
550 F.3d 542 (2008)
Stephen Michael WEST, Petitioner-Appellant,
v.
Ricky BELL, Warden, Respondent-Appellee.
Nos. 05-5132, 05-6219.
United States Court of Appeals, Sixth Circuit.
Argued: February 7, 2008.
Decided and Filed: December 18, 2008.
*545 ARGUED: Stephen Alan Ferrell, Federal Defender Services, Columbus, Ohio, for Appellant. Jennifer Lynn Smith, Office of the Tennessee Attorney General, *546 Nashville, Tennessee, for Appellee. ON BRIEF: Stephen Alan Ferrell, Federal Defender Services, Columbus, Ohio, for Appellant. Jennifer Lynn Smith, Office of the Tennessee Attorney General, Nashville, Tennessee, for Appellee.
Before: BOGGS, Chief Judge; and NORRIS and MOORE, Circuit Judges.
BOGGS, C.J., delivered the opinion of the court, in which NORRIS, J., joined. MOORE, J. (pp. 567-70), delivered a separate opinion dissenting in part and concurring in the judgment only in part.

OPINION
BOGGS, Chief Judge.
Stephen Michael West appeals the district court's dismissal of his petition for habeas corpus filed pursuant to 28 U.S.C. § 2254. West argues that the state trial court erred by refusing to admit two exculpatory pieces of evidence, that the trial was prejudiced by prosecutorial misconduct, and that he received ineffective assistance of counsel during the sentencing phase of his trial. We reject these arguments and affirm the district court.

I. BACKGROUND

A. Factual and Procedural History

1. The crime
We briefly summarize the facts of the two murders that led to West's arrest. On March 17, 1986, twenty-three year-old West and seventeen year-old Ronnie Martin left their jobs at a McDonald's in Lake City, Tennessee. They had known each other only about two weeks. After driving around and drinking in Martin's car for several hours, Martin told West that he knew a girl who would "give them some sex." Martin was referring to fifteen year-old Sheila Romines, a classmate of Martin who had previously rebuffed his advances and embarrassed him in front of other students. Martin and West went to the Romineses' house, but did not approach it. Instead the two laid in wait until around 5:20 A.M., when Mr. Romines left for work. They knocked on the door and Wanda Romines, Sheila's mother, let the two into the house. Sometime between 6:00 A.M. and 8:30 A.M., Wanda and Sheila were brutally murdered. Dr. Cleland Blake, a forensic pathologist, testified that Sheila had been raped prior to being stabbed seventeen times in the abdomen. Fourteen of those wounds were torture-type cuts. Wanda Romines had also suffered a large number of deep stab wounds, including torture-type wounds. West and Martin were arrested the next day.

2. The trial
Both West and Martin were charged with the rape and double homicide, but the trials of the two defendants were severed and the state prosecuted West first. During West's initial criminal trial in the Criminal Court of Union County he was represented by two attorneys: Richard McConnell, who was hired by West's family and was the lead counsel, and Thomas K. McAlexander, a court appointed co-counsel. At trial, the defense argued that though West was present during the murders, Martin was the architect of the crime and that West participated only because Martin threatened to kill him and his then-pregnant wife. Dr. Blake, however, testified that (1) two different knives were used; (2) two people were involved in the infliction of the wounds. Martin did not testify at West's trial. On March 24, 1987, a jury convicted West of two counts of first-degree murder, two counts of aggravated kidnaping, one count of aggravated rape, and one count of larceny.
*547 During the sentencing phase, six people testified on West's behalf. Three of them were family friends who had known West for three, twelve, and fourteen years respectively. The sheriff testified that West had not caused any problems during the year he was incarcerated awaiting trial. West's sister testified that West was the baby in the family and had never been in trouble, and that his mother could not come to court because she had recently suffered a heart attack. West's wife testified that they had a good relationship and that West was a good father to their eleven-month-old daughter. Finally, West himself testified. He admitted to being present during the crimes but denied that he had participated in the murders of the two victims. He also stated that he had no prior criminal record, had been an honor student in school, and had never had any disciplinary problems. Despite West's mitigating evidence, the jury ultimately sentenced him to death.
West directly appealed his conviction and sentence to the Tennessee Supreme Court. West asserted numerous claims, including prosecutorial misconduct and that the trial court erred in excluding two pieces of evidence. West did not claim ineffective assistance of counsel. On February 6, 1989, the Tennessee Supreme Court rejected all of his arguments. State v. West, 767 S.W.2d 387 (Tenn.1989).

3. Post-conviction attack on prosecutorial misconduct and ineffective assistance of counsel
On October 23, 1990, West filed for post-conviction relief in the Criminal Court of Union County, Tennessee. West argued that he received ineffective assistance of counsel during the sentencing phase of his trial because his counsel should have discovered existing mitigating evidence. Judge John K. Byers held evidentiary hearings on September 24 and October 22, 1996. The federal district court and state court of criminal appeals summarized the evidence introduced in the evidentiary hearings, so we review it only briefly here. West, No. 3:01-cv-91, slip op. at 17-36; West v. Tennessee, 04C01-9708-CR-00321, slip op. at 3-14.
Dr. Eric Engum, a clinical psychologist, conducted a two-day comprehensive psychological and neuropsychological evaluation of West. He testified that the test results did not indicate any signs of brain damage or cognitive compromise and that West's intelligence, memory, and other skills were within normal limits. Dr. Engum also testified that West suffered from chronic, significant depression and that West had a severe mixed-personality disorder with self-defeating, avoidant, dependant, and schizoid features. According to Dr. Engum, West's test results indicated that he was somewhat unstable, moody, changeable, and lacked a strong sense of self. Dr. Engum also stated that West's test results demonstrated that he was withdrawn, introverted, brooding, a loner, and stayed to himself, and also that he had a lot of bottled-up anger. Dr. Engum was asked whether there was any indication that West had been abused as a child. He responded that while there was no test that could "specifically tell what somebody experienced or what events occurred in somebody's life" West's "personality characteristics or behavioral or emotional characteristics" were "consistent with or reflect[ed] prior abuse." West, No. 3:01-cv-91, slip op. at 18.
West's oldest sister, Debbie West, testified that West was born on September 16, 1962, in a mental institution in Anderson, Indiana and that her mother abused West. Id. at 21. Debbie West described the abuse as follows:

*548 I can remember when Steve was a baby, and he was kept in the back bedroom, and I would get a whipping for going and giving him a bottle. If he cried, he was picked up by one arm and one leg and slammed against the wall to shut him up. If my other brother did something wrong, Steve got beat for it. My sister and I would try to get between them, and we would get beat, and then his beating was finished, and this was not just one or two times. This was from the time I can remember Steve coming home from the hospital.
Ibid. Debbie West also testified that West was slapped in the head, hit with shoes, and received a blow to the head which caused him to become cross-eyed. Debbie West described her father as a violent alcoholic who became more violent when he drank. Finally, Debbie West claimed that prior to West's criminal trial she told West's attorney, Mr. McConnell, about the abuse; however, according to Ms. West, he told her the information about the alleged abuse was not relevant, and that, furthermore, her parents were paying him and would not admit to the abuse.
Two other family members, West's older sister, Patricia Depew, and his aunt Ruby West, also testified as to the abuse West suffered. Patricia was present at some of the meetings with the trial attorneys, but she said that she was never asked about the abuse, and she never offered any information about the abuse. Ruby testified that she was not contacted by the trial attorneys.
McAlexander, West's court-appointed co-counsel, testified that he: (1) did a tremendous amount of research in preparing different motions which were filed on Petitioner's behalf; (2) met with West many times to discuss all aspects of the case; (3) met with West's family on more than one occasion; (4) met at least thirty-five times with McConnell in preparing for trial; and (5) spent 547.4 hours on West's case. McAlexander also testified that to the best of his recollection, West's sister, did not tell him that West had been abused and that there was nothing that raised "any kind of red flag in my mind about that being a factor that should have been inquired into." West, No. 3:01-cv-91, slip op. at 22. McAlexander also explained that while they had hired a mental health expert, Dr. Ben Bursten, to explore West's competency and the possibility of an insanity defense, the court had rejected the defense's request for funds to hire an expert to explore a duress defense. The court ruled that way because the parties had been battling over mental exams and West had previously objected to the trial court's sua sponte ordering of a psychological examination to determine competency. Id. at 27. McAlexander stated they talked about using the competency expert's testimony during the sentencing phase, but ultimately decided against using such testimony because Bursten told them that his evaluation could not support the support the conclusion that West had "untoward mental reactions at the time of the offense." West, 3:01-cv-91, slip op. at 31.
McConnell, West's privately-retained counsel, also testified. Mr. McConnell testified he was paid a total of $10,000 by Petitioner's family to represent him. In addition, Petitioner's family paid the bills of a private investigator[1] and the competency expert. McConnell testified that while he did not think $10,000 was a reasonable fee for the case because of its magnitude, he agreed to that fee due to *549 the financial situation of Petitioner and his family. He denied complaining about his fee, but acknowledged he and co-counsel joked about the fact that co-counsel, who was court-appointed, would make more money representing Petitioner than Mr. McConnell, retained counsel. McConnell also admitted that he had contacted the family requesting an additional $5,500 in fees and expense money.
As for McConnell's investigation of West's background, he testified that he conducted a complete investigation into West's life although he had no recollection of obtaining any of West's employment records, birth records, or medical records. The district court noted, however, that the state post-conviction record indicates the defense did file a subpoena requesting Petitioner's school records after the trial was in progress. McConnell also explained that while he interviewed West's family, the only member who was cooperative was West's sister, Debbie. McConnell also denied that Debbie West told him about West's physical abuse and denied that he told her that the abuse was not relevant. He also stated that West, himself, did not mention any physical or sexual abuse. As for the military records, McConnell explained that the defense team made a strategic decision not to introduce them because the records indicated that West had drug and alcohol problems during his service in Germany.
Attorney Paul Morrow also testified at the state post-conviction hearing as an expert on professional standards. In Morrow's opinion, the alcohol abuse documented in Petitioner's military records was a "red flag or I would say a rocket going off saying that you better look back into that person's history." In addition, it was Mr. Morrow's opinion that West's inability to remember his first ten years of life was a red flag that should have made the trial counsel investigate possible abuse.
The State called Dr. Bursten. Bursten testified that West's description of his father as an alcoholic led him to ask West if he had been abused as a child. West denied any abuse. Dr. Bursten also testified regarding Dr. Engum's report. He agreed that West had an adequate IQ, however, he disagreed, based on the records, including Dr. Engum's report, with the conclusion that West was abused as a child. With regard to Dr. Engum's diagnosis of West's depression and personality disorder, Dr. Bursten explained that while West might suffer from those conditions, their presence would not necessarily indicate that West, at the time of the crimes, was actually under extreme duress.
On April 14, 1997, the Criminal Court denied West's claim of ineffective assistance of counsel. West v. Tennessee, No. 629 (Tenn.Crim. Ct. April 14, 1997).

