, the district court must make a ruling on each issue presented to allow the appellate court to conduct a meaningful review. In King, this Court did remand the case with instructions to provide reasons for the denial of each claim presented. See id. Unlike the instant case, in King, the district court had denied relief in a one-sentence order. See id. at 518. Here, the district court denied relief in a thoughtful, 36-page order. We decline Tucker's invitation to remand; instead, we will address the merits of his claim. See Willie v. Maggio, 737 F.2d 1372, 1376-77 (5th Cir. 1984) (addressing all petitioner's claims and denying relief even though the district court had ruled on some but not all the petitioner's claims).

Tucker argues that counsel rendered ineffective assistance at the punishment phase because (1) they did not investigate and present evidence to explain his aggravated assault on his cellmate, Louis Savant, and (2) a reasonably competent defense attorney would have developed evidence demonstrating that he acted in "self defense." This strategy, Tucker asserts, would have rebutted the State's arguments with respect to future dangerousness. We will assume solely for purposes of this appeal that counsel's performance was deficient with respect to this claim and focus on whether Tucker has shown prejudice.

Tucker contends counsel should have presented evidence that he believed the Aryan Brotherhood had a contract on his life and that his cellmate was the "hitman." Such evidence would demonstrate that this was not simply an unprovoked attack on an unarmed man. He therefore was prejudiced by counsel's failure to place his assault in proper context. In other words, this would have been mitigating evidence with respect to the jury's determination of his future dangerousness.

During his habeas proceedings, Tucker did submit prison records demonstrating he had reported to the authorities that he feared for his life because he knew the identity of certain members of the Aryan Brotherhood. Prior to the assault, there apparently was no evidence that his cellmate was in any way connected to the Aryan Brotherhood. It was only after stabbing Savant that Tucker informed the authorities Savant had attacked him on behalf of the Aryan Brotherhood. The prison records also reveal that Tucker admitted he had a verbal confrontation with Savant prior to the stabbing. In a letter to the prison disciplinary committee, Tucker explained that prior to the verbal dispute he discovered Savant had reported him to the prison authorities for having homemade weapons in their cell. In his letter, Tucker wrote that:

I did what I could do to get along with [Savant] until I found out that he had told Lt. Jenkins that I had a shank. . . . The shank was found. I was then told to go back to my cell. I then confronted [Savant] about what he had done and he told me then that he had. We had a verbal [fight] about it and all was forgotten.

The next part of the letter is partially illegible but it appears to provide that Tucker was informed that Savant had been hired to kill him. Tucker maintained that Savant attacked him. Tucker "got [his] two shanks and proceeded to defend [him]self." According to Tucker: "I stab[bed] him [once] in each temple, [once] at the base of the back of the skull, [twice] at the bottom of the throat. I left one in his throat and one in his temple. . . ." Additionally, the records indicate that Savant apparently did not have a weapon, and the authorities suspected that Tucker's superficial wounds were self-inflicted.

Assuming the jury believed that the brutal assault was motivated by his fear of the Aryan Brotherhood rather than the fact that Savant had informed the prison authorities regarding his shanks in their cell, the evidence arguably does have some mitigating value. Nonetheless, because the newly proffered records contain damaging evidence that allows a jury to infer the attack was precipitated by Savant's report of Tucker's homemade weapons, and the jury heard overwhelming evidence that Tucker had committed two, unrelated armed robberies after killing Humphreys, we are not prepared to conclude that Tucker has shown prejudice at the punishment stage. As such, the state court's decision to reject this claim of ineffective assistance cannot be deemed unreasonable or contrary to federal law.

D. KNOWING PRESENTATION OF FALSE TESTIMONY

The Supreme Court has held that due process is violated when the State knowingly offers false testimony to obtain a conviction and fails to correct such testimony. See Napue v. Illinois, 360 U.S. 264, 79 S.Ct. 1173, 1176-78, 3 L.Ed.2d 1217 (1959). Applying this teaching, we have recognized that relief is warranted if (1) the statements in question are shown to be actually false; (2) the prosecution knew that they were false; and (3) the statements were material. See Thompson v. Cain, 161 F.3d 802, 808 (5th Cir. 1998). Further, we have recognized that the issue of materiality involves a mixed question of law and fact. See id.

