
619 F.3d 586 (2010)
Charles Walton WRIGHT, Petitioner-Appellant,
v.
Ricky BELL, Warden, Riverbend Maximum Security Institution, Respondent-Appellee.
No. 07-5305.
United States Court of Appeals, Sixth Circuit.
Argued: June 17, 2010.
Decided and Filed: August 31, 2010.
*588 ARGUED: Kelley J. Henry, Federal Public Defender's Office, Nashville, Tennessee, for Appellant. James E. Gaylord, Office of the Attorney General, Nashville, Tennessee, for Appellee. ON BRIEF: Kelley J. Henry, Federal Public Defender's Office, Nashville, Tennessee, for Appellant. James E. Gaylord, Office of the Attorney General, Nashville, Tennessee, for Appellee.
Before: COLE, ROGERS, and McKEAGUE, Circuit Judges.

OPINION
ROGERS, Circuit Judge.
Charles Walton Wright, sentenced to death for committing two 1984 murders, appeals from a district court judgment denying his petition for a writ of habeas corpus. The following issues have been certified for appellate review: (1) whether the trial court's admission of a medical examiner's testimony speculating about the sequence in which the two victims were killed denied Wright a fundamentally fair trial; (2) whether trial counsel provided effective assistance at trial and sentencing; (3) whether the prosecution offered Wright a life sentence in exchange for a guilty plea and, if so, did such an offer constitute relevant mitigating evidence; and (4) whether certain of the claims raised in Wright's amended habeas petition were procedurally defaulted. Because each of these issues was correctly resolved in the Warden's favor, the district court properly denied Wright habeas relief.

I.
A Tennessee jury convicted Wright of two counts of premeditated murder in the first degree for the shooting deaths of Douglas Alexander and Gerald Mitchell. Wright received a life sentence for the killing of Mitchell, but was sentenced to death for Alexander's murder. In an opinion affirming Wright's sentence on direct *589 appeal, the Supreme Court of Tennessee described the facts as follows:
Testimony in the case was both protracted and conflicting. Appellant himself gave numerous conflicting and convoluted versions of the events which led to the homicides in the afternoon of July 18, 1984, in a public park in Davidson County, Tennessee. Appellant and both victims were residents at that time of Murfreesboro, in Rutherford County, Tennessee, although appellant had in the past resided in Nashville. Appellant and the victim Mitchell were, by appellant's own admission, involved in trafficking in illegal narcotics. Alexander may also have been involved. Their involvement was such that police officials in Murfreesboro had prepared a search warrant to search the residence of appellant for possession and sale of marijuana, but the warrant was never actually issued or served because of the homicides.
It appears without question that all three men came to Nashville in the afternoon of July 18, 1984, for the purpose of purchasing contraband narcotics with the intent to traffic therein.
At the trial, appellant admitted shooting and killing Mitchell and leaving the bodies of both Mitchell and Alexander in the public park. It was his contention that Mitchell had previously shot Alexander. The jury obviously concluded otherwise.
The homicides occurred in the late afternoon, probably around 6 p.m. Several persons in the park heard three shots. When the bodies were found, Alexander had been shot twice. One bullet penetrated his forearm, apparently a defensive wound, and then penetrated his face, entering at the corner of his mouth on the right side and being found lodged in the left cheek. This shot apparently did not cause death and would not necessarily have been fatal. The second shot was in the left rear portion of his skull. According to the only medical expert who testified, this shot would have produced unconsciousness instantly and death within a short time.
Mitchell was shot once, below the left ear. The medical expert testified that this shot would have produced unconsciousness immediately and death within a few minutes. The body of Mitchell was found face down on the top of a knoll in the park. The body of Alexander was some 50 to 60 feet away, downhill, and near the top of a flight of steps leading to the knoll from a small parking area below.
A vehicle later identified as that belonging to Alexander was observed being driven by a single occupant away from the park. The next day the car was found in Murfreesboro, and appellant admitted that he drove the vehicle from the park in Nashville to a park in Murfreesboro where he abandoned it. Appellant admitted borrowing a pistol from one Jessie King in Murfreesboro. Ballistics showed that this was the weapon from which the fatal shots were fired. Appellant admitted being in possession of the pistol after the homicide and returning it to King. It was his contention, however, that prior to the homicide he had let Mitchell borrow the pistol. He said that Mitchell shot Alexander, and appellant then retrieved the pistol from Mitchell and shot the latter.
Appellant denied any involvement in the homicide for several days and gave highly misleading and false information to many witnesses who testified, as well as to investigating police officials. The numerous discrepancies in the various versions which he gave of the events of July 18 were explored in depth at the trial, including introduction at the instance of *590 his own counsel of a lengthy and admittedly false statement given to the police. It is not necessary here to review the convoluted and often confusing testimony. Essentially, appellant insisted that the three men had come to Nashville to purchase drugs and to sell them later in Murfreesboro. He admitted his own rather extensive involvement in illicit narcotics. Appellant said, however, that Mitchell knew the contact in Nashville from whom the marijuana was to be purchased. He testified that he did not accompany Alexander and Mitchell in making the purchase, although both he and Mitchell supplied substantial funds for the purchase. He remained where they let him out of the car. He said that when Alexander and Mitchell returned to pick him up in Alexander's automobile, they were quarreling. He testified that the drug transaction was only partly completed, and the parties were going to have to wait for about an hour to obtain the rest of the marijuana. Appellant testified that he suggested that they go to the park, which is located not far from the residence of appellant's mother, and that they proceed to bag such marijuana as had already been obtained. He said that Mitchell and Alexander went to the top of the knoll while he stayed in the car, that he heard two shots and then ran up the steps. There he found that Alexander had been shot by Mitchell. He took the pistol from Mitchell, struck the latter with his fist, and then shot him behind the ear.
It is clear that the jurors were not bound to accept this testimony, which was given at trial but which was markedly different from the numerous previous accounts which had been given by appellant. There was abundant testimony from which the jury could have found, as it did, that appellant committed both murders. The jury acquitted appellant of counts of murder committed in the perpetration of robbery in connection with each homicide, but it found that each homicide was premeditated murder in the first degree.