4. Further state appeals and West's federal habeas petition
On May 2, 1996, West appealed the denial of his post-conviction relief to the Tennessee Court of Criminal Appeals. On June 12, 1998, the court rejected his appeal. West v. Tennessee, 04C01-9708-CR-00321 (Ct.Crim.App. June 12, 1998). West then filed a petition for rehearing and, when that was denied, an application for permission to appeal to the Tennessee Supreme Court. The Tennessee Supreme Court allowed West to appeal only the issue of whether there was sufficient evidence to establish the aggravating circumstance, but the court ultimately affirmed the denial of post-conviction relief. West then filed for a petition for rehearing, which was denied on June 7, 2000.
On February 20, 2001, West filed a petition for a writ of habeas corpus under 28 U.S.C. § 2254 in the United States *550 District Court for the Middle District of Tennessee. The case was subsequently transferred to the Eastern District and assigned to the Honorable Thomas A. Varlan. West asserted 22 grounds for granting his habeas petition. On September 30, 2004, the district dismissed West's petition and denied a certificate of appealability ("COA"). On August 18, 2006, after a series of appeals, this court granted West a COA on four issues:
1. Whether the state court was unreasonable in its determination of the facts or its application of the law when it dismissed petitioner's claim that his counsel rendered ineffective assistance during the sentencing phase of trial.
2. Whether the trial court improperly excluded the proffered testimony of Libby Wood during the guilt/innocence phase of the trial?
3. Whether the trial court improperly excluded secretly taped conversations between Martin and his cellmate?
4. Whether the prosecutor engaged in various instances of misconduct that prejudiced the outcome of the trial?

II. DISCUSSION
Whether the district court properly dismissed West's § 2554 petition is a question of law that we review de novo. Martin v. Overton, 391 F.3d 710, 712 (6th Cir.2004). We review the court's factual findings for clear error, except where the factual findings are based on the district court's review of state court trial transcripts or other court records, in which case they are reviewed de novo. Dando v. Yukins, 461 F.3d 791, 796 (6th Cir.2006).
This court's review is governed by the Antiterrorism and Effective Death Penalty Act of 1996 ("AEDPA"). We may grant West's habeas petition only if his constitutional rights were violated in the underlying criminal proceedings, 28 U.S.C. § 2254(a), and only if the original or subsequent state court proceedings:
(1) resulted in a decision that was contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States; or
(2) resulted in a decision that 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).

A. Ineffective Assistance of Counsel

1. Procedural default, exhaustion, and fair presentment
West claims that his trial counsel rendered ineffective assistance during the sentencing phase by failing to investigate West's abusive childhood and its effects on his actions and state of mind during the crime. Appellant's Br. 17. West first raised this argument in his initial state post-conviction review. West v. State of Tennessee, No. 629 (Crim. Ct. Union County, Tenn. April 14, 1997), slip at 6-7. J.A. 1632-33. Thus, there is no procedural default.
Nevertheless, West attached several pieces of evidence to his federal habeas petition, which the district court did not consider because West failed to present it to the state courts.[2] A writ of habeas *551 corpus may not be granted unless the petitioner has exhausted available state-court remedies. 28 U.S.C. § 2254(b)(1). In order to satisfy the exhaustion requirement, "a petitioner's claim must be `fairly presented' to the state courts before seeking relief in the federal courts." Whiting v. Burt, 395 F.3d 602, 612 (6th Cir.2005) (citing Baldwin v. Reese, 541 U.S. 27, 29, 124 S.Ct. 1347, 158 L.Ed.2d 64 (2004)). In other words, "the substance of a federal habeas corpus claim must first be presented to the state courts." Picard v. Connor, 404 U.S. 270, 278, 92 S.Ct. 509, 30 L.Ed.2d 438 (1971).
Rule 7 of the Rules Governing Section 2254 Cases, however, provides:
(a) ... [T]he judge may direct the parties to expand the record by submitting additional materials relating to the petition;
(b) ... The materials that may be required include letters predating the filing of the petition, documents, exhibits, and answers under oath to written interrogatories propounded by the judge. Affidavits may also be submitted and considered as part of the record.
U.S.C. Sec. 2254 Cases, R7.
In Vasquez v. Hillery, 474 U.S. 254, 106 S.Ct. 617, 88 L.Ed.2d 598 (1986), the Supreme Court held that courts may consider additional affidavits and records so long as "the supplemental evidence presented by [the petitioner] d[oes] not fundamentally alter the legal claim already considered by the state courts...." Id. at 260, 106 S.Ct. 617; see also Richey v. Bradshaw, 498 F.3d 344, 351 (6th Cir.2007); Satterlee v. Wolfenbarger, 453 F.3d 362, 366 (6th Cir. 2006).
The decision of whether to expand the record, however, is within the sound discretion of the district court. Ford v. Seabold, 841 F.2d 677, 691 (6th Cir. 1988). Because the district court did not abuse its discretion in declining to expand the record, we will consider only the evidence presented before the state court during the post-conviction proceedings.

2. Supreme Court precedent governing claims of ineffective assistance of counsel: Strickland v. Washington

In Strickland v. Washington, the Supreme Court delineated a two-prong test for determining whether a defendant's counsel was so ineffective as to constitute a violation of the defendant's constitutional rights:
First, the defendant must show that counsel's performance was deficient. This requires 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.
466 U.S. 668, 687, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984). Deficiency requires a showing that "counsel's representation fell below an objective standard of reasonableness." Id. at 688, 104 S.Ct. 2052. This court should "indulge a strong presumption that counsel's conduct falls within the wide range of reasonable professional assistance...." Id. at 689, 104 S.Ct. 2052. To establish prejudice, West must show that "there is a reasonable probability that, but for counsel's unprofessional errors, the result of the proceeding would have been different. A reasonable probability is a probability sufficient to undermine *552 confidence in the outcome." Id. at 694, 104 S.Ct. 2052.
The Supreme Court has held that a failure to investigate a defendant's background or present mitigating evidence can constitute ineffective assistance of counsel. See Rompilla v. Beard, 545 U.S. 374, 125 S.Ct. 2456, 162 L.Ed.2d 360 (2005); Wiggins v. Smith, 539 U.S. 510, 123 S.Ct. 2527, 156 L.Ed.2d 471 (2003); Williams v. Taylor, 529 U.S. 362, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000).[3]