Tucker argues that the district court erred in concluding that the State did not elicit materially false testimony from Peter Kindig, a New Mexico state police officer who apprehended Tucker after a high-speed chase in New Mexico. More specifically, Tucker claims that Officer Kindig testified falsely at trial because his official report, which was not disclosed to the defense, provided that the high speed chase concluded when Tucker pulled over on the shoulder of the road for "no apparent reason." This statement, Tucker argues, contradicts Officer Kindig's trial testimony that he aimed his gun at Tucker during the chase, which prompted Tucker to slowly pull over and stop his vehicle.

The state court found that this was a minor inconsistency and constituted insufficient proof that Kindig's testimony was false or misleading. In reviewing this finding, we must accord it a presumption of correctness, which can only be rebutted by "clear and convincing evidence." Thompson, 161 F.3d at 811; 28 U.S.C. § 2254(e)(1). The district court held that Tucker had not "established reason to disregard this finding." We agree.

At trial, Officer Kindig testified as follows with respect to stopping Tucker during the pursuit:

I rolled down my window . . . and pointed the weapon directly at the back of Mr. Tucker's head. As doing so, we approached this curve and this hill. As we approached this curve and hill, Mr. Tucker while driving just — as he commonly would, looked back over his shoulder to see me. As he looked the first time, I noticed him — he quickly looked back again. He realized that I was pointing a weapon at him. He realized that it was almost over.

Just before we got to that point where I knew I could discharge my weapon, as he — the last time that he shucked his face back towards me very quickly, he gently applied the brake. I saw the brake lights come on. He very slowly began to move from that fast lane very slowly over to the slower lane, and all the way to the shoulder. This took over a half mile, that he began to slowly stop.

In his offense report, Kindig had stated that "pursuit continued to milepost 269 where suspect vehicle, for no apparent reason, stopped on the shoulder of westbound I-40." (emphasis added). Tucker points out that the offense report did not provide that the officer had his weapon aimed at Tucker. He argues that the statement that Tucker stopped for "no apparent reason" conflicts with Officer Kindig's trial testimony that indicated that Tucker stopped because of the weapon aimed at him.

However, as the State asserts, during a pretrial hearing Officer Kindig testified that after Tucker observed him aiming his rifle, Tucker stopped "for no apparent reason." Although it is unclear what Officer Kindig meant to convey by the phrase "for no apparent reason," under these circumstances, it certainly does not prove that his testimony was false. Put another way, because the officer used that particular phrase in the context of testifying that Tucker stopped his vehicle upon observing the weapon, it does not logically follow that he used that phrase in his report to indicate no weapon was exhibited. Accordingly, Tucker has not rebutted with clear and convincing evidence the state court's finding that this was a minor inconsistency and constituted insufficient proof that the testimony was false or misleading. Thus, the claim fails on the first prong.

Even assuming Tucker has shown the testimony was actually false, the state court's finding that the testimony was not material is not unreasonable. Tucker asserts that Officer Kindig's "false" testimony with respect to the high speed chase was material in regard to the sentencing phase — the jury's affirmative answer to the future dangerousness inquiry. According to Tucker's trial counsel, Kindig's description of the high speed chase was a "key element of the state's case" that had a "dramatic effect on the jury." This argument is not persuasive. Kindig's testimony did describe high speed pursuit at gun point, which no doubt involves some drama. Significantly, the chase ultimately ended with no injuries to persons or property. Viewing this testimony in the context of the State's other evidence (Tucker confessed to killing Humphreys, committing two other armed robberies after killing Humphreys, and brutally assaulting his cellmate during a previous incarceration), we do not believe it is material whether Tucker surrendered for "no apparent reason" or because Officer Kindig aimed his weapon at him. In conclusion, Tucker has failed to show the state court's decision that the challenged testimony was not material was contrary to, or involved an unreasonable application of, established federal law.

E. SHOWING OF CAUSE FOR FAILURE TO OBJECT

During his state habeas proceedings, Tucker argued that evidence of his prior conviction for the aggravated assault of his cellmate was inadmissible because it was based on an involuntary guilty plea and entered without the effective assistance of counsel. The state court found the claim procedurally barred.

Tucker now contends that the district court erred in concluding (without a hearing) that Tucker could not show cause for counsel's failure to object to the admission of his prior conviction for aggravated assault at sentencing. If a state court has explicitly relied on a procedural bar, a state prisoner may not obtain federal habeas relief absent a showing of cause for the default and actual prejudice that is attributable to the default. See Coleman v. Thompson, 501 U.S. 722, 111 S.Ct. 2546, 2565, 115 L.Ed.2d 640 (1991). Ineffective assistance of counsel may constitute "cause." Ellis v. Lynaugh, 883 F.2d 363, 367 (5th Cir. 1989).