In the numerous issues presented on appeal by counsel for appellant, the sufficiency of the evidence to sustain the verdicts at the guilt hearing is not questioned and need not be further discussed in detail.
At the sentencing hearing the State announced that it would not seek the death penalty in the homicide of Mitchell. It was the theory of the State that Mitchell and appellant had had a quarrel over previous drug transactions. There was hearsay testimony, not objected to, that some children in the park had heard quarreling taking place just before the shots were fired in the present case. It was one theory of the State that appellant shot Mitchell as a result of this quarrel and then shot Alexander to eliminate him as a witness or to prevent appellant's apprehension and arrest. The other theory of the State was that the two homicides were intimately connected and that, regardless of the order in which they occurred, the second was committed while appellant was in the course of committing, attempting to commit or escaping from the first homicide.
Only two aggravating circumstances were relied upon by the State in its pretrial notice that the death penalty would be sought. At the sentencing hearing the trial judge submitted both circumstances to the jury, the two provisions being T.C.A. § 39-2-203(i)(6), to the effect that the murder was committed for the purpose of avoiding, interfering with, or preventing a lawful arrest or prosecution of the accused or of another, and T.C.A. § 39-2-203(i)(7), to the effect *591 that the homicide was committed while the accused was engaged in committing, attempting to commit, or fleeing after committing another first degree murder. The jury did not find the evidence sufficient to sustain the first of the foregoing statutory provisions but did find that the second was supported by the evidence. It found no mitigating circumstances sufficient to outweigh this aggravating circumstance and recommended the death penalty. The trial judge concurred in the conclusion of the jury.
State v. Wright ("Wright I"), 756 S.W.2d 669, 671-73 (Tenn.1988).
After the Supreme Court of Tennessee affirmed Wright's conviction and sentence on direct appeal, Wright filed several petitions for post-conviction relief in the Tennessee state courts. In May of 1989, Wright, without the assistance of counsel, filed his first petition for post-conviction relief. In September of that year, Wright filed an amended petition (the "1989 petition"), this time with the assistance of counsel. The trial court conducted an evidentiary hearing, but denied the petition. The Tennessee Court of Criminal Appeals affirmed the trial court's decision. Wright v. State ("Wright II"), No. 01C01-9105-CR-00149, 1994 WL 115955, at *22 (Tenn. Crim.App. Apr.7, 1994). The Supreme Court of Tennessee denied Wright's application for permission to appeal in September of 1994. In August of 1991, while the 1989 petition was still pending, Wright, acting pro se, filed a second petition for post-conviction relief (the "1991 petition"). The trial court denied the motion as "redundant and unnecessary," and Wright did not appeal that decision.
In January of 1995, Wright, once again assisted by counsel, moved to vacate the order dismissing the 1991 petition and also filed a third petition for post-conviction relief in the state trial court (the "1995 petition"). The trial court denied both the 1995 petition and the motion to vacate the order dismissing the 1991 petition. On appeal, the Tennessee Court of Criminal Appeals affirmed both aspects of the trial court's decision. Wright v. State ("Wright III"), No. 01C01-9506-CR-00211, 1997 WL 126818, at *1 (Tenn.Crim.App. Mar.20, 1997). The Tennessee Supreme Court granted review to determine whether Wright's due process rights were violated when the lower courts applied the three-year statute of limitations to a Brady claim not relevant to the instant appeal, but held that the state's interest in preserving final judgments outweighed Wright's interest in litigating the claim. Wright v. State (Wright IV), 987 S.W.2d 26 (Tenn.1999).
In October of 1999, Wright filed a pro se petition for a writ of habeas corpus in federal district court. The district court appointed counsel, and Wright filed an amended petition in June of 2000. The State moved for summary judgment, which the district court denied in part and granted in part. The court addressed eleven claims from Wright's original petition for post-conviction relief and concluded that each claim lacked merit. Memorandum of February 16, 2006, at 27-58. The court determined (1) that any error in the admission of testimony from Dr. Harlana medical examiner who speculated at the sentencing phase of the trial that Mitchell was shot before Alexanderwas harmless error that did not deprive Wright of a fundamentally fair trial, Memorandum of February 16, 2006 at 47. The court also determined (2) that Wright's attorneys had not performed deficiently at the sentencing phase of the trial. Memorandum of February 16, 2006 at 34-39. The court then held an evidentiary hearing on Wright's claim that he should have been allowed to present evidence of the plea negotiations at the sentencing phase of the trial; the *592 court then granted the State's motion for summary judgment. The court determined that (3) the State never offered Wright a life sentence in exchange for a guilty plea, Memorandum of February 15, 2007, at 9-10, and (4) that Wright's claims that were not otherwise addressed had been procedurally defaulted. Memorandum of February 15, 2007 at 60. Wright obtained a certificate of appealability on the four above issues and filed this timely appeal.

II.
The district court correctly determined that Wright was not entitled to habeas relief. As the Supreme Court of Tennessee determined, the admission of Dr. Harlan's testimony at the sentencing phase of the trial was harmless because, under the aggravating circumstance found by the jury, the sequence of the murders did not matter. With respect to Wright's ineffective assistance of counsel claim, the state appellate court's decision that Wright's attorneys' performance at the sentencing phase was not constitutionally deficient was neither contrary to clearly established federal law nor an unreasonable application of federal law. Third, regardless of whether the State ever actually offered Wright a life sentence in exchange for a guilty plea prior to trial, the evidence of plea negotiations was not relevant mitigation evidence. Finally, the district court correctly determined that the state courts had applied a procedural time bar to the claims presented for the first time in Wright's 1991 and 1995 petitions for post-conviction relief, and that therefore, Wright has procedurally defaulted the claims brought only in those petitions. Accordingly, Wright is not entitled to habeas relief.

A. The Admission of Dr. Harlan's Testimony
The Supreme Court of Tennessee correctly determined that any error relating to the admission of Dr. Harlan's testimony as to the sequence of the murders was harmless because, under the aggravating circumstance ultimately accepted by the jury, the sequence of the murders did not matter.
