OPINION
KAREN NELSON MOORE, Circuit Judge.
Petitioner-Appellant Donald Middle-brooks appeals from the district court’s denial of his petition, for a writ of habeas corpus. Middlebrooks was convicted in Tennessee state court for the 1987 kidnapping and murder of Kerrick Majors, a foürteen-year-old African American. A jury sentenced Middlebrooks to death. This is Middlebrooks’s second appeal from the denial of his habeas claims. In 2010, we affirmed the district court’s first dismissal of Middlebroóks’s petition; the Supreme Court vacated our decision, however, in light of the Court’s holding in
Martinez v. Ryan,
566 U.S. 1, 132 S.Ct. 1309, 182 L.Ed.2d 272 (2012). On remand, the district court concluded that Middlebrooks was not entitled to relief under
Martinez
and
Trevino v. Thaler,
— U.S. —, 133 S.Ct. 1911, 185 L.Ed.2d 1044 (2013). For the reasons discussed below, we AFFIRM the district court’s judgment denying Middlebrooks’s habeas petition.
I. BACKGROUND
The Tennessee Supreme Court summarized the evidence presented during Mid-dlebrooks’s capital trial as follows:
[O]n the evening of Sunday, April 26, 1987, around 7:00 p.m., the victim, Ker-rick Majors, a 14-year-old black male, was with four friends on Gallatin Road in East Nashville, Tennessee, when they saw a table with a “lot of stuff’ being set up across the street as a flea market by three homeless street persons: the defendant, Donald Middlebrooks (a 24-year-old white male); his wife, 17-year-old Tammy Middlebrooks; and their companion, 16-year-old Roger Brewing-ton. The five boys ran across Gallatin Road and were looking at the flea market when Tammy Middlebrooks called out, “Hey, leave our stuff alone!” The boys started running. The defendant and Brewington chased them until they caught Majors. Brewington grabbed Majors in a “sleeper hold” around his neck and head. The defendant held his hand. When Majors said, “Hey man, you know me,” Brewington responded, “Shut up, you nigger.” Shannon Stewart and another of the boys, Tony Watson, saw the two men drag Majors toward the table and observed the defendant strike him in the face, knocking him to the ground. Frightened, the boys took off running. Later that evening, they reported these events to the victim’s mother, who called the police.
The next aftprnoon, Kerrick Majors’ nude body was discovered lying face up in a dry creek bed under a foam mattress in a heavily wooded area, behind a drugstore on Gallatin Road in the area where the defendant and Brewington had caught Majors. A bloodstained T-shirt was tied around his neck. A red rope belt was tied around Majors’ left wrist, and there was a two-inch laceration in his right wrist. Abrasions, swelling, and bruising were present on the victim’s head, his left eye, his nose, his lips, and inside his mouth. An “X” with a vertical line running through it had been cut into his chest. The forensic pathologist, Dr. ’ Charles Harlan, testified that these incisions had been made while Majors was alive. There were two deep stab wounds in the center of the body. One of these penetrated the left lung and pulmonary artery and caused the victim to bleed to death over a period of ten to thirty minutes, during part of which Majors was conscious. Investigating officers noticed a smell of urine about the face, and there were bruises and skinned areas on the back. A wooden stick with blood stains on one end was found lying close to the victim’s head.
Around 1:10 a.m. on April 28, police investigators met Brewington at a doughnut shop several miles from the Gallatin Road area. Brewington directed the officers to the location of a knife with a brass knuckle handle, which was bloodstained. Dr. Harlan testified that this knife could have inflicted the deep stab wounds on the victim’s body. Brew-ington also directed the police to a wooded area between Gallatin Road and Ellington Parkway in Nashville where, around 7:00 a.m. on-April 28, Donald and Tammy Middlebrooks were apprehended at a small plywood shack. The defendant, who resisted the arresting officers, had a knife with him. He-was arrested with the aid of police dogs, taken to the hospital for treatment of the dog bites, and later transported to police headquarters.