Assuming arguendo that counsel's failure to object to the admission of the prior conviction at the punishment phase constituted deficient performance, we do not believe he can establish that he was prejudiced as a result. As such, Tucker has failed to show the required cause and prejudice to overcome the procedural default.

During the punishment phase of Tucker's trial, the State introduced evidence of the official conviction and also presented the testimony of Chad Sparkman, a correctional officer who was first on the scene of the assault and conducted the investigation. Sparkman saw Tucker's injured cellmate immediately after the attack with two homemade weapons still protruding from the victim's temple and throat. While still in the cell with Savant, Tucker stated to Sparkman that he "killed his cellie." Even assuming arguendo that counsel could have successfully excluded evidence of this allegedly unconstitutional conviction, Tucker has not shown that Sparkman's testimony regarding the circumstances of the attack would have been inadmissible. As a result, Tucker has not established prejudice. Thus, the district court properly concluded that Tucker failed to overcome the procedural bar to his claim that his prior conviction was inadmissible.

F. ADMISSION OF EVIDENCE OF OTHER CRIMES

Tucker's final claim on appeal is that the district court erred in finding that the admission of evidence of other crimes at the guilt phase constituted harmless error. In his taped confession, Tucker stated that he had stolen two checks from his brother's checkbook on the morning of the murder, which were used to purchase a firearm (the murder weapon) in violation of his parole. He further confessed to committing two armed robberies — one in Arlington, Texas, and one in New Mexico — after shooting and killing Humphreys.

On direct appeal, the Court of Criminal Appeals concluded that this evidence was irrelevant to the issue of Tucker's guilt. However, the Court found the error harmless because the evidence was not emphasized by the prosecution, Tucker had confessed both verbally and in writing to the killing, and there was no evidence specifying the offense for which he had been serving parole.

Tucker argues that the Court of Criminal Appeals' finding that the prosecutor did not mention the evidence during the jury argument is misleading. He states that the prosecutors repeatedly directed the jury's attention to Tucker's taped confession, which contained the "other crimes" evidence. Of course, aside from the evidence of the other crimes on the tapes, the prosecutor had a very legitimate reason to direct the jury's attention to the tapes, i.e., Tucker confessed to shooting Humphreys (albeit unintentionally) with his pistol. In any event, we found only one explicit reference to "other crimes" during the prosecutor's closing argument. The prosecutor referred to Tucker taking his brother's checks and illegally buying a gun. The prosecutor refrained from mentioning the armed robberies Tucker committed after the murder. Tucker has failed to rebut the state court finding that the evidence of the crimes was not emphasized.

As set forth above, the Court of Criminal Appeals found that the admission of evidence of the other crimes was error. The State argues that the state court's conclusion that the error was harmless was not an unreasonable application of federal law. More specifically, the State contends that the evidence of the other crimes did not have a substantial and injurious effect or influence in determining the jury's verdict under Brecht v. Abrahamson, 507 U.S. 619, 113 S.Ct. 1710, 123 L.Ed.2d 353 (1993). We will assume that the admission of the evidence of other crimes was error and determine whether such error was harmless under Brecht. See Corwin v. Johnson, 150 F.3d 467, 476 (5th Cir. 1998) (assuming admission of evidence constituted error and determining whether the petitioner was entitled to federal habeas relief pursuant to Brecht). We have articulated this standard as follows:

Under Brecht, a constitutional trial error is not so harmful as to entitle a defendant to habeas relief unless there is more than a mere reasonable possibility that it contributed to the verdict. It must have had a substantial effect or influence in determining the verdict. We recognize, however, that if our minds are in virtual equipoise as to the harmlessness, under the Brecht standard, of the error, then we must conclude that it was harmful. Moreover, the Brecht standard does not require in order for the error to be held harmful that there be a reasonable probability that absent the error the result would have been different.

Id. at 500 (brackets, internal citations and quotation marks omitted).

In light of Tucker's confession, the overwhelming evidence of guilt, and the fact that the State did not emphasize the other crimes, we are persuaded that the evidence did not have a substantial effect or influence in determining the jury's verdict. Accordingly, we conclude that the state court's determination of harmlessness was not contrary to, or an unreasonable application of, established federal law.

For the above reasons, the judgment of the district court is AFFIRMED.