During the sentencing phase of the trial, the trial court admitted, over Wright's objection, the testimony of medical examiner Charles Harlan, who testified at the guilt phase about his examination of the bodies at the scene of the crime. Dr. Harlan's testimony at the sentencing hearing concerned, among other things, his theory that Mitchell had been shot first and Alexander had been shot immediately thereafter. The Supreme Court of Tennessee determined that the trial judge should not have allowed Harlan to testify as to the sequence of the murders:
In our opinion, the trial judge erred in admitting Dr. Harlan's opinion as to the sequence of events. His testimony as to the nature and extent of the wounds and the effect of the gunshots upon the victims was obviously within the range of his expertise. His conclusion that Alexander was shot later than Mitchell was based on the assumption that Alexander had fled downhill. This conclusion is nothing more than speculation.
Wright I, 756 S.W.2d at 673. The court held that the error was harmless, however, because the jury rejected the first aggravating circumstance offered by the statemurder to avoid arrest or prosecutionand therefore the jury did not accept Dr. Harlan's testimony that Alexander was shot after Mitchell to prevent Wright's arrest. Id. The district court denied Wright habeas relief for the same reason, stating that Wright "has not shown that *593 the admission of Dr. Harlan's testimony resulted in fundamental unfairness given the jury's rejection of his opinion." Memorandum of February 16, 2006, at 48.
The admission of Dr. Harlan's testimony does not warrant habeas relief because it did not have a substantial and injurious effect on Wright's trial. Before the state courts, Wright framed his claims relating to Dr. Harlan's testimony as violations of state evidentiary law; he never presented any federal claims relating to that testimony.[1] A federal court conducting collateral habeas review of a state-court judgment involving constitutional error will grant habeas if the error "`had substantial and injurious effect or influence in determining the jury's verdict.'" Brecht v. Abrahamson, 507 U.S. 619, 623, 113 S.Ct. 1710, 123 L.Ed.2d 353 (1993) (quoting Kotteakos v. United States, 328 U.S. 750, 776, 66 S.Ct. 1239, 90 L.Ed. 1557 (1946)). The Supreme Court of Tennessee correctly determined that any error in admitting Dr. Harlan's testimony was harmless because the jury did not accept Dr. Harlan's sequence of events. As the state court discussed, the jury did not find the evidence sufficient to sustain the aggravating circumstance then listed in Tenn.Code Ann. § 39-2-203(i)(6), "murder committed for the purpose of avoiding, interfering with, or preventing a lawful arrest or prosecution of the accused or of another." Wright I, 756 S.W.2d at 672. The jury therefore declined to accept the conclusions of Dr. Harlan's testimony that may have exceeded the scope of his expertise that Wright shot Alexander as Alexander fled after seeing Wright shoot Mitchell. Because the jury rejected the speculative portion of Dr. Harlan's testimony and the only conclusion permitted from all of the evidence presented at trial was that the two murders occurred in close succession, Dr. Harlan's testimony did not have a substantial or injurious effect or influence in determining the jury's verdict.
That Dr. Harlan's testimony also implicated the aggravating factor which the jury did find does not require a different result. The jury recommended the death penalty on the basis of then Tenn.Code Ann. § 39-2-203(i)(7), finding that the homicide "was committed while the accused was engaged in committing, attempting to commit, or fleeing after committing another first degree murder." It is true that Dr. Harlan did speculate that the murders were committed in close succession, and this was the only evidence presented as to the timing of the murders at the penalty phase of the trial. But that the two murders occurred in close succession was the only inference permitted from the evidence presented at the guilt phase of the trial. As the state court stated, "Under all of the proof, the two murders occurred practically simultaneously or, at most, within a short time of each other. Even under [Wright's] own testimony as to the killing of Mitchell, that homicide occurred within a few seconds after Alexander had been shot." Id. at 673-74. Contrary to Wright's assertions, under the aggravating factor that the jury did find, the sequence of events was not relevant either murder could have occurred first and Alexander's murder would still have happened during the commission of Mitchell's murder. Therefore, the Supreme Court of Tennessee correctly determined *594 that the admission of Dr. Harlan's testimony was harmless error.
Wright argues that the state court's harmless error analysis was not reasonable because it did not include consideration of the mitigation evidence, but such consideration is not required where the purported error had no effect on the aggravating circumstance that the jury in fact found. The jury weighed the mitigation evidence against the properly-found aggravating factor and determined that the death penalty was appropriate. Wright relies on Williams v. Taylor, 529 U.S. 362, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000), and Clemons v. Mississippi, 494 U.S. 738, 110 S.Ct. 1441, 108 L.Ed.2d 725 (1990), for the proposition that a court conducting harmless error analysis must always consider mitigating evidence, but those cases are different. In Williams, the Supreme Court held that it was unreasonable for the Virginia Supreme Court to determine that a capital defendant was not prejudiced by counsel's deficient performance without re-weighing evidence that should have been discovered by counsel and mitigation evidence that was presented at trial against the aggravating factors. 529 U.S. at 397-98, 120 S.Ct. 1495. A re-weighing of all the mitigating and aggravating factors was required to conclude that the erroneous omission of a mitigating factor was harmless. In contrast, no factor was erroneously omitted or erroneously included in this case. Clemons involved appellate re-weighing to cure a lower court error; the Court stressed the importance of weighing mitigating evidence against the remaining aggravating circumstances when the jury had found multiple aggravating factors and one of those aggravating factors was later invalidated. 494 U.S. at 751, 110 S.Ct. 1441. Here, because we do not disturb the only aggravating circumstance upon which the jury relied, the court could make a harmlessness determination by focusing on the lack of any adverse effect from Dr. Harlan's testimony.
Because the admission of Dr. Harlan's testimony did not have a substantial and injurious effect or influence in determining the jury's verdict, Wright was not entitled to habeas relief on that basis.