At 12:30 p.m. that day, the defendant gave a lengthy video-taped- statement about his involvement in the death of Kerrick Majors. The defendant admitted participating in the beating and mistreatment of Majors, but described his role as minor and depicted Roger Brew-ington as the primary perpetrator of the offense. After Majors was caught, Mid-dlebrooks said Brewington suggested they “have some fun,” and the three of them took Majors back into the woods.
His hands were tied. Brewington slapped him, beat him with the knife’s brass knuckles, hit him with a stick, and urinated into his mouth. The defendant admitted striking Majors with his open hand and on the leg with a switch. Defendant said that his wife Tammy had slapped Majors and burned Majors’ nose with a cigarette lighter as Brewington urged her on, Brewington hit Majors on his testicles, threatened to cut “it” open, stuck a stick up Majors’ anus, hit him some more with the brass knuckles, wiped the victim’s blood on himself, beat his mouth and tongue with a stick, dropped the knife on him, gagged him, and slashed his wrist. Finally, when the defendant asked Brewington to stop because the victim’s crying and pleading were getting on his nerves, Brewington gave the victim “the kiss of death” on the forehead. Brewington then gave the defendant the knife and told him to stab Majors. When the defendant refused, Brewington stabbed Majors. The defendant then reluctantly stabbed the victim, according to him, “to prove to Roger that I guess I was cooler” and to put Majors out of his misery. In a previous statement, however, the defendant had said that he had stabbed Majors twice. The victim’s ordeal began at 7:30 p.m. and ended at 11:00 p.m. that night with the stabbing.
The next day, the defendant said he and Brewington went back to where they had left the body. Brewington kicked it and made, the “X” lacerations at this time. The defendant said he then covered Majors with a foam mattress. The defendant admitted that before beating and killing Majors, he and Brewington had drunk alcohol and smoked marijuana. .
The defendant presented no proof.
State v. Middlebrooks,
840 S.W.2d 317, 323-25 (Tenn. 1992).
As we explained in our prior opinion, “[o]n the basis of this evidence, the jury convicted Middlebrooks of felony murder and aggravated kidnapping but acquitted him of first-degree premediated murder, armed robbery, and aggravated sexual battery.”
Middlebrooks v. Bell,
619 F.3d 526, 532 (6th Cir. 2010),
cert. granted, vacated sub ñom. Middlebrooks v. Colson,
566 U.S. 902, 132 S.Ct. 1791, 182 L.Ed.2d 612 (2012). The jury sentenced Middlebrooks to . death.
Middlebrooks,
619 F.3d at 532. “[T]he jury found two aggravating circumstances — that the murder was especially heinous, atrocious, and cruel in that it involved torture or depravity of mind, and that it was committed while Middlebrooks perpetrated a felony.”
Id.
-
The Tennessee Supreme Court upheld Middlebrooks’s convictions on direct appeal but vacated Middlebrooks’s death sentence, finding that the second aggravating circumstance “duplicated the offense of felony murder and therefore failed to narrow the class of death-eligible defendants under Article I, § 16 of the Tennessee Constitution.”
State v. Middlebrooks,
995 S.W.2d 550, 552-53 (Tenn. 1999);
see also State v. Middlebrooks,
840 S.W.2d at 323.
The Tennessee Supreme Court remanded the case for a second sentencing proceeding, and the following evidence was presented:
According to the State’s proof, fourteen-year-old Majors was small for his age. He was described as a good student who loved school. He was not a violent person, nor did he carry a weapon. Since his murder, his mother’s health has deteriorated. She has been on medication and will not leave the house except for doctor appointments. She has had a nervous breakdown, suffers from panic attacks, and has not been able to sleep at night since the murder. Majors’ older brother blames himself for Majors’ death and
now suffers from mood swings. Shannon Stewart testified that he had spoken with Middlebrooks the morning of the murder. Middlebrooks had told Stewart that he was a member of the KKK, that .he “hated niggers,” and that he punched a black man just for saying hello, Stewart also testified that he overheard Mid-dlebrooks order Majors to “shut up nigger.”