3. The state courts' determinations of the facts and application of the law
The Criminal Court for Union County, Tennessee was the first state court to review West's petition for post-conviction relief. After holding two evidentiary hearings, the court denied West's petition. In its order, the court explicitly delineated the Strickland test for assessing claims of ineffective assistance of counsel, but it also stated an incorrect burden of proof. The court wrote:
The petitioner contends that he was denied his Sixth Amendment right to the effective assistance of counsel. In order to be granted relief on the grounds of ineffective assistance of counsel, the petitioner must establish that the advice given or the services rendered were not within the range of competence demanded of attorneys in criminal cases and that "there is a reasonable probability that, but for counsel's unprofessional errors, the result of the proceeding would have been different." Strickland v. Washington, 466 U.S. 668, 693, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984). If the petitioner fails to prove by a preponderance of the evidence that the result would have been different had counsel acted differently, i.e., the prejudice prong, it is unnecessary to address the competency of counsel prong.
West, No. 629, slip at 6-7. J.A. 1632-33 (emphasis added). The correct burden of proof under Strickland, however, is "reasonable probability," not preponderance of the evidence. This is a point we will return to in the discussion below as to whether the state court's decision was contrary to Strickland. In dismissing West's claim, the court pointed out that there was conflicting evidence regarding the possible mitigation evidence that trial counsel failed to present. The court concluded, "after a thorough review of the overwhelming evidence presented," that West had "failed to meet his burden of proof with respect to the allegations. In particular, [West] has failed to show how he was prejudiced by any of counsel's acts or omissions." Id. at 7 (emphasis added).
The Court of Criminal Appeals of Tennessee, the second state court to review West's post-conviction began by reviewing the evidence presented at the September 24, 1996, evidentiary hearing held in the court below. It then addressed the authority presented by West in support of his claim of ineffective assistance. In doing so, the court did cite Strickland, but not for the particular part of the opinion that delineates the two-part test for evaluating ineffective-assistance claims. The court then adopted the state's argument, including the state's citation to Lockhart v. Fretwell, that:

*553 [A]n analysis focusing solely on mere outcome determination, without attention to whether the result of the proceeding was fundamentally unfair or unreliable, is defective. To set aside a conviction or sentence solely because the outcome would have been different but for counsel's error may grant the defendant a windfall to which the law does not entitle him.
West v. State, 1998 WL 309090, *8, 1998 Tenn.Crim.App. LEXIS 636, *22 (Tenn. Crim.App.1998) (citing Lockhart v. Fretwell, 506 U.S. 364, 369-70, 113 S.Ct. 838, 122 L.Ed.2d 180 (1993)).
After reviewing the arguments of both West and the State, the court held:
We agree with the post-conviction court's assessment that "there existed conflicting testimony regarding mitigation evidence that trial counsel failed to present." We also agree with the court that Dr. Engum's testimony reflected that the petitioner's evaluation showed no signs of trauma or organic brain damage. We agree with the post-conviction court that in light of this conflicting evidence, the petitioner did not meet his burden with respect to the allegation of ineffective counsel at the sentencing phase. Regarding all of the ancillary and subissues, after a thorough review, we conclude that the petitioner has failed to meet his burden of proof as to these allegations. We agree with the post-conviction hearing court that the petitioner has failed to show how he was prejudiced by any acts or omissions of counsel.
West v. State, 1998 WL 309090, *9, 1998 Tenn.Crim.App. LEXIS 636, *23-24 (Tenn.Crim.App.1998).

4. West's habeas claims
West argues that the state courts' rejections of his ineffective assistance claim were contrary to and involved an unreasonable application of Strickland because the criminal court relied on the wrong standard of proof and because the court of criminal appeals erroneously relied on Lockhart.

a. AEDPA and the state court's error concerning the burden of proof
Clearly, the Criminal Court for Union County stated the wrong standard for proving prejudice in a claim of ineffective assistance. Moreover, the Supreme Court has used this exact mistake as an example of when a decision would be "contrary to" Strickland:
Take, for example, our decision in Strickland v. Washington, 466 U.S. 668, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984). If a state court were to reject a prisoner's claim of ineffective assistance of counsel on the grounds that the prisoner had not established by a preponderance of the evidence that the result of his criminal proceeding would have been different, that decision would be "diametrically different," "opposite in character or nature," and "mutually opposed" to our clearly established precedent because we held in Strickland that the prisoner need only demonstrate a "reasonable probability that ... the result of the proceeding would have been different." Id. at 694, 104 S.Ct. 2052.
Williams, 529 U.S. at 405-06, 120 S.Ct. 1495 (emphasis added).
While West is correct that his situation satisfies requirements of 28 U.S.C. § 2254(e), we cannot grant habeas unless West is "in custody in violation of the Constitution or laws or treaties of the United States." 28 U.S.C. § 2254(a). As Justice Stevens put it: "We all agree that state-court judgments must be upheld unless, after the closest examination of the state-court judgment, a federal court is *554 firmly convinced that a federal constitutional right has been violated." Williams, 529 U.S. at 389, 120 S.Ct. 1495 (Stevens, J., concurring). Though the state court clearly applied an incorrect standard, it reached the correct outcome. A careful review of the record demonstrates that West's counsel was not so ineffective as to constitute a denial of his constitutional rights. For this reason, we must deny West's petition for a grant of habeas corpus even though the state court decision was an unreasonable application of clearly established federal law.

b. West's representation was constitutionally sufficient
On appeal to this court, West emphasizes the following facts as evidence that his attorneys were ineffective:
(1) Defense counsel interviewed only West, his parents and one sister and that they opted not to conduct separate interviews of the other siblings outside of the presence of West's parents.
(2) While defense counsel hired Dr. Bursten to conduct a mental examination of West to determine his competency and any bases for an insanity-type defense, counsel did not hire a second expert to testify during the mitigation phase.
(3) Counsel failed to investigate West's employment records or interview West's employers.
(4) Counsel failed to introduce West's school records, though apparently they did subpoena them. West v. Bell, No. 3:01-cv-91, slip op. at 24 (E.D.Tenn. Sept. 30, 2004).
(5) Counsel did not introduce West's military records.
(6) Defense counsel also failed to subpoena or examine West's medical records.
We are not convinced, however, that all of these are actually errors, let alone errors that rise to the level of ineffective assistance of counsel.
Under Strickland, we must give a high level of deference to the defense counsel's decisions; there is also a presumption that counsel was competent:
Judicial scrutiny of counsel's performance must be highly deferential. It is all too tempting for a defendant to second-guess counsel's assistance after conviction or adverse sentence, and it is all too easy for a court, examining counsel's defense after it has proved unsuccessful, to conclude that a particular act or omission of counsel was unreasonable. A fair assessment of attorney performance requires that every effort be made to eliminate the distorting effects of hindsight, to reconstruct the circumstances of counsel's challenged conduct, and to evaluate the conduct from counsel's perspective at the time. Because of the difficulties inherent in making the evaluation, a court must indulge a strong presumption that counsel's conduct falls within the wide range of reasonable professional assistance; that is, the defendant must overcome the presumption that, under the circumstances, the challenged action might be considered sound trial strategy.
Strickland, 466 U.S. at 689, 104 S.Ct. 2052 (internal citations omitted).
This high level of deference means that we "we address not what is prudent or appropriate, but only what is constitutionally compelled." United States v. Cronic, 466 U.S. 648, 665, n. 38, 104 S.Ct. 2039, 80 L.Ed.2d 657 (1984) (emphasis added). In Burger v. Kemp, the trial counsel had interviewed "all potential witnesses who had been called to his attention," and, on that basis, decided that "an explanation of petitioner's history would not have minimized *555 the risk of the death penalty." 483 U.S. 776, 794-95, 107 S.Ct. 3114, 97 L.Ed.2d 638 (1987). The Court held that the trial counsel's decision "not to mount an all-out investigation into petitioner's background in search of mitigating circumstances was supported by reasonable professional judgment." Id. at 794, 107 S.Ct. 3114.
We came to a similar conclusion in Scott v. Mitchell, 209 F.3d 854, 881-82 (6th Cir. 2000). Though we noted that Scott's attorneys "would certainly have been well-advised to conduct more research into mitigating factors than they did.... [T]he decision of Scott's attorneys to pursue a residual-doubt strategy in this case was not objectively unreasonable, because it was adequately (if not ideally) informed and was quite arguably the best course of action available." Ibid.
In the case at hand, the most significant alleged errorthe failure to adequately investigate West's past abuseis also the most contested. Debbie West claims she informed McAlexander and McConnell about the abuse, but the attorneys strongly deny that. The two psychologists, Engum and Bursten, disagree over whether West's evaluations contain evidence of abuse; and Bursten testified that West specifically denied being abused.
As for West's other objections, the record demonstrates that West's counsel, in fact, did a fair amount of investigation in preparation for the mitigation phase. West's defense counsel interviewed West's family multiple times. They met individually with West's sister, Debbie, multiple times. They examined numerous historical records. Even if they could not remember doing so (which is understandable considering that ten years had elapsed between West's criminal trial and the post-conviction hearing), the record demonstrates that they subpoenaed West's school records. West v. Bell, No. 3:01-cv-91, slip op. at 24 n. 10 (E.D.Tenn. Sept. 30, 2004). Indeed, West testified that he had been on the honor roll and in the Beta Club. Id. at 15. They also examined West's military record but made a decision not to put it into evidence as the record noted that West had a "pattern of misconduct," though it did not elaborate on what that misconduct consisted of. Id. at 27.
The attorneys also investigated West's mental state. Originally, West had been evaluated on motion of the state by a psychologist, Dr. Ford. Not being satisfied with the results, the defense hired Dr. Bursten to determine competency and sanity. As mentioned above, Dr. Bursten's evaluation was not used for the purpose of mitigation. Nevertheless, Dr. Bursten's evaluation did not lead counsel to suspect anything along the lines of the "long-term personality disorder" diagnosed by Dr. Engum nine and a half years after West's trial and conviction. As Mr. McConnell explained, "I had had Mr. West examined by a very competent psychiatrist, Dr. Bursten, who obviously did a thorough history, et cetera, and none of that ever came out." Id. at 26. They also requested from the trial court additional funds to hire a second psychologist in order to pursue a possible duress defense to at least the rape (duress is never a defense to murder). The court refused the request on the grounds that West had objected to the trial court's sua sponte ordering of a psychological examination to determine competency. Id. at 27. Our circuit addressed a similar situation in Fautenberry v. Mitchell, 515 F.3d 614 (6th Cir.2008). There, the defense counsel had hired an expert for the express purpose of conducting a neuropsychological examination, but the defendant refused to be examined. Our court held that the counsel's "inability to discover or establish organic brain damage *556 is directly attributable to [the defendant's] refusal to cooperate, rather than any insufficiency in the investigation." 515 F.3d at 625. We declined to "find counsel deficient simply because they did not succeed in discovering [the defendant's] brain damage or pursue unspecified, alternate avenues (which may or may not have revealed the brain damage)." Ibid. In this case, West's earlier refusal to submit to examination was the reason the court blocked his request for another examination. Like the defendant in Fautenberry, West's lack of cooperation is part of the reason why his counsel did not discover some potentially mitigating evidence.
Finally, we note that even if West could prove that his counsel was ineffective for all of the reasons he cited, he has not shown that "there is a reasonable probability that, but for counsel's unprofessional errors, the result of the proceeding would have been different. A reasonable probability is a probability sufficient to undermine confidence in the outcome." Strickland, 466 U.S. at 694, 104 S.Ct. 2052. West's trial counsel attempted to appeal to the jury's sympathy, decency, and common sense. They attempted to show that West had been a good and decent citizen: that he had never before been in trouble with the law, that he was a veteran who served his country, and that he was a loving husband and a soon-to-be father. The jury was not persuaded. We are not convinced that the school, military, and employment records that West now argues should have been submitted would have affected the jury's verdict.
As for the evidence of the past abuse, it is possible that had West's attorneys discovered it, they might have taken the alternative approach of portraying West as the product of an unstable and abusive home. The jury might have believed that the abuse made West the kind of person who was psychologically unable to confront or disobey strong, threatening people such as Martin. The jury might have pitied West and chosen to spare his life. However, the very same evidence may have had the opposite effect on the jury. They might have believed that violence begets violence and that West's past abuse made him the kind of person who could have raped and tortured a fifteen year-old girl. They might have despised West and sentenced him to death with greater zeal.
It is not enough for this court to speculate that the jury would have chosen the former path. There must be "a reasonable probability" that the proceeding would have been different. Given the strength of the evidence against West presented at trial and the weakness of the mitigating evidence that West presented during the post-conviction proceedings, we cannot conclude that there was reasonable probability that the jury would have chosen to spare West's life.