B. Ineffective Assistance of Counsel
Wright's trial counsel did not render ineffective assistance at the penalty phase of the trial. Wright asserts that his trial attorneys failed to investigate fully and present compelling mitigating evidence at the sentencing phase of the trial. However, the record shows that Wright's attorneys conducted a complete investigation into Wright's personal characteristics, including extensive discussions with his family members and a psychological evaluation. The record also indicates that the district court correctly determined that the decision not to call Dr. Anchor, a psychologist who had examined Wright prior to trial at the request of the defense attorneys, was a reasonable strategic decision. Because the state court's determination that the performance of Wright's trial counsel was not constitutionally deficient was not an unreasonable application of federal law or contrary to clearly established federal law, the district court correctly determined that Wright is not entitled to habeas relief on this ground.
During the sentencing phase of the trial, Wright's defense team presented only three witnesses. Although all three of Wright's attorneys were involved in all aspects of the trial, the most junior attorney, Gary Jones, led the mitigation investigation and sentencing phase of the trial. The first witness, Reverend Ingle, testified that he had met regularly with Wright following his incarceration, that Wright had undergone substantial changes since *595 the murders, and that Wright had expressed genuine remorse over the killings. Hattie McGee, Wright's GED instructor in the prison system, testified that Wright was a conscientious student who arrived early to class, volunteered, was generally helpful to others, and exhibited a real desire to receive an education so he could get a job if he was eventually released from prison. Finally, Wright's mother also testified that the family had been forced to move around before finally settling in a project, where all ten children, Wright's grandmother, Wright's mother, and her husband all lived in a one-bathroom apartment. Wright's mother also indicated that some of Wright's family members were in attendance, and stated that she loved Wright and asked the jury to spare his life.
Dr. Anchor, a clinical psychologist who had conducted a psychological evaluation of Wright at the request of Wright's attorneys, did not testify at the sentencing hearing. After performing his examinations, Dr. Anchor met with Wright's attorneys and prepared a one-page testing report summarizing his findings. Had Dr. Anchor testified about the results of his examination of Wright, Dr. Anchor would have stated that Wright had an IQ of 82, which put him near the bottom ten percent of the population; that Wright was depressed and impulsive and that Wright likely panicked during the murders; and that Wright's behavior showed signs of a reactive personality, poor judgment, and a lack of control. After Wright's trial, Dr. Anchor stated that his opinions of Wright were consistent with Wright's version of events, which was that Wright shot Mitchell after seeing Mitchell shoot Alexander.
Wright raised the issue of ineffective assistance of counsel in the 1989 petition for post-conviction relief. After granting an evidentiary hearing, the trial court determined that Wright's attorneys had not been constitutionally deficient. The Tennessee Court of Criminal Appeals affirmed the trial court's decision on appeal, determining that
[t]he record reflects that the petitioner's attorneys conducted substantial investigation and preparation for the sentencing phase of the trial. Numerous persons were considered by the attorneys to be witnesses on behalf of the petitioner, although only three ultimately testified. The record supports the conclusion that the attorneys' decisions about which witnesses were to testify were strategic decisions based upon the circumstances then existing.
Wright II, 1994 WL 115955 at *13.
The state courts correctly determined that Wright's trial counsel did not render ineffective assistance at the penalty phase of the trial. "In order to establish the ineffective assistance of counsel, [a petitioner] must first show that his `counsel's representation fell below an objective standard of reasonableness.' Second, [the petitioner] must establish prejudice by showing `that there is a reasonable probability that, but for counsel's unprofessional errors, the result of the proceeding would have been different.'" Awkal v. Mitchell, 613 F.3d 629, 638-39 (6th Cir.2010) (en banc) (quoting Strickland v. Washington, 466 U.S. 668, 688, 694, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984)). Here, the state appellate court determined that Wright's attorneys performed a reasonable mitigation investigation and that the failure to call Dr. Anchor was a reasonable strategic decision. Wright II, 1994 WL 115955 at *13. When a state court has adjudicated the merits of a habeas petitioner's claim, a federal court may not reach a different result "simply because that court concludes in its independent judgment that the relevant state-court decision applied clearly established federal law erroneously *596 or incorrectly. Rather, that application must also be unreasonable." Williams, 529 U.S. at 411, 120 S.Ct. 1495 (O'Connor, J., concurring). Because the record amply supports the determination that Wright's trial counsel made strategic decisions about which witnesses to call at the penalty phase of the trial and that those decisions were supported by a reasonable investigation, Wright was not entitled to habeas relief.
The decisions about which witnesses to call were supported by a reasonable mitigation investigation. Before this court, Wright focuses his arguments on the investigation conducted by Wright's trial counsel, which was led by the most junior attorney on the trial team, and argues that the mitigation investigation "really consisted of obtaining Mr. Wright's prison file and talking to Mr. Wright[']s mother and some of his brothers and sisters." Appellant Br. at 28. Yet as the state appellate court determined, Wright's attorneys "conducted substantial investigation and preparation for the sentencing phase of the trial." Wright II, 1994 WL 115955 at *13. Jones, the public defender who led Wright's trial team during the sentencing phase of the trial, testified at the post-conviction evidentiary hearing that he had anticipated the possibility of the State's raising aggravating factors and seeking the death penalty prior to trial, and that he thought he discussed the issue with Wright's other two attorneys long in advance of the State's giving notice that it was seeking the death penalty. Jones enlisted the assistance of an investigator employed by the public defender's office, Bernie Klose, and together they researched Wright's prior criminal records, had what Jones called "extensive" communications with Wright's family members, and met with Wright's mother and several of his brothers and sisters at their home on one or more occasion to discuss Wright's childhood, upbringing, and other information relevant to Wright and the case. Jones also testified that his requests for funding for a criminologist and a juristic psychologist were denied, but that the judge granted the motion for a general psychological evaluation, which led to Dr. Anchor's involvement. Wright's attorneys also conducted an investigation into Wright's behavior in prison, as evidenced by the trial testimony of Reverend Ingle and Hattie McGee. As the state courts correctly determined, Wright's attorneys' mitigation decisions were supported by a reasonable investigation.