The defense introduced mitigation evidence as follows: Middlebrooks’ cousins, James and Carol Sue Little, and his half-sister, Sharon Fuchs, testified about Middlebrooks’ childhood. Middlebrooks grew up in Texas. His father died when he was four. His mother remarried and had another child, Ms. Fuchs, before she again divorced, Middlebrooks’ mother either left the children at night with relatives or else would take them to bars with her.
According to the proof, Middlebrooks’ mother would often bring men to the house, and the children sometimes heard or saw their mother having sex. Ms. Fuchs testified that sometimes these men would molest her while her mother watched. She further testified that she, Middlebrooks, and other children in the family were molested by different family members. For example, Middlebrooks was often left alone with a male relative who had sexually abused him, and Mid-dlebrooks’ mother would grab him between his legs and also watch him use the bathroom. According to Sharon Fuchs, the small town in which they grew up lacked counseling services or social service agencies where they could seek help for sexual abuse. According to her, no one in the family ever discussed or admitted the family’s problems.
The proof further indicated that Middle-brooks was often angry and got into trouble. He was sent to a Methodist Home for- Children in Waco for two years. Later, he was twice sent to prison. Between prison stays, Middlebrooks started to have seizures. On one,occasion he climbed a water tower and threatened to commit suicide. He was hospitalized more than once at a mental institution.
A psychologist, Dr. Jeffrey L, Smalldon, performed neuropsychological and psychological evaluations of Middlebrooks. From these evaluations, interviews, testing, and prior education and medical records, Smalldon concluded that Mid-dlebrooks has a severe borderline personality disorder. Middlebrooks exhibited several characteristics of the disorder including inconsistent behavior, instability of mood, a marked identity disturbance, impulsive and reckless behavior,' poor anger control, and recurring suicidal or self-destructive acts. Smalldon testified that the documents from other mental health professionals who have evaluated Middlebrooks indicate that he suffers from substance abuse, psychotic personality disorder, and schizophrenia. Middlebrooks also suffers a mild degree of organic brain impairment which causes him to be more impulsive and less able to delay his responses. Finally, Smalldon testified that Middlebrooks has also exhibited characteristics of adults who were sexually abused as children.
During cross-examination, Dr. Smalldon admitted that Middlebrooks confessed to á greater involvement in Majors’ death than-he had in the video-taped confession. For instance, Smalldon disclosed that Middlebrooks admitted to him that it was his idea to hold Majors for ransom, that he helped tie Majors up, and that he urinated on Majors. -In an attempt to resolve the discrepancies between the videotaped confession to the police and the confession made to him in the interview, Smalldon explained that Middlebrooks is a chronic liar. Dr.
Smalldon conceded that Middlebrooks had never expressed any remorse to him. Smalldon agreed that there were some indications in the medical records of Middlebrooks’ malingering, but testified that these indications were not inconsistent with mental illness.
In rebuttal, the State introduced the testimony of two experts indicating that Middlebrooks was exaggerating his mental illness symptoms, that he was competent to stand trial, that he did not have a defense of insanity, and that he was not committable. One expert testified that he could not say whether Mid-dlebrooks was mentally ill. The other expert testified that he made no finding of mental illness and did not consider a personality disorder to be a mental illness.
State v, Middlebrooks,
995 S.W.2d at 554-56. Following the presentation of this evidence, the jury found “that the murder was ‘especially heinous, atrocious, or cruel in that it involved torture or depravity of mind,’ ” and that this “outweighed the evidence of mitigating factors.”
Id:
at 556 (quoting Tenn. Code Ann. § 39-2-203(i)(5)). Middlebrooks was resentenced to death, and this sentence was affirmed on direct appeal by the Tennessee Supreme Court,
See id,
at 553.