B. The Exclusion of Libby Woods's Testimony and the Martin-Hunley Tapes

1. The proffered evidence
West's theory of the case was that it was Ronnie Martin and not West who actually killed Wanda Romines and her daughter, Sheila. In order to demonstrate this, West sought to introduce two pieces of evidence: (1) the testimony of Libby Woods, an acquaintance of both Martin and Sheila; and (2) two taped conversations between Martin and his cellmate, Steve Hunley.
According to West:
Woods was prepared to testify that Martin said he would kill Sheila Romines; that he was upset with her for embarrassing him on one occasion where Sheila actually struck him in front of other *557 students at school; that he wanted to date her and he wanted to have sex with her and she resisted his advances; and, that Martin said that he owed her, and that is why he would kill her.
Appellant's Br. 6-7.
The two taped jailhouse conversations supposedly demonstrated that Martin was the main perpetrator and that West did not take part in the killings. The first conversation proceeded as follows:
Hunley: Hey, Ronnie
Martin: Yeah?
Hunley: One more time before I go to bed to ease my mind, Steve [West] do that shit?
Martin: No.
Hunley: Huh?
Martin: No
Hunley: O.K. Thank you.
Hunley: These guys back here don't believe me that you said Steve didn't kill them women. Will you tell them you did?
Unknown: Who's back there?
Hunley: All of us.
Martin: Yeah, I did it.
Hunley: You killed both them women?
Martin: Yeah.
Hunley: Why?
Martin: I don't know. I don't want to talk about it.
In the second conversation, Martin discussed his plan to falsely take an insanity plea. During the conversation he tacitly agreed that he, and not Steve, had killed the Romineses.
Hunley: Yea, but you said Steve didn't kill those women, you did. Don't you think that's crazy?
Hunley: Huh
Martin: Huh
Hunley: You told me Steve didn't do that but you did, don't you think that's crazy?
Martin: I don't think it's crazy, no.
West argues that the state court violated his Sixth, Eighth, and Fourteenth Amendment rights under Chambers v. Mississippi, 410 U.S. 284, 93 S.Ct. 1038, 35 L.Ed.2d 297 (1973), and Green v. Georgia, 442 U.S. 95, 99 S.Ct. 2150, 60 L.Ed.2d 738 (1979), by excluding these pieces of evidence.

2. Procedural default
The State argues that West procedurally defaulted on his claims because he raised them solely as issues of state law before the state courts. We do not agree. While West failed to cite either the United States Constitution or federal case law in his argument concerning Woods's testimony, he did cite federal law in his argument concerning the taped recordings. Specifically, he cited the Constitution and Chambers for the general proposition that, "[t]he right of an accused in a criminal trial is, in essence, the right to fair opportunity to defend against the state's accusations." 410 U.S. at 294, 93 S.Ct. 1038. Furthermore, West concluded the section dealing with both Woods's testimony and the Martin-Hunley tapes by arguing that:
[West] attempted to introduce several pieces of evidence.... The failure of the trial judge to permit this resulted in a denial of [West's] Due Process rights as guaranteed by the Sixth and Fourteenth Amendments to the United States Constitution as well as Article I, Sections 7, 8, and 9 of the Tennessee State Constitution.
"A litigant wishing to raise a federal issue can easily indicate the federal law basis for his claim in a state court ... by citing in conjunction with the claim the federal source of law ... or a case deciding *558 such a claim on federal grounds, or by simply labeling the claim `federal.'" Baldwin, 541 U.S. at 32, 124 S.Ct. 1347. Thus, even though West did not raise a constitutional issue in his main discussion of the exclusion of Woods's testimony, he did preserve his federal claim in regard to the exclusion of Woods's testimony by referring to the United States Constitution in the summary of his argument.
The fact that the Tennessee Supreme Court analyzed his claim in regards to Woods's testimony only under state law is irrelevant. A state Supreme Court's failure to analyze a petitioner's federal claim, "does not deprive this court of jurisdiction." Newton v. Million, 349 F.3d 873, 877 (6th Cir.2003); see also Smith v. Digmon, 434 U.S. 332, 333, 98 S.Ct. 597, 54 L.Ed.2d 582 (1978) (per curiam) ("[W]hether the exhaustion requirement of 28 U.S.C. § 2254(b) has been satisfied cannot turn upon whether a state appellate court chooses to ignore in its opinion a federal constitutional claim squarely raised in petitioner's brief in the state court....").