Wright's trial attorneys' presentation of witnesses during the sentencing phase of the trial also constituted reasonable professional assistance. The Supreme Court has defined the deference owed to "strategic judgments in terms of the adequacy of the investigations supporting those judgments: `[S]trategic choices made after thorough investigation of law and facts relevant to plausible options are virtually unchallengeable.'" Wiggins v. Smith, 539 U.S. 510, 521, 123 S.Ct. 2527, 156 L.Ed.2d 471 (2003) (quoting Strickland, 466 U.S. at 690, 104 S.Ct. 2052). Here, the choice not to call Dr. Anchor was made after a complete investigation where Dr. Anchor twice met with Wright, performed several tests and evaluations, and then discussed those findings with Wright's attorneys. Although Wright contends that Wright's attorneys should have allowed more time for evaluations, the state courts determined after evaluating the testimony of two additional experts at the evidentiary hearing that additional testing would not have revealed any information beyond that provided by Dr. Anchor. Wright II, 1994 WL 115955 at *7. As the state appellate court determined, the most reasonable explanation for not calling Dr. Anchor was a determination *597 that the potential harm from the testimony would have outweighed the benefits. Id. at *13. Dr. Anchor's evaluation finding that Wright exhibited impulsive behavior was arguably inconsistent with the version of events the jury acceptedthat Wright committed both murders and then went to great lengths to avoid detection, including extensive lying to investigators. More importantly, the state court determined, interpreting its own evidentiary law, that Dr. Anchor's testimony may have opened the door to a statement Wright had allegedly made that "killing ni* * * * * is like killing flies." Reasonable strategic decisions made after thorough investigation do not amount to ineffective assistance of counsel. See Wiggins, 539 U.S. at 521-22, 123 S.Ct. 2527 (2003). Wright's attorneys could not recall, years later at the post-conviction evidentiary hearing, the exact reason they did not call Dr. Anchor to testify, but that does not change the reasonableness of the decision. "[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 quotation marks omitted). Wright has not shown that the state court's determination that Wright's attorneys did not perform deficiently at the sentencing phase of the trial was an unreasonable application of, or contrary to, clearly established federal law.
Wright argues that the decision not to call Dr. Anchor could not have been strategic because Wright's attorneys merely forgot to call Dr. Anchor, or that the witness fell by the wayside during the cursory last-minute mitigation investigation, but there is no support in the record for this contention. The state appellate court specifically rejected the argument that the attorneys forgot to call Dr. Anchor or that they made a purposeful decision not to call a valuable witness in order to preserve an ineffective assistance of counsel claim. Wright II, 1994 WL 115955 at *14. "A federal court is to apply a presumption of correctness to state court findings of fact for habeas corpus purposes unless clear and convincing evidence is offered to rebut this presumption." James v. Brigano, 470 F.3d 636, 643 (6th Cir. 2006). By Wright's own admission, the record here shows that at the end of the guilt phase of the trial, Wright's attorneys expressed concern to the judge about being able to schedule Dr. Anchor's testimony, but they later informed the judge that scheduling Dr. Anchor was no longer an issue. The only support offered by Wright that his attorneys forgot to call Dr. Anchor is arguments of counsel; such evidence is plainly not sufficient to rebut the presumption of correctness accorded to a state court finding of fact.
As Wright sees it, the mitigation investigation conducted by his attorneys constituted deficient performance because it failed to comply with the American Bar Association's standards for mitigation investigations in capital cases, but the Supreme Court recently held that strict reliance on the 2003 ABA standards in evaluating prevailing professional norms for trials that took place during the 1980's is not appropriate. Bobby v. Van Hook, ___ U.S. ___, 130 S.Ct. 13, 16-17, 175 L.Ed.2d 255 (2009) (per curiam). Moreover, the investigation here substantially complied with the requirements of the ABA standards that Wright identifies: Wright's attorneys investigated his family background, including both his childhood and adult years; they consulted with Dr. Anchor as an expert witness for insight into Wright's mental and emotional state; they presented testimony from *598 Wright's teacher and his spiritual advisor as to Wright's post-incarceration conduct; and they presented the testimony of Wright's mother about the adverse impact Wright's execution would have on the family. Therefore, in this case, "defense counsel's `decision not to seek more' mitigating evidence from the defendant's background `than was already in hand' fell `well within the range of professional reasonable judgments.'" Id. at 19.
Wright also argues that the declaration of his sister, Rose Wright, shows the kind of valuable mitigation evidence that Wright's attorneys either failed to discover or ignored, but that argument fails for several reasons. First, Wright's claim that his trial attorneys failed to investigate and present evidence of his troubled family background is procedurally defaulted. In the ineffective assistance of counsel claim raised in Wright's 1989 petition for post-conviction relief, Wright did not argue that his attorneys failed to interview his family members and adequately investigate his troubled childhood. Therefore, the trial court did not address that claim at the evidentiary hearing, and none of the state courts ever addressed that claim on the merits. The district court therefore addressed Wright's ineffective assistance of counsel claim only as raised in his 1989 post-conviction petition. Memorandum of Feb. 16, 2006 at 34-36. A district court has broad discretion to consider additional evidence presented to a federal court that does not "fundamentally alter the legal claim already considered by the state courts," West v. Bell, 550 F.3d 542, 551 (6th Cir.2008), but Wright's later claim that his attorneys failed to investigate his family background was fundamentally different from the claim addressed by the state courts.
Second, nothing in the additional declarations presented by Wright's family members renders the state court's determination unreasonable, or contrary to clearly established federal law. The decision not to call any family members other than Wright's mother was made after a reasonable investigation, including extensive contact with Wright's family members. Critically, Wright never alleges that his attorneys failed to speak to Rose Wright, and her declaration states only that she would have testified if asked. Rose Wright's testimony would have painted a much more vivid picture of the tragic circumstances of Wright's family life; however, Wright's mother testified as to Wright's impoverished upbringing, and the most vivid images from Rose Wright's testimony, those of criminal neglect and sexual abuse, concern Wright's sisters, rather than Wright himself.