Middlebrooks filed á petition for post-conviction relief in state court in November 1999. Appellee App, at 1. Middlebrooks raised several grounds for relief in his petition, including numerous arguments that he received ineffective assistance of counsel.
See id.
at 8-9. After an evidentiary hearing, the state court dismissed Middlebrooks’s petition in July 2001,
Id.
at 47. Middlebrooks appealed, and the Tennessee Court of Criminal Appeals affirmed.
Middlebrooks v. State,
No. M2001-01865-CCA-R3-PD, 2003 WL 61244, at *13 (Tenn. Ct. Crim. App. Jan. 9, 2003).
Middlebrooks filed- a petition for habeas corpus in federal district court in 2003, and amended his petition in 2004.
See
Appellant App. at 168. The district court denied relief on May 26, 2005, finding that many of Middlebrooks’s claim's were procedurally defaulted and others were non-meritorious.
See id.
at 206-83. The district court denied a Certificate of Appealability (“COA”) for all of Middlebrooks’s claims.
Id.
at 283;
see also Middlebrooks v. Bell,
No. 3:03-0814, 2007 WL 760441 (M.D. Tenn. Mar. 8, 2007). We granted a COA on seven issues, and ultimately affirmed the district court’s denial of Middlebrooks’s habeas petition.
Middlebrooks v. Bell,
619 F.3d at 536-44.
On March 26, 2012, the United States Supreme Court granted certiorari, vacated our judgment, and remanded the case for further consideration in light of
Martinez v. Ryan,
566 U.S. 1, 132 S.Ct. 1309, 182 L.Ed.2d 272 (2012).
See Middlebrooks v. Colson,
566 U.S. 902, 132 S.Ct. 1791, 182 L.Ed.2d 612 (Mem.) (2012). We remanded to the district court, and the district court requested additional briefing. Middle-brooks argued that his habeas corpus petition presented twenty-six “substantial” ineffective-assistance-of-trial-counsel claims that “were never properly raised or presented during initial collateral review proceedings” due to his post-conviction counsel’s ineffectiveness, and thus that he was entitled to an evidentiary hearing and habeas relief under
Martinez
and
Trevino v. Thaler,
— U.S. —, 133 S.Ct. 1911, 185 L.Ed.2d 1044 (2013). R. 102 (Pet.
Martinez
Br. at 14) (Page ID #612).
On August 1, 2014, the district court again denied Middlebrooks’s petition, finding that his ineffective-assistance~of-trial-counsel claims were not “substantial” under
Martinez
and thus did not warrant an evidentiary hearing or habeas relief, R. 105 (08/01/14 D. Ct. Op. at 25) (Page ID
#810). The district court granted a COA “on the issues of whether Petitioner’s claims about his trial and post conviction counsels omissions justify an evidentiary-hearing and habeas relief under
Martinez
and
Trevino.” Id.
Middlebrooks timely appealed. R. 107 (Notice of Appeal) (Page ID #838).
II. DISCUSSION
A.
Martinez
and
Trevino
Do Not Assist Middlebrooks’s Habeas Claims
Middlebrooks first argues that the district court erred in denying his habeas petition in light of
Martinez
and
Trevino.
Appellant Br. at 31. This court reviews de novo a district court’s denial of a petition for writ of habeas corpus.
See Maples v. Stegall,
340 F.3d 433, 436 (6th Cir. 2003). Under the Antiterrorism and Effective Death Penalty Act of 1996 (“AEDPA”), a federal court cannot grant habeas relief for “any claim that was adjudicated on the merits” by the state court unless the state court’s adjudication “resulted in a decision that was contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court,” or was “based on an unreasonable determination of the facts.” 28 U.S.C. § 2254(d). Further, because federal courts must defer to “a State’s application of its own firmly established, consistently followed, constitutionally proper procedural rules,”
Trevino,
133 S.Ct. at 1917, a federal court is barred from granting habeas relief if the petitioner has procedurally defaulted his claims in state court.