3. State-court analysis
In rejecting West's claims in regard to Woods's testimony, the Tennessee Supreme Court reasoned that testimony of Libby Woods was distinguishable from the excluded evidence at issue in Green v. State, 154 Tenn. 26, 285 S.W. 554 (1926), and Hensley v. State, 28 Tenn. 243 (1848)the two state court decisions on which West based his arguments. The state court reasoned that (1) the testimony at issue in West's case would be attributed to a co-defendant so that any such proof would be cumulative where the State concedes the co-defendant's guilt and (2) West's defense that "his participation was commanded at gun point by Martin would not have been corroborated by the excluded evidence." West, 767 S.W.2d at 396.
The state court also rejected West's argument as to exclusion of the Martin-Hunley tapes. Ibid. In Chambers, the Court reasoned that because the facts of the underlying crime tended to prove that there was only one perpetrator, any confession that implicated another party tended to also exculpate the defendant. In West's case, however, the evidence was consistent with there being two perpetrators. Thus, any evidence implicating Martin did not necessarily exculpate West.
The state court also raised concerns about corroboration and reliability. Ibid. The tapes were not recorded by jailhouse personnel. Rather they were made by an unknown inmate or inmates, without Martin's knowledge. West acquired the tapes through Ken Holt, a private investigator. Holt swore in an affidavit that he had acquired the tapes from Byron Bryan, Steve Hunley's attorney.
The court concluded that the tapes were properly excluded because: (1) unlike the defendant in Chambers, Martin was unavailable to the State or the defendant because he would have invoked the privilege against self-incrimination (a statement confirmed by West's attorney, who had spoken with Martin's attorney); (2) the record was completely silent as to whether the tape recordings were corroborated; and (3) Chambers does not require the admission of uncorroborated hearsay statements against penal interest. See West, 767 S.W.2d at 395-96.

4. West's habeas claims
In order for West to succeed on his claim he must demonstrate that the state court decision "(1) ... was contrary to, or involved an unreasonable application of, clearly established Federal Law, as determined by the Supreme Court of the United States; or (2) ... was based on an unreasonable determination of the facts...." 28 *559 U.S.C. § 2254(d). The relevant federal law was articulated by the Supreme Court in Chambers.
In Chambers, the issue was whether the trial court erred in preventing the defendant from introducing three witnesses, each of whom would have testified that another person had confessed to being the actual shooter of the victim. The trial court excluded proffered testimony as inadmissible under Mississippi's hearsay rule, which totally excluded hearsay statements against penal interest. Because the state's theory was that there was only a single shooter, the proffered testimony would have directly contradicted the state's argument that Chambers was that shooter. 410 U.S. at 298, 93 S.Ct. 1038. It also would have directly exculpated him by pointing to another suspect as the shooter. In holding that Chambers's due process rights were violated the Court wrote:
Few rights are more fundamental than that of an accused to present witnesses in his own defense. In the exercise of this right, the accused, as is required of the State, must comply with established rules of procedure and evidence designed to assure both fairness and reliability in the ascertainment of guilt and innocence. Although perhaps no rule of evidence has been more respected or more frequently applied in jury trials than that applicable to the exclusion of hearsay, exceptions tailored to allow the introduction of evidence which in fact is likely to be trustworthy have long existed. The testimony rejected by the trial court here bore persuasive assurances of trustworthiness and thus was well within the basic rationale of the exception for declarations against interest. That testimony also was critical to Chambers' defense. In these circumstances, where constitutional rights directly affecting the ascertainment of guilt are implicated, the hearsay rule may not be applied mechanistically to defeat the ends of justice.
Id. at 302, 93 S.Ct. 1038 (internal citations omitted).

i. Libby Woods's testimony
As noted above, the state court did not analyze the exclusion of Woods's testimony under federal law. Thus, the state cannot defend the decision as a reasonable application of federal law. Nevertheless, the decision might still be contrary to federal law if "the state court arrives at a conclusion opposite to that reached by [the Supreme] Court on a question of law .... [or] if the state court confronts facts that are materially indistinguishable from a relevant Supreme Court precedent and arrives at a result opposite to" that of the Supreme Court. Williams, 529 U.S. 362, 405-06, 120 S.Ct. 1495.
The state trial court, as with the trial court in Chambers, excluded Woods's testimony as inadmissible hearsay. Both parties agreed that the statement was actually hearsay and if it were to come in, it would have to be admitted under one of the hearsay exceptions. The trial judge asked West's attorney if he was offering the statement to prove the truth of the matter asserted. West's attorney did not address that question, but stated that he "would offer those statements against penal interest for the jury's deliberations as to whether or not my client is guilty of this particular murder."
The Tennessee Supreme Court, in reviewing the trial court's decision to exclude Woods's testimony, emphasized the cumulative nature of the evidencethat is, because the state had conceded that Martin was also a participant in the murders, Woods's testimony that Martin intended to kill Sheila Romines did not refute the *560 State's theory nor did it exculpate West. Furthermore, the testimony shed no light on West's theory that he was either under duress or was being dominated and forced by Martin to commit the murders. Though the state court did not consider Chambers, had it done so, there would have been more than adequate ground to distinguish Woods's testimony from the type of testimony at issue in Chambers. Thus, the Tennessee Supreme Court's decision in regard to Woods's testimony was not contrary to Chambers.

ii. Martin-Hunley tapes
In reviewing the trial court's decision to exclude the Martin-Hunley tapes from the guilt/innocence phase of the trial,[4] the Tennessee Supreme Court explicitly applied Chambers. Thus, the question is whether it unreasonably applied Chambers or arrived at a conclusion contrary to Chambers.
The state court again focused on the fact that the Martin-Hunley tapes were cumulative evidence and did "not exonerate [West], who was present, participating, aiding and abetting and his defense that his participation was commanded at gun point by Martin would not have been corroborated by the excluded evidence." West, 767 S.W.2d at 396. The court also noted that in Chambers, the would-be declarant, McDonald, was available for cross examination, whereas the would-be declarant in West's case, Martin, was unavailable to the State or to West because Martin invoked his Fifth Amendment rights. Thus, the Tennessee Supreme Court had adequate grounds to distinguish the Martin-Hunley tapes from the evidence in Chambers. The decision, therefore, was neither contrary to or an unreasonable application of Chambers.

C. Prosecutorial Misconduct
West alleged several instances of prosecutorial misconduct grouped into four categories: (1) the prosecutor deliberately misinformed the jury that the law was "self-executing" and that choosing or not choosing the death penalty was not their responsibility; (2) the prosecutor claimed that defense counsel was attempting to deceive or mislead the jury; (3) the prosecutor called West a liar and expressed his personal belief that West was a liar; and (4) the prosecutor asserted inflammatory facts not supported by the evidence. We address the first category of alleged misconduct separately, and the last three jointly.

1. The role of the jury in determining a capital sentence

a. The alleged misconduct
West objected to the following statements made by the prosecutor during closing argument:
The decision you are going to be called upon to make obviously is very serious, it is one of the most serious you will ever make. But, on the other hand, if you will listen to what the Judge tells you the law is, you will see that it is not necessarily a difficult decision in that sense. In the application of the law. Because the law provides certain guidelines, certain perimeters within which you are to consider the verdict, your secondary verdict in this case.

*561 . . .
See, the law in Tennessee, and the law of the land, in this sense, is self-executing, in the sense that the law mandates, requires a death sentence in certain situations, unless it is outweighed by other factors.
The law is clear. Your responsibility once again is to weigh proof, to make a finding of fact, apply the applicable law to those facts and the law provides the punishment, not you, not you. You do not set punishment in this case, per se. You make decisions based upon fact and the law, self-executing, based upon your weighing the facts.
. . .
Was [the mitigating evidence] enough to outweigh torture, the depravity, the atrociousness, and all of the other things the State contends it has shown? See. You have to weigh them. That is your function. And if the State tips the scales and proves those things to you beyond a reasonable doubt, and what you heard for the defendant today doesn't outweigh this ... then the penalty is death. That is the law. That is the law.
As the law states, and the Judge will tell you this, once the State proves aggravating circumstances, one or more, beyond a reasonable doubt, if they are not outweighed by mitigating circumstances the defendant shows you, the punishment shall be death. That is a matter of law. It is a matter of law.
I am not going to stand here and tell you that that is an easy application of the law, because it is not. It is a difficult application. But, just keep in mind, you don't impose the sentence, the law provides the sentence, you are merely finders of fact.
. . .
In this case, the State feels like justice in its purest form, once again, would be best served by the administration of the law.
West argues that these comments were constitutionally impermissibly under Caldwell v. Mississippi, 472 U.S. 320, 105 S.Ct. 2633, 86 L.Ed.2d 231 (1985).

b. State-court analysis
In Caldwell, the Supreme Court held that "it is constitutionally impermissible to rest a death sentence on a determination made by a sentencer who has been led to believe that the responsibility for determining the appropriateness of the defendant's death rests elsewhere." Id. at 328-29, 105 S.Ct. 2633. On direct appeal, the Tennessee Supreme Court addressed West's claims and agreed that the statements were inappropriate:
We agree that the district attorney's statements that "the law is self-executing", that the law "provides the punishment, not you", and the concluding statement that "you don't impose the sentence, the law provides the sentence, you are merely finders of fact", violate Caldwell. Such statements minimize the jury's role and allows [sic] them to feel that the responsibility for a death sentence rests elsewhere.
West, 767 S.W.2d at 399. The court then analyzed whether the violations were harmless, and determined that they were:
We are of the opinion that the three or four brief erroneous characterizations of the jury's role in determining the appropriateness of a death sentence were sufficiently corrected by the trial judge and the accurate portions of the district attorney's and the defendant's arguments stressing the proper responsibility of the jury. These clarifying measures contrast sharply with the situation in Caldwell... where the trial judge endorsed *562 the prosecutor's remarks. Thus we find that the errors were harmless beyond a reasonable doubt.
Id. at 399-400.