The district court correctly determined that the state appellate court's determination that Wright's attorneys provided reasonable assistance at the sentencing phase of the trial was not contrary to, or an unreasonable application of, clearly established federal law.

C. Admission of the State's Alleged Offer of a Life Sentence in Exchange for a Guilty Plea
It was also reasonable for the state court to determine that Wright was not permitted to introduce evidence of plea negotiations during the penalty phase of the trial. Although the Supreme Court held in Lockett v. Ohio, 438 U.S. 586, 98 S.Ct. 2954, 57 L.Ed.2d 973 (1978), that a capital defendant has a constitutional right to present mitigation evidence relating to "any aspect of a defendant's character or record and any of the circumstances of the offense that the defendant proffers as a basis for a sentence less than death," id. at 604, 98 S.Ct. 2954 (plurality opinion), the state court's determination that evidence *599 of the plea negotiations did not constitute admissible evidence of mitigating circumstances was not an unreasonable application of federal law or contrary to clearly established federal law. This conclusion is directly supported by our recent decision in Owens v. Guida, 549 F.3d 399 (6th Cir.2008). Owens held that a petitioner's constitutional rights were not violated when the state courts refused to admit evidence of failed plea negotiations as mitigation evidence showing that the petitioner's willingness to plead guilty in exchange for a life sentence indicated acceptance of responsibility. Because the state court's decision was not contrary to, or an unreasonable application of, clearly established federal law, Wright is not entitled to habeas relief.
Wright alleges that, during trial, the state offered a life sentence in exchange for a guilty plea. At trial, Wright's attorneys argued that they were entitled to present evidence of the alleged offer as mitigation evidence during the sentencing trial, and they filed a motion for a new trial after the court refused to admit the evidence. The trial court held an evidentiary hearing on the motion for a new trial, but again determined that Wright was properly denied the opportunity to present evidence of the plea negotiations. Wright appealed the decision to the Supreme Court of Tennessee, which held that evidence of the alleged agreement was irrelevant and inadmissible because the evidence did not constitute evidence of a mitigating circumstance. Wright I, 756 S.W.2d at 675. In its pre-Owens ruling, the district court found on the evidence that the state did not make the offer of a plea agreement.
However, because our decision in Owens supports the determination that the Supreme Court of Tennessee's decision was not contrary to or an unreasonable application of clearly established federal law, we need not reach the factual issue of whether the State ever offered a plea agreement. In Owens, this court held that the Supreme Court of Tennessee did not unreasonably apply or violate clearly established federal law in holding that a petitioner was not entitled to present evidence that the state had offered, and the defendant had accepted, an offer of a life sentence in exchange for a guilty plea, the deal having later fallen through because the petitioner's co-defendant rejected the offer. 549 F.3d at 418-22. We relied on the fact that while the Supreme Court's decision in Lockett required that a capital defendant be allowed to present any relevant mitigating evidence, "`relevant evidence' means evidence having `any tendency to make the existence of any fact that is of consequence to the determination of the action more probable or less probable than it would be without the evidence.'" Id. at 419 (quoting Tennard v. Dretke, 542 U.S. 274, 284, 124 S.Ct. 2562, 159 L.Ed.2d 384 (2004)). Here, the Tennessee Supreme Court determined that the evidence was not relevant because it did not relate to Wright's character or the circumstances of the offense. "Footnote 12 in Lockett explicitly stated that lower courts could continue to exclude as irrelevant evidence not bearing on the defendant's character, prior record, or the circumstances of the offense." Id. Because the alleged offer of a life sentence in exchange for a guilty plea did not bear on the defendant's character, prior record, or the circumstances of the offense, Wright was not constitutionally entitled to present evidence of the failed plea negotiations.
This decision is consistent with those of other courts that have addressed the relevance of plea negotiations to capital sentencing. Although our opinion in Owens did not address the specific rebuttal argument that Wright has made before this *600 courtthat Wright should be allowed to present evidence of the alleged plea offer to rebut statements by the State at closing argument suggesting that Wright might pose a danger to other inmates if he received a life sentence rather than the death penaltythe court's determination that plea negotiations are not relevant evidence of mitigating circumstances is still relevant here. In supporting our holding in Owens, we noted that all of the other courts to address the question of whether the Constitution required the admission of failed plea negotiations as relevant mitigation evidence had held that the Constitution did not prevent the exclusion of such evidence. Id. at 421-22. We reasoned that the common thread underlying those decisions was the consideration of the strong policies in favor of plea bargains, which the Oklahoma Court of Criminal Appeals had clearly expressed:
Allowing a defendant to use plea negotiations in mitigation would clearly discourage plea negotiations in capital cases as prosecutors would correctly fear that during the second stage proceedings, they would be arguing against themselves. Plea bargaining is to be encouraged, not discouraged, and therefore is improper evidence to present in mitigation.
Ross v. State, 717 P.2d 117, 122 (Okla.Cr. App.1986). The Owens court stated: "This reasoning persuades us, and explains why every court to hear Owens's argument has rejected it." 549 F.3d at 422. Because the offer of a plea agreement is not relevant to the defendant's characteristics or the circumstances of the crime, the state court's decision was not contrary to or an unreasonable application of clearly established federal law.