See Hodges v. Colson,
727 F.3d 517, 529-30 (6th Cir. 2013). We review de novo “[w]hether a petitioner’s federal habeas claim is barred by procedural default.”
Id.
at 529. A prisoner may overcome a state-court procedural default only if the petitioner can establish “cause” and “prejudice,” or a “manifest miscarriage of justice.”
Sutton v. Carpenter,
745 F.3d 787, 790-91 (6th Cir. 2014) (citing
Coleman v. Thompson,
501 U.S. 722, 749-50, 111
S.Ct.
2546, 115 L.Ed.2d 640 (1991)).
We held in our prior opinion that Middlebrooks was not entitled to habeas relief for his ineffective-assistance-of-counsel claims because (1) Middlebrooks procedurally defaulted two of his claims at the Tennessee Court of Criminal Appeals and could not establish “cause” to excuse the default; (2) Middlebrooks abandoned one claim on appeal to our court; and (3) the Tennessee state court did not unreasonably apply federal law in resolving Middlebrooks’s remaining claim on the merits.
See Middlebrooks,
619 F.3d at 535-41. The Supreme Court vacated our judgment and remanded the decision in light
Martinez v. Ryan.
Accordingly, prior to evaluating Middlebrooks’s claims, we first discuss the holding of
Martinez.
1. The Supreme Court’s Decisions in
Martinez
and
Trevino
The Court in
Martinez
established an exception to the general rule of
Coleman v. Thompson,
501 U.S. at 756-57, 111 S.Ct. 2546.
See Sutton,
745 F.3d at 791.
Coleman
held that, although counsel’s ineffectiveness during
direct
appeal may establish “cause” to excuse a petitioner’s procedural default, a petitioner cannot establish “cause” to excuse default that results from counsel’s ineffectiveness during
post-conviction
proceedings.
See Coleman,
501 U.S. at 756-57, 111 S.Ct. 2546. This is because “a criminal defendant has no right to counsel beyond his first appeal in pursuing state discretionary or collateral review.”
Id.
at 756, 111 S.Ct. 2546.
Martinez
modified
Coleman’s
rule in a narrow circumstance: where state law requires that a defendant bring an ineffective-assistance-of-trial-counsel claim in post-conviction proceedings, rather than on direct appeal, an attorney’s constitu
tionally deficient performance in the initial-review collateral proceeding can establish “cause” to excuse the default of the petitioner’s ineffective-assistance-of-trial-counsel claim.
Martinez,
132 S.Ct. at 1318. “To overcome the default, a prisoner must also demonstrate that the underlying ineffective-assistanee-of-trial-counsel claim is a substantial one, which is to say that the prisoner must demonstrate that the claim has some merit,”
Id.
at 1318-19 (citing
Miller-El v. Cockrell,
537 U.S. 322, 123 S.Ct. 1029, 154 L.Ed.2d 931 (2003)).
In
Trevino,
the Court expanded
Martinez
and held that
Martinez’s
exception also applies “when a state’s procedural framework makes it ‘highly unlikely’ that a defendant in a typical case will have a meaningful opportunity’ to raise ineffective-assistance claims on direct appeal,” even if the state does not explicitly require ineffective-assistance-of-trial-counsel claims to be brought only on collateral review.
Sutton,
745 F.3d at 791 (quoting
Trevino,
133 S.Ct. at 1921). Cur determination of whether the
Martinez-Trevino
rule applies depends on proceedings in the state trial court on its initial post-conviction review, and “does not extend to ‘appeals from initial-review collateral proceedings ....’”
Abdur’Rahman v. Carpenter,
805 F.3d 710, 713 (6th Cir. 2015) (quoting
Martinez,
132 S.Ct. at 1320). We have held that the
Martinez-Trevino
rule applies in Tennessee cases.