c. West's habeas claims
Because the Tennessee Supreme Court concluded that the prosecutor's statements during closing arguments did violate Caldwell, but were nevertheless harmless, the relevant "clearly established federal law" is both Caldwell and the harmless error rule of Brecht v. Abrahamson, 507 U.S. 619, 113 S.Ct. 1710, 123 L.Ed.2d 353 (1993). See Fry v. Piller, 551 U.S. 112, 127 S.Ct. 2321, 168 L.Ed.2d 16 (2007); Wilson v. Mitchell, 498 F.3d 491, 503 (6th Cir.2007). Brecht requires a court to ask "whether the error had substantial and injurious effect or influence in determining the jury's verdict." Brecht, 507 U.S. at 637, 113 S.Ct. 1710 (quoting Kotteakos v. United States, 328 U.S. 750, 776, 66 S.Ct. 1239, 90 L.Ed. 1557 (1946)).
The comment made by the prosecutor here is distinguishable from the comments at issue in Caldwell. In Caldwell, the prosecutor told the jury that the responsibility for determining the appropriateness of a death sentence did not rest with them but rather with the appellate court which would later review the case. See 472 U.S. at 325, 105 S.Ct. 2633. Additionally, the judge also told the jury that its decision would automatically be reviewed by the State Supreme Court. Ibid. By contrast, the prosecutor in this case clearly told the jury that it was the prosecutor's duty to prove aggravating factors and the jury's duty to weigh the evidence and then decide if there were aggravating factors and if those factors were outweighed by any mitigating circumstances. The judge also instructed the jurors that it was their duty to fix West's punishment as either death or life imprisonment and that each one must decide whether any mitigating circumstances were sufficiently substantial to outweigh the aggravating circumstances.
The Tenth Circuit reviewed a set of comments similar to the ones challenged here in Parks v. Brown, 860 F.2d 1545 (10th Cir.1988) (en banc), rev'd on other grounds sub nom. Saffle v. Parks, 494 U.S. 484, 110 S.Ct. 1257, 108 L.Ed.2d 415 (1990). There, the prosecutor told the jury:
But, you know, as you as jurors, you really, in assessing the death penalty, you're not yourself putting Robyn Parks to death. You just have become a part of the criminal-justice system that says when anyone does this, that he must suffer death. So all you are doing is you're just following the law, and what the law says, and on your verdict  once your verdict comes back in, the law takes over. The law does all of these things, so it's not on your conscience. You're just part of the criminal-justice system that says that when this type of thing happens, that whoever does such a horrible, atrocious thing must suffer death.
Now that's man's law. But God's law is the very same. God's law says that the murderer shall suffer death. So don't let it bother your conscience, you know.
Parks, 860 F.2d at 1549. The Tenth Circuit concluded "that Caldwell is inapplicable here because `none of the [prosecutor's] comments could have had the effect of misleading the jury into thinking that it had a reduced role in the sentencing process.'" Parks, 860 F.2d at 1550 (quoting Darden v. Wainwright, 477 U.S. 168, 184 n. 15, 106 S.Ct. 2464, 91 L.Ed.2d 144 (1986)).
The prosecutor's comments in Parks were more akin to the comments in this case than were the comments at issue in Caldwell. In Parks, as here, there was *563 no erroneous statement that appellate review relieves the jury of its obligations. Indeed, the prosecutor's comment in Parks that the decision to sentence a man to death is "not on your conscience" may be more troubling than the prosecutor's comments at issue here. Furthermore, as both the state court and the district court noted, the trial judge corrected the statements that allegedly minimized the jury's role. West, 767 S.W.2d at 399-400; West, No. 3:01-cv-91, slip op. at 78. For these reasons we hold that it was not unreasonable, under Caldwell and Brecht, for the Tennessee Supreme Court to conclude that the prosecutorial error in regard to minimizing the role of the jury did not have a "substantial and injurious effect or influence in determining the jury's" imposition of West's capital sentence.

2. The prosecutor: claimed that defense counsel was attempting to deceive or mislead the jury; called West a liar; and made inflammatory remarks not supported by the evidence

a. The alleged misconduct
West alleges that during his closing argument, the prosecutor told the jury that the defense counsel was attempting to mislead or confuse the jury on eleven separate occasions. Of those eleven instances, ten involved variations of the phrase "[t]hat is an attempt to blow a little smoke in your eyes," or "[a]nother attempt to throw a little sand in your eyes." In the eleventh instance the prosecutor referred to one of defense counsel's arguments as an "attempt that defense counsel has made in this case, in order to confuse you...."
West also objected to statements made during the prosecution's closing in which the prosecutor called West a liar. "Now you are a gifted liar, Mr. West. You are not just a liar...." West also objects to several other statements made during closing arguments:
* Can you believe that he had the audacity to say that Sheila Romines consented to have sex with him ... the most ludicrous, cruel lie that has ever been told in Union County history.
* I guess the truth is not important, at least to Mr. West.
* He said that Ronnie [Martin] took the knife and killed both women. We know that that is a lie. We know that that is a lie.
Finally, West argues that the prosecutor made the following inflammatory comments not supported by the evidence:
* [I don't] know whether West or Martin, or both, had taken anything other than alcohol.
* Are we going to turn Stephen West loose, let him escape from responsibility for the crimes that he has committed, because he and Mr. Martin were able to successful dispose of the murder weapons or successfully wash the blood off the murder weapons.
* [A]fter the butchery, [West and Martin] go in and clean themselves up before they leave.
West objects to several comments in which the prosecutor speculated as to Martin and West's actions during the commission and cover-up of the crime, arguing that they were not supported by the record. We do not repeat them all here as they are explored in detail in the district court opinion. West, No. 3:01-cv-91, slip op. at 117-20.

b. Procedural default and fair presentment
The State argues that West procedurally defaulted in challenging the first and third sets of statements by failing to raise them in the state court proceedings as "federal *564 constitution violations." Appellee's Br. 43. While it is true that West cited only state law in those arguments, there are other ways in which he could have fairly presented his constitutional claim to the state courts. See Baldwin, 541 U.S. at 32, 124 S.Ct. 1347. As we stated in McMeans v. Brigano, 228 F.3d 674 (6th Cir.2000):
This court has noted four actions a defendant can take which are significant to the determination whether a claim has been "fairly presented": (1) reliance upon federal cases employing constitutional analysis; (2) reliance upon state cases employing federal constitutional analysis; (3) phrasing the claim in terms of constitutional law or in terms sufficiently particular to allege a denial of a specific constitutional right; or (4) alleging facts well within the mainstream of constitutional law.
Id. at 681.
West's allegations in regard to the first set of statements were sufficiently particular and well within the mainstream of constitutional law. West specifically stated that the prosecutor's comments about defense counsel attempting to mislead the jury were "highly prejudicial and improper." He used the same phrase in objecting to the prosecutor's statements that were allegedly unsupported by the record. Though this statement was not close to an invocation of the Supreme Court's standard for judging prosecutorial misconduct, it was evocative of language that we articulated in United States v. Leon, 534 F.2d 667 (6th Cir.1976). As we stated in Leon, we evaluate claims of prosecutorial misconduct using four factors, including "whether the remarks tended to mislead the jury or to prejudice the accused." Id. at 679. See United States v. Carroll, 26 F.3d 1380, 1384 (6th Cir.1994) (explaining Leon). Indeed, in Leon, the court found that the remarks at issue were "improper and highly prejudicial," Leon, 534 F.2d at 678, the very same phrase used by West. As for West's arguments about the second set of statements, West quoted from State v. Smith, 456 A.2d 16 (Me.1983), explicitly noting that the state case was citing a federal case, United States v. Gonzalez Vargas, 558 F.2d 631 (1 st Cir.1977). West also cited United States v. Bess, 593 F.2d 749 (6th Cir.1979). We accordingly hold that West fairly presented his federal claims to the state court and that he is not procedurally barred from pursuing those claims here.

c. State-court analysis
The state court analyzed West's claim under state law, relying on State v. Buck, 670 S.W.2d 600, 609 (Tenn.1984) and State v. Beasley, 536 S.W.2d 328 (Tenn.1976), which held that a prosecutor's argument should be supported by evidence introduced at trial and the reasonable inferences to be drawn from that evidence and that a lawyer's personal opinion as to the credibility of a witnesses should not be injected into argument. However, as the state court noted, Beasley cited with approval a number of cases in which the courts refused to find misconduct when the prosecutor's reference to a "lying" defendant or defense witnesses was supported by evidence in the record. West, 767 S.W.2d at 394.
The court ultimately found that some of the prosecutor's references had "borderline support" and could "through reasonable inference [ ] be drawn from evidence" and that some were not based upon evidence or proper inferences therefrom. For example, the comment that he didn't "know whether Mr. West or Mr. Martin, or both, had taken anything other than alcohol," was unsupported. Id. at 394-95. The state court also acknowledged that, under state law, it was "improper for the *565 district attorney to tell the jury that defense counsel was `trying to throw sand in the eyes of the jury' and `blowing smoke in the face of the jury.'" West, 767 S.W.2d at 395. The court dismissed the weight of the improper comments, however, holding that "viewed in the context in which the improper remarks occurred and in light of the overwhelming evidence of defendant's guilt the instances of prosecutorial misconduct were harmless beyond a reasonable doubt." Ibid.