Wright contends that regardless of the policies in favor of plea bargaining and the potential influence admitting plea negotiations might have, the Supreme Court's decision in Lockett compels the admission of plea negotiations as rebuttal evidence. But nothing in the Lockett opinion, which addressed an Ohio death penalty statute that "did not permit the sentencing judge to consider, as mitigating factors, [the petitioner's] character, prior record, age, lack of specific intent to cause death, and her relatively minor part in the crime," addressed the relevance of plea agreements to a capital sentencing. 438 U.S. at 597, 98 S.Ct. 2954. The petitioner in Lockett had rejected plea offers from the state, but the Court did not address the admissibility of those offers in the opinion. Id. at 591, 98 S.Ct. 2954. The factors the opinion did address, the defendant's character, prior record, age, lack of intent to cause death, and role in the crime, were all directly relevant to either the petitioner's personal characteristics or her role in the crime. Similarly, the Court in Eddings v. Oklahoma, 455 U.S. 104, 113, 102 S.Ct. 869, 71 L.Ed.2d 1 (1982), held that a state court's refusal to admit evidence of a 16-year-old defendant's personality disorder and his turbulent and abusive family history violated the principles of Lockett. As the Court explained in Eddings, "the rule in Lockett followed from the earlier decisions of the Court and from the Court's insistence that capital punishment be imposed fairly, and with reasonable consistency, or not at all." 455 U.S. at 112, 102 S.Ct. 869. Evidence of plea negotiations does not affect the sentencer's ability to impose an individual sentence consistent with the characteristics of the defendant and the circumstances of the crime. Lockett and Eddings stand for the important principle that a capital defendant must be able to present any relevant mitigating evidence in order to allow the sentencing court to conduct an individualized sentencing, but do not imply that evidence of a state's plea offer is relevant mitigating evidence.
*601 For the same reason, the Supreme Court's decision in Skipper v. South Carolina, 476 U.S. 1, 106 S.Ct. 1669, 90 L.Ed.2d 1 (1986), does not require a different result. In Skipper, the Supreme Court applied Lockett and Eddings to determine that a petitioner should have been entitled to present evidence that he had behaved well in prison prior to trial because "evidence that the defendant would not pose a danger if spared (but incarcerated) must be considered potentially mitigating." Id. at 5, 102 S.Ct. 869. But nothing in the alleged plea offer constitutes relevant evidence that Wright would not pose a danger if given a life sentence. The existence of a plea offer might indicate only that the state believed its important interests in judicial efficiency and finality of judgments were sufficient to outweigh any potential risk associated with a life sentence, not that those risks did not exist. Moreover, Wright was not denied the opportunity to present evidence of his good behavior in prison that the petitioner in Skipper was denied. Wright presented testimony from Reverend Ingle and Hattie McGee to show that Wright expressed remorse over the murders and had been a model prisoner since his incarceration. The Supreme Court of Tennessee's decision did not deny Wright the opportunity to present relevant mitigation evidence or rebut evidence offered by the prosecution; therefore, Wright was not entitled to habeas relief on this ground.

D. The District Court's Procedural Default Determination
Finally, the district court correctly determined that Wright's claims brought in his 1991 and 1995 petitions, not otherwise ruled upon, were procedurally defaulted. Wright presented claims to the state courts in his direct appeal, his 1989 petition for postconviction relief, his 1991 petition for post-conviction relief, and his 1995 petition for post-conviction relief. In resolving the procedural default issue, the district court stated that "beyond the claims actually decided on the merits by the state courts and in this Court's earlier Memorandum ... Petitioner's remaining claims in his amended federal petition are procedurally defaulted for the reasons stated by the state courts." Memorandum of Feb. 15, 2007, at 60. Because the Tennessee Court of Criminal Appeals applied procedural bars to determine that Wright had failed to appeal the dismissal of his 1991 petition, and his 1995 petition failed to comply with the applicable statute of limitations, claims raised for the first time in those petitions were procedurally defaulted.
After his conviction and direct appeal, Wright filed several petitions for post-conviction relief in the Tennessee state courts. Wright filed his first pro se petition in May, 1989. Wright subsequently filed an amended petition, this time with the assistance of counsel, in September of 1989. The trial court conducted an evidentiary hearing, but denied the petition. The Tennessee Court of Criminal Appeals affirmed the trial court's decision. Wright II, 1994 WL 115955 at *22. While Wright's appeal of his 1989 petition was pending, Wright filed a second petition in 1991, without the assistance of counsel. The trial court dismissed that petition as "redundant and unnecessary," and Wright did not appeal that decision. In January of 1995, once again assisted by counsel, Wright filed a motion to vacate the order dismissing his 1991 petition, and also filed a third petition for post-conviction relief. The trial court denied the motion and the petition, and the Tennessee Court of Criminal Appeals affirmed that decision. Wright III, 1997 WL 126818 at *9.
The district court correctly determined that Wright had procedurally defaulted the *602 claims contained in the 1991 petition, which claims are the primary focus of Wright's present appeal. In resolving the 1991 and 1995 petitions together, the Tennessee Court of Criminal Appeals devoted two paragraphs to the 1991 petition:
Appellant first argues that the trial court erred in dismissing his 1991 post-conviction petition. Appellant, who concedes that he failed to file a timely notice of appeal, contends that this requirement should be waived "in the interests of justice" citing both Rule 4(a) of the Tennessee Rules of Appellate Procedure and Laney v. State, 826 S.W.2d 117 (Tenn.1992).
Appellant filed his second post-conviction petition on [August] 29, 1991, was denied relief, and, for whatever reason, failed to appeal the judgment within the statutorily-mandated thirty-day period. See Tenn. R.App. P. 4(a). Now, over three years later, Appellant seeks to have the requirement for a timely appeal waived. Given the excessive delay, and the lack of any evidence that Appellant's attorney, who drafted both the first and third petitions, was unaware of the filing of the second petition, we are not inclined to waive the timeliness requirement. In any event, it appears that issues proffered in the second petition have been either previously determined, waived, or are repeated in the third petition, which we address infra. Thus, we conclude that the trial court's dismissal of Appellant's 1991 post-conviction petition was proper.
Wright III, 1997 WL 126818 at *3. The 30-day time period for filing a notice of appeal contained in Tennessee Rule of Appellate Procedure 4(a) plainly applies to this case, and by not appealing from the district court's dismissal of his 1991 petition, Wright failed to comply with the rule. In its 1997 opinion, the Tennessee Court of Criminal Appeals applied this bar in denying Wright's motion to vacate the trial court's order dismissing the 1991 petition. In denying the motion, the court first identified Rule 4(a), acknowledged the exception in the interests of justice, and stated, "Given the excessive delay, and the lack of any evidence that Appellant's attorney, who drafted both the first and third petitions, was unaware of the filing of the second petition, we are not inclined to waive the timeliness requirement." Wright III, 1997 WL 126818 at *3. Therefore, the state appellate court determined that the procedural bar governing the filing of a notice of appeal applied to Wright's case, and Wright has not alleged that Tennessee Rule of Appellate Procedure 4(a) is not an independent and adequate state ground upon which to rest the procedural default determination. Howard v. Bouchard, 405 F.3d 459, 477 (6th Cir.2005) (stating the requirements for procedural default).