Sutton,
745 F.3d at 792.
2. Application of
Martinet
and
Trevino
to Middlebrooks’s Claims
On remand to the district court, Middle-brooks argued that
Martinez
and
Trevino
apply to excuse the procedural default of twenty-six of the ineffective-assistance-of-trial-counsel claims that he raised in his habeas petition.
See
R. 102 (Pet.
Martinez
Br. at 14) (Page ID #612). The district court concluded that relief was not warranted because Middlebrooks’s ineffective-assistance-of-trial-counsel Claims 9a and 9b — two claims addressed by our prior decision — were not “substantial” under
Martinez.
R. 105 (08/01/14 D. Ct. Op. at 25) (Page ID #810). Middlebrooks contends on appeal that the district court used the wrong standard to determine whether his claims were “substantial.” Appellant Br. at 45-46. Moreover, Middlebrooks argues that the district court erroneously failed to consider the twenty-four remaining claims presented in his habeas petition.
Id.
at 50-51.
We agree with Middlebrooks that the district court erred in its “substantiality” inquiry. The district court determined that Claims 9a and 9b were insubstantial because we held in our prior opinion that Middlebrooks failed to establish “cause” and “prejudice” to excuse their default. R. 105 (08/01/14 D. Ct. Op. at 25) (Page ID #810);
see also Middlebrooks,
619 F.3d at 537-38. Under
Martinez,
however, an underlying ineffective-assistance-of-trial-counsel claim is “substantial” if it “has some merit,” á different inquiry.
Martinez,
132 S.Ct. at 1318-19 (citing
Miller-El,
537 U.S. 322, 123 S.Ct. 1029). Despite this error, we affirm the district court’s judgment for an alternative reason.
See Loftis v. United Parcel Serv., Inc.,
342 F.3d 509, 514 (6th Cir. 2003). After carefully reviewing the record, we find that
Martinez
and
Trevino
do not affect Middlebrooks’s habe-as claims because these claims were either (1) defaulted on post-conviction appeal; (2) defaulted on appeal to our court; or (3) resolved’ on the merits in state court and our prior opinion.
a. Claims 9a and 9b
Following the district court’s initial denial of Middlebrooks’s habeas petition, we granted a COA to address four of Middle-brooks’s ineffective-assistance claims.
Middlebrooks,
619 F.3d at 535. Middlebrooks argues that two of the claims that we
addressed in our prior opinion — Claims 9a and 9b — fall under the rule of
Martinez-Trevino.
Appellant Br. at 47-49. We disagree.
' Claim 9a of Middlebrooks’s habeas petition asserts that his counsel was ineffective in failing to investigate and present evidence of Middlebrooks’s brain damage. Appellant App. at 171. Claim 9b alleges that Middlebrooks’s trial counsel was ineffective in “failing] to investigate Mr. Middlebrooks’s history of severe physical and sexual abuse.”
Id.
at 174;
see also Middlebrooks,
619 F.3d at 637. In denying Mid-dlebrooks relief on the basis of these claims, our prior opinion held that Middlebrooks procedurally defaulted both of these issues by “fail[ing] to offer any authority in support ... on postconviction appeal” to the Tennessee Court of Criminal Appeals.
Middlebrooks,
619 F.3d at 535-36. Specifically, Middlebrooks failed to comply with Tennessee Court of Criminal Appeals Rule 10(b), which states that “[tissues which are not supported by argument, citation to authorities, or appropriate references to the record will be treated as waived.”
Id.
at 535-36 (quoting Tenn. Ct. Crim. App. R. 10(b)). Middlebrooks raised his trial counsel’s failure to investigate his brain damage and his trial counsel’s failure to investigate his history of abuse “in an addendum to his appellate brief,” but Middlebrooks provided no further argument or citations.,
Id.
at 536, 538. The Tennessee Court of Criminal Appeals accordingly held that Middlebrooks/waived these claims.
Id.
at 536, 538;
see also Middlebrooks,
2003 WL 61244, at *12.
Significantly, the
Martinez-Tremno
exception does not apply to save procedural defaults that occur in “appeals from initial-review collateral proceedings.”