d. West's habeas claims
Again, the issue is whether the state court decision was contrary to or an unreasonable application of clearly established federal law. Under the relevant Supreme Court precedent, prosecutorial misconduct is grounds for reversal if that conduct "`so infected the trial with unfairness as to make the resulting conviction a denial of due process.'" Darden, 477 U.S. at 181, 106 S.Ct. 2464 (quoting Donnelly v. DeChristoforo, 416 U.S. 637, 643, 94 S.Ct. 1868, 40 L.Ed.2d 431 (1974)). The appropriate standard for review on a claim of prosecutorial misconduct alleged in a petition for a writ of habeas corpus is "the narrow one of due process, and not the broad exercise of supervisory power." Donnelly, 416 U.S. at 642, 94 S.Ct. 1868. "We do not possess supervisory powers over state court trials." Byrd v. Collins, 209 F.3d 486, 529 (6th Cir.2000) (citing Cook v. Bordenkircher, 602 F.2d 117, 119 n. 5 (6th Cir.1979), for the proposition that "it is the responsibility of the [state courts] to police their prosecutors; we have no such authority."). As we explained in Byrd:
In making this determination, we must bear in mind that the touchstone of due process analysis ... is the fairness of the trial, not the culpability of the prosecutor. Therefore, even if the prosecutor's conduct was undesirable or even universally condemned, it does not constitute a due process violation unless the conduct was `so egregious so as to render the entire trial fundamentally unfair.' Indeed, our case law demonstrates the extreme nature of prosecutorial misconduct required for a federal court to issue the writ.
209 F.3d at 529 (internal citations and quotation marks omitted).
It is improper to personally attack defense counsel or argue that counsel is attempting to mislead the jury. Broom v. Mitchell, 441 F.3d 392, 412-13 (6th Cir. 2006). A prosecutor should not give his own opinion as to the credibility of witness. Hodge v. Hurley, 426 F.3d 368, 378-79 (6th Cir.2005); see also Caldwell v. Russell, 181 F.3d 731, 737 (6th Cir.1999) ("Ordinarily, a prosecutor may not express a personal opinion concerning the guilt of the defendant or the credibility of trial witnesses, because such personal assurances of guilt or vouching for the veracity of witnesses by the state's representative exceeds the legitimate advocate's role by improperly inviting the jurors to convict the defendant on a basis other than a neutral independent assessment of the record proof."); United States v. Carroll, 26 F.3d 1380, 1387-89 (6th Cir.1994); United States v. Dandy, 998 F.2d 1344, 1353 (6th Cir.1993).
Nevertheless, this does not mean that the prosecution cannot attack the defendant's credibility or even assert that the defendant is lying. As we explained in United States v. Francis, 170 F.3d 546 (6th Cir.1999):
This Court has held that a prosecutor may assert that a defendant is lying during her closing argument when emphasizing discrepancies between the evidence and that defendant's testimony. To avoid impropriety, however, such *566 comments must reflect reasonable inferences from the evidence adduced at trial. Again, misconduct occurs when a jury could reasonably believe that the prosecutor was, instead, expressing a personal opinion as to the witness's credibility.
Id. at 551 (internal citations and quotation marks omitted).
Assessing West's claims therefore is a two-step process. First, the court must determine whether a prosecutor's conduct and remarks were improper. Second, the court must determine whether the conduct warrants habeas relief. The four factors considered when evaluating whether relief is warranted are:
(1) "the degree to which the remarks complained of have a tendency to mislead the jury and to prejudice the accused;"
(2) "whether they are isolated or extensive;"
(3) "whether they were deliberately or accidentally placed before the jury;" and
(4) "the strength of the competent proof to establish the guilt of the accused."
Pritchett v. Pitcher, 117 F.3d 959, 964 (6th Cir.1997).
The Tennessee Supreme Court used a similar set of factors from Buck in assessing West's claims on direct appeal. The Buck factors are:
(1) "the conduct complained of viewed in context and in light of the facts and circumstances of the case;"
(2) "the curative measures undertaken by the Court and the prosecution;"
(3) "the intent of the prosecutor in making the improper statement;"
(4) "the cumulative effect of the improper conduct and any other errors in the record;" and
(5) "the relative strength or weakness of the case."
670 S.W.2d at 609.
Though the Tennessee Supreme Court did not walk through each of the factors, it clearly applied them. The district court gave a more detailed analysis of the alleged misconduct. Both courts came to the conclusion that the misconduct did not amount to reversible error. We agree.
While it is true that the prosecutor asserted his personal opinion as to West's credibility, the error was harmless given the evidence submitted to the jury that West had contradicted himself on numerous occasions and had given varying accounts of crimes. The same is true for the prosecutor's comments that defense counsel was intentionally misleading the jury. As the district court pointed out, the state's closing argument took up thirty pages of trial transcript. While there were eleven instances of inappropriate comments, none were lengthy; they were all short asides.
As for the comments allegedly not supported by the record, many of them were actually supported. For example, West complains of the prosecutor's speculation about West and Martin cleaning the murder weapon. However, one of West's statements to the police was read to the jury by Agent Scott. In that statement West had stated, "I wiped off the guns and took them to the mother's bedroom." J.A. 1732. The district court opinion explores more of the allegedly-unsupported statements, demonstrating that many of the inferences were based on testimony and evidence in the record and we need to repeat the analysis here.
Moreover, even if every statement was not fully supported, the comments at issue could hardly be said to have "so infected the trial with unfairness as to make the *567 resulting conviction a denial of due process." Darden, 477 U.S. at 181, 106 S.Ct. 2464. Accordingly, we affirm the district court's denial of relief on prosecutorial misconduct.