Wright argues that the Tennessee appellate court's dismissal did not constitute a "clear and express" statement of a state procedural bar because the state court offered three alternate reasons for dismissal, but the record does not support this claim. In habeas, "a procedural default does not bar consideration of a federal claim ... unless the last state court rendering judgment in the case clearly and expressly states that its judgment rests on a state procedural bar." Harris v. Reed, 489 U.S. 255, 263, 109 S.Ct. 1038, 103 L.Ed.2d 308 (1989) (internal quotation marks omitted). Wright argues that the only clear and express statement provided by the state court in denying Wright's motion to reinstate the 1991 petition was the court's statement that, "[i]n any event, it appears that all issues proffered in the second petition have been either previously determined, waived, or are repeated in the third petition," Wright III, 1997 WL *603 126818 at *3, but for that to be true, one would have to ignore the bulk of the state court's two paragraphs devoted to the 1991 petition. The court addressed the 1991 petition by noting that Wright conceded that he failed to appeal the trial court's order dismissing his 1991 petition, identifying the procedural rule barring consideration, discussing the exception, and then determining that the court was not inclined to waive the timeliness requirement. Id. This court has routinely used the words "we are not inclined to" in asserting a basis for a holding or in denying a contention made by a party. See, e.g., United States v. Johnson, 302 Fed.Appx. 453, 457 (6th Cir.2008) ("While the district court's finding regarding Johnson's Sentencing-Guidelines range was less than ideal, we are not inclined to find it procedurally unreasonable"); In re Delta Air Lines, 310 F.3d 953, 961 (6th Cir.2002) ("An interlocutory review of the class certification decision will entangle the merits of the case ... with the more routine consideration of class certification factors, which involve commonality and typicality. We are not inclined to extend the jurisdiction conferred by Rule 23(f) in this direction."). That the court also devoted a single sentence to explain further that, "[i]n any event," it was not denying Wright the opportunity to present otherwise meritorious claims does not change the analysis.
This reading of the state appellate court's decision is consistent with the Supreme Court of Tennessee's interpretation of the appellate court's language. In resolving the issue of whether Wright's Brady claim raised in his 1995 petition for post-conviction relief was barred by the three-year statute of limitations, the Supreme Court of Tennessee outlined the procedural history of Wright's appeals. Wright IV, 987 S.W.2d at 27. The court addressed the 1991 petition in a footnote:
This petition is actually the petitioner's third. The second, filed pro se on August 29, 1991, was dismissed by the trial court without a hearing. Although no appeal was filed at that time, the appellant sought to resurrect that appeal in the present case. The Court of Criminal Appeals properly ruled that it was untimely and refused to review the issues therein.
Id. at 27 n. 1. As the Supreme Court of Tennessee determined, the Tennessee Court of Criminal Appeals applied Rule 4(a) to determine that Wright's appeal of the dismissal of his 1991 petition was not timely. A petitioner's failure to appeal a state court decision denying relief represents a procedural default resulting in waiver of the claim. Howard v. Wolfe, 199 Fed.Appx. 529, 533 (6th Cir.2006).
With respect to the 1995 petition, Wright has not articulated any arguments as to why the district court erred in determining that those claims were procedurally defaulted. Of the seventeen claims that the Tennessee Court of Criminal Appeals analyzed in Wright's 1995 petition, the state court denied sixteen on statute-of-limitations grounds. Wright III, 1997 WL 126818 at *4-9. The court held that only one claim, Wright's argument that he was denied the right to confront Jackie King at her deposition, was "previously determined." Id. at *7. However, the district court resolved that claim on the merits. Memorandum of February 16, 2006, at 43-44. Therefore, claims raised in the 1995 petition were properly subject to the district court's procedural default determination.
Wright argues the Supreme Court's decision in Cone v. Bell, ___ U.S. ___, 129 S.Ct. 1769, 173 L.Ed.2d 701 (2009), which was decided after the district court's decision *604 in this case, requires remand, but that case does not affect the procedural default analysis. It is true, as Wright argues, that the Supreme Court's decision in Cone means that "[w]hen a state court declines to review the merits of a petitioner's claim on the ground that it has done so already, it creates no bar to federal habeas review." Id. at 1781. But the statements by the Tennessee Court of Criminal Appeals that some of Wright's claims had been "previously determined" was not the basis for the procedural default as in Cone; instead, the bases were the 30-day time limit to file an appeal for the 1991 petition, and the three-year statute of limitations for post-conviction relief for the 1995 petition. Of course, the state court's determination that the claims in the 1991 and 1995 petitions were time-barred has no impact on claims that were raised in either Wright's direct appeal or the 1989 petition and repeated in the 1991 or 1995 petitions, but Wright has not identified any claims that received a merits determination from the state courts, yet were held to be procedurally defaulted by the district court. Because the district court correctly determined that Wright had procedurally defaulted claims raised for the first time in Wright's 1991 and 1995 petitions for post-conviction relief, and because Wright cannot identify any claims raised either on direct appeal or in the 1989 petition that did not receive a merits determination from the district court, Wright has not shown that he is entitled to habeas relief on the basis of the district court's procedural default determination.

III.
For these reasons, the judgment of the district court is affirmed.
NOTES
[1]  The State therefore claims that Wright has procedurally defaulted any constitutional claim relating to Dr. Harlan's testimony; Wright counters that the State waived the defense of procedural default by defending Wright's Fourteenth Amendment claim in the district court. Because Wright's claim is easily disposed of on the merits, we need not determine whether the State waived the procedural default defense.