Martinez,
132 S.Ct. at 1320;
see West v. Carpenter,
790 F.3d 693, 698 (6th Cir. 2015). “[Attorney error at state postconviction appellate proceedings cannot excuse procedural default under the
Martinez-Tremno
framework.”
West,
790 F.3d at 699.
Had Middlebrooks not procedurally defaulted on Claims 9a and 9b at the appellate stage of his initial state post-conviction review, habeas relief on these claims would still be inappropriate under
Martinez-Tre-mno
because both were presented on initial state postconviction review and rejected by the court on the merits. Habeas relief is thus not warranted for Claims 9a and 9b because those claims were raised and rejected on the merits by the initial postconviction court, and ineffective assistance of counsel on post-conviction appeal cannot establish “cause” to excuse Middle-brooks’s procedural default, which occurred only in the Tennessee Court of Criminal Appeals. For those reasons,
Martinez
and
Trevino
do not apply to Claims 9a or 9b.
b. Middlebrooks’s Remaining Claims
The district court did not discuss the substantiality of Middlebrooks’s remaining twenty-four claims of ineffective assistance that were not included in the COA that we granted in Middlebrooks’s initial appeal. The state argues that, because we denied a COA for these claims, we have already determined that these claims were not “substantial” within the meaning of
Martinez,
and thus relief is not warranted. Appellee Br. at 25-27. Middlebrooks contends, by contrast, that it was error for the district court not to address these claims and that remand is appropriate for the district court to address the “substantiality” of these claims in the first instance. Appellant Br. at 51-52.
We need not decide whether our previous denial of a COA sufficiently determines the “substantiality” of these claims. Here, the record establishes that none of Middlebrooks’s remaining claims.fall under the
Martinez-Trevino
rule, even if the underlying’ ineffective-assistance-'of-trial
counsel claim is deemed “substantial” We consider each of Middlebrooks’s remaining claims below.
i. Claims Relating to Trial Counsel’s Failure to Present Evidence of Mid-dlebrooks’s Mental Illness and Brain Damage
Middlebrooks’s habeas petition presents several claims relating to his trial counsel’s “failure] to investigate and present evidence of mental illness and brain damage,” including Claims 9g,
9j,
and 9cc.
Appellant App. at 176, 178-79;
see
Appellant Br. at 52. As the government argues, however, these claims are cumulative of Claim 9a of Middlebrooks’s habeas petition, which alleges that "[tjrial counsel failed to investigate and present evidence of Donald Middlebrooks’s seizure disorder to the jury, failed to investigate and present evidence that Donald Middlebrooks does in fact suffer severe mental illness ... and failed to investigate and present evidence ... that Donald Middlebrooks suffers brain injury and/or brain dysfunction.” Appellant App. at 171;
see
Appellee Br. at 28. As discussed above, we determined in our prior opinion that Middlebrooks defaulted Claim 9a on post-conviction appeal to the Tennessee Court of Criminal Appeals.
Middlebrooks,
619 F.3d at 535-36. Because these additional claims duplicate Claim 9a, Middlebrooks is similarly not entitled to relief on these claims.
ii. Claims Relating to Trial Counsel’s Failure to Present Evidence of Brew-ington’s Relative Culpability
Middlebrooks also raises several claims that his trial counsfel was ineffective in failing to make arguments or develop evidence relating to the relative culpability of his co-defendant Brewington, including Claims 9c,
9d,
9q,
9gg,
and 9ii,
See
Appellant Br. at 61. These claims are duplicative of Claim 9hh of Middlebrooks’s federal habeas petition, however, which alleges that “[t]rial counsel failed to recognize, investigate, pursue, develop and
present mitigating evidence regarding co-defendant Brewington’s relative dominance over Donald Middlebrooks.” Appellant App. at 179. “[T]he Tennessee Court of Criminal Appeals resolved this claim on the merits on postconviction review,” concluding that Middlebrooks could not establish prejudice under
Strickland v. Washington,
466 U.S. 668, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984).
Middlebrooks,
619 F.3d at 538-39. We held in our prior opinion that, “[constrained by AEDPA, we must affirm because we cannot say that the state court’s application of
Strickland’s
prejudice prong was unreasonable.”