III. CONCLUSION
The district court's denial of West's petition for habeas corpus is AFFIRMED.
KAREN NELSON MOORE, Circuit Judge, dissenting in part and concurring in the judgment only in part.
After paying mere lip-service to recent Supreme Court precedent, the majority in this case applies a pre-Wiggins v. Smith, 539 U.S. 510, 123 S.Ct. 2527, 156 L.Ed.2d 471 (2003), and Rompilla v. Beard, 545 U.S. 374, 125 S.Ct. 2456, 162 L.Ed.2d 360 (2005), interpretation of the Strickland v. Washington, 466 U.S. 668, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984), standard for ineffective-assistance-of-counsel claims. Because I conclude that, under the Strickland standard as explained in Wiggins and Rompilla,[1] West has met his burden of proof for his claim of ineffective assistance of counsel at the penalty phase, I respectfully dissent.
The majority correctly states that, to prove ineffective assistance of counsel, a defendant must show that (1) counsel's performance was deficient and (2) the deficient performance prejudiced the defendant. The majority then correctly concludes that the state courts' applications of Strickland and Lockhart v. Fretwell, 506 U.S. 364, 113 S.Ct. 838, 122 L.Ed.2d 180 (1993), were contrary to or involved an unreasonable application of established Federal law. However, the majority then cites Burger v. Kemp, 483 U.S. 776, 107 S.Ct. 3114, 97 L.Ed.2d 638 (1987), for the proposition that counsel need not "mount an all-out investigation into petitioner's background in search of mitigating circumstances [if the decision] was supported by reasonable professional judgment." Majority Op. at 555 (quoting Burger, 483 U.S. at 794, 107 S.Ct. 3114). Applying this law, the majority holds that "West's counsel, in fact, did a fair amount of investigation in preparation for the mitigation phase," and thus West has not shown ineffective assistance of counsel. Majority Op. at 555-57.
The majority's opinion ignores both recent Supreme Court cases that have explained the standard applied to claims of ineffective assistance of counsel under Strickland and Sixth Circuit precedent. Under Strickland, failure reasonably to investigate a defendant's background and to present mitigating evidence at sentencing can amount to ineffective assistance of counsel. Wiggins, 539 U.S. at 522, 123 S.Ct. 2527 (noting counsel has an "obligation to conduct a thorough investigation of the defendant's background" before making tactical decisions regarding what mitigating evidence to present) (quoting Williams v. Taylor, 529 U.S. 362, 396, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000)). The court must consider whether a reasonable attorney, given the same evidence as the counsel in question, would have investigated something further. Wiggins, 539 U.S. at 527, 123 S.Ct. 2527 ("In assessing the reasonableness of an attorney's investigation, however, a court must consider not only the quantum of evidence already known to counsel, but also whether the *568 known evidence would lead a reasonable attorney to investigate further.") (emphases added). Further, counsel cannot simply rely upon information the defendant and his family provided. See Rompilla, 545 U.S. at 389, 125 S.Ct. 2456 (requiring counsel to review a prior-conviction file rather than rely solely on statements made by the defendant and his family). As this circuit has repeatedly held, counsel has an independent duty to investigate mitigating evidence, even if the defendant is reluctant. Harries v. Bell, 417 F.3d 631, 638 (6th Cir.2005); Hamblin v. Mitchell, 354 F.3d 482, 492 (6th Cir.2003); Coleman v. Mitchell, 268 F.3d 417, 449-50 (6th Cir.2001); Carter v. Bell, 218 F.3d 581, 596-97 (6th Cir.2000).[2]
Applying the Strickland standard, I conclude that it is clear that West has met his burden. Several pieces of evidence demonstrate that West's counsel was deficient. First, Jerry Summers ("Summers") and Paul Morrow ("Morrow"), two seasoned attorneys who had tried several capital cases, testified during the post-conviction hearing that counsel was deficient in this case. J.A. at 1674, 1677 (Tenn. Ct.Crim. App. Op. at 10, 13). Second, West's sister testified at the post-conviction hearing that she informed counsel of West's childhood abuse and that counsel told her that it was not relevant. Third, Summers testified that two facts should have raised red flags to counsel that West may have suffered abuse: (1) the fact that West was born in a mental hospital and (2) West's statement that he had no memories before the age of ten. J.A. at 1673-74 (Tenn. Ct.Crim.App. Op. at 9). West's counsel ignored these key pieces of evidence that would have led a reasonable attorney to investigate further. Thus, I conclude that West's counsel was deficient.
I further conclude that West was prejudiced by this deficiency. To prove prejudice, a defendant must show that "there is a reasonable probability that, but for counsel's unprofessional errors, the result of the proceeding would have been different." Strickland, 466 U.S. at 694, 104 S.Ct. 2052. In this case, had counsel presented evidence of abuse and its effects on West, it is extremely likely that at least one juror would have determined that West's explanation for what happened to him while the crime took placeessentially that he frozewas plausible, making the death penalty unwarranted. As summarized by the Tennessee Court of Criminal Appeals, Morrow "testified that the prejudice that was shown in this case was that the jury did not hear the `psychological or lay witnesses that would have made somewhat comprehensible his actions on that day [day of the murders].'" J.A. at 1677 (Tenn. Ct.Crim.App. Op. at 13) (alteration in original). Further, if money had been available originally for doctors, Dr. Coleman's and Dr. Dudley's evidence of West's psychological makeup would have been provided, in addition to the various witnesses who could have spoken about West's childhood abuse.[3]
*569 Finally, though Dr. Bursten testified at the post-conviction hearing that West stated during their interview that he had not been abused, the relevance of such evidence is questionable for two reasons. First, Morrow testified during the post-conviction hearing that West's statement to Dr. Bursten was not necessarily reliable because often defendants who have truly been abused are "the worst person to talk to" about the abuse "because he or she is usually embarrassed or does not understand its significance." J.A. at 1676 (Tenn. Ct.Crim.App. Op. at 12). Second, the fact that West stated that he was not abused is not dispositive when a wealth of evidence points to the conclusion that he was abused. See, e.g., Coleman, 268 F.3d at 450 ("`The sole source of mitigating factors cannot properly be that information which defendant may volunteer; counsel must make some effort at independent investigation in order to make a reasoned, informed decision as to their utility.'") (quoting Carter v. Bell, 218 F.3d 581, 596 (6th Cir.2000)).
Counsel's failure to present this evidence of abuse was prejudicial because it would have served to mitigate the prosecution's theory that West stabbed the victims, allowing the jury to believe both (1) Dr. Evans's interpretation that only one person made the stab wounds instead of Dr. Blake's interpretation that two people stabbed the victims, State v. West, 767 S.W.2d 387, 392 (Tenn.1989), and (2) that, even though West was physically larger than Martin, he was mentally unable to stop Martin from stabbing the victims. This evidence would have changed West's mitigation case from one about West's character as "a good and decent citizen," "never before ... in trouble with the law," "a veteran," and "a loving husband and a soon-to-be father," Majority Op. at 556, to one that actually explained why West behaved the way that he behaved. As in Rompilla, "[t]his evidence adds up to a mitigation case that bears no relation" to the mitigation case actually presented by counsel. Rompilla, 545 U.S. at 393, 125 S.Ct. 2456.
The majority claims that, although the jury may have believed West's evidence and "chosen to spare his life," the jury may also have been unswayed by the evidence. The majority concludes that "[i]t is not enough for this court to speculate that the jury would have chosen the former path." Majority Op. at 556. This statement flies in the face of Supreme Court precedent:
[A]lthough we suppose it is possible that a jury could have heard [all the evidence] and still have decided on the death penalty, that is not the test. It goes without saying that the undiscovered mitigating evidence, taken as a whole, might well have influenced the jury's appraisal of [the defendant's] culpability, and the likelihood of a different result if the evidence had gone in is sufficient to undermine confidence in the outcome actually reached at sentencing.
Rompilla, 545 U.S. at 393, 125 S.Ct. 2456 (emphasis added) (internal quotation marks and citations omitted); see also Harries, 417 F.3d at 640. Therefore, I conclude that, taken as a whole, West's evidence provides "a reasonable probability" that the result of the proceeding would have been different. Thus, I would hold that West has proven ineffective assistance of counsel at the penalty phase of his trial, and I would REVERSE the judgment of the district court regarding the penalty *570 phase. With respect to the guilt phase issues addressed by the majority, I concur in the judgment only. Thus, I would GRANT a conditional writ of habeas corpus with respect to the penalty phase.
NOTES
[1]  The investigator was hired to find evidence that Martin was a member of a satanic cult and to prove that Martin had the motive and mental capacity to torture the victims, whereas West did not.
[2]  (1) An affidavit of Dr. Keith Caruso, a psychiatrist who never examined West, but who gave an evaluation of West's competency based records and documents provided to him; (2) an affidavit of Debra West Harless, West's sister; (3) a birth record from Community Hospital; (4) an affidavit of Karen West Bryant, West's former wife; (5) an affidavit of Vestor West, West's father; (6) West's military discharge papers; (7) An affidavit of Patty Rutherford, West's manager at McDonald's; (8) a case report of Dr. Claudia Coleman, who conducted a clinical interview with West, administered several psychological tests, and reviewed West's case file; and (9) a case report of Dr. Richard Dudley, a psychologist who evaluated West based on records and other materials.
[3]  Though AEDPA constrains the court to look to the law as clearly established at the time of the time the state conviction became final, Williams v. Taylor, 529 U.S. 362, 380, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000), this court may rely on any later decisions analyzing or explaining the law (as opposed to creating new law). Strickland was clearly established well before West's criminal trial concluded in 1987. We can rely on Rompilla, Wiggins, and Williams because they merely explain Strickland.
[4]  The trial judge ruled that West could introduce the Martin-Hunley tapes at the sentencing phase (in accordance with Green v. Georgia, 442 U.S. 95, 99 S.Ct. 2150, 60 L.Ed.2d 738 (1979)). However, the trial judge cautioned that if West admitted those tapes, he would also allow the State to introduce recordings of Martin's statements to the police, which implicated West. West subsequently chose not to introduce the tapes during the sentencing phase.
[1]  Because Rompilla and Wiggins merely explain the Strickland standard and do not establish new law, it is appropriate to rely on those cases when deciding West's ineffective-assistance-of-counsel claim "even though those cases were decided after [West's] convictions became final." Jells v. Mitchell, 538 F.3d 478, 491 n. 2 (6th Cir.2008); see also Hamblin v. Mitchell, 354 F.3d 482, 487 (6th Cir.2003).
[2]  The majority does not cite any of these binding Sixth Circuit cases in its opinion.
[3]  The majority contends that West's objection "to the trial court's sua sponte ordering of a psychological examination to determine competency" resulted in the trial court later denying West's counsel funds for experts and led to counsel's failure to discover mitigating evidence. Majority Op. at 555. The majority cites Fautenberry v. Mitchell, 515 F.3d 614 (6th Cir.2008), for the proposition that West's "lack of cooperation" in some way hinders his current claim of ineffective assistance of counsel. Majority Op. at 555-56. Fautenberry is distinguishable from this case. There, the defendant refused to be examined by the expert charged with discovering brain impairments relevant to mitigation. Fautenberry, 515 F.3d at 625. In this case, West did not object to any examination aimed at discovering ailments pertinent to mitigation, only to an examination focused on the issue of competency.