Id.
at 541. Because Claims 9c, 9d, 9q, 9gg, and 9ii are cumulative of Claim 9hh — a claim that was not defaulted on initial-review collateral proceeding but rather was determined on the
merits
— Martinez-
Trevino
does not apply, and Middlebrooks is not entitled to relief or further evidentiary development on the basis of these claims.
See Moore v. Mitchell,
708 F.3d 760, 785 (6th Cir. 2013).
We note that Claim 9c, which faults counsel for “failing] to argue to the jury that the death sentence was improper where Roger Brewington only received a life sentence,” is the most distinctive of these claims (as it contends that counsel failed to make a specific sentencing argument to the jury), and that a colorable argument could be made that 9c was therefore not. considered by the state court. In that scenario, we would remand Claim 9c to the district court for analysis of whether the claim is substantial under
Martinez.
We conclude that remand on Claim 9c is unnecessary, because even if Claim 9c is determined to be substantial, we are convinced by the record in its entirety and the arguments raised in and rejected by the initial post-conviction court that any failure of trial counsel to argue for a lesser sentence as contemplated by this claim did not prejudice Middlebrooks because there is not a reasonable probability that counsel’s failure to make the argument affected the outcome of his sentencing. .
iii. Claims Relating to Trial Counsel’s Failure to Prepare Defense Expert Dr. Smalldon
Middlebrooks’s habeas petition raised numerous claims relating to trial counsel’s failure to communicate with Dr. Smalldon and adequately prepare for his testimony, including Claims 9k
and 91.
See
Appellant Br. at 52. The record demonstrates, however, that these claims are cumulative of Claim 9e of Middlebrooks’s habeas petition, which asserts that .“[t]rial counsel failed to adequately prepare for the testimony of its expert, Dr. Jeffrey Smalldon.” Appellant App. at 176. We explained in our prior opinion that Middlebrooks abandoned Claim 9e on appeal to our court because Middlebrooks presented no argument in his opening brief and failed to raise any argument on reply, even after the state addressed Middlebrooks’s omission.
Middlebrooks,
619 F.3d at 538. Accordingly, because Claims 9k and 91 duplicate a claim that Middlebrooks abandoned on appeal to our court,
Martinez
and
Trevino
do not apply.
iv. Claim Relating to Trial Counsel’s Failure to Object to the Victim’s Mother at the Prosecution Table
Claims 9s and 9nn of Middlebrooks’s petition allege that trial counsel was ineffective for fading “to make sufficient objections to the presence of the mother of the victim at counsel table for the prosecution and to her behavior at trial,” and for failing to argue this on direct appeal. Appellant App. at 177, 182-83;
see
Appellant Br. at 64. A review of the record establishes that Middlebrooks raised the issue of the victim’s mother sitting at the prosecution table in his initial-review proceedings in Tennessee state court: this claim was labeled as Claim (9)(n)
in his state post-conviction petition. Appellee App. at 9. Middlebrooks included Claim (9)(n) in the addendum that he filed in the Tennessee Court of Criminal Appeals, but presented no additional argument or citations.
Id.
at 105. Because these claims were considered and rejected on the merits by the initial state post-conviction court,
Martinez
and
Trevino
cannot apply to cure any procedural default that may have occurred át the state appellate court.
v. Claim Relating to Trial Counsel’s Failure to Suppress Middlebrooks’s Statements to the Police
Claim 9r of Middlebrooks’s habeas petition contends that trial counsel was ineffective in “fail[ing] to investigate and develop appropriate evidence to suppress Donald Middlebrooks’s statements to the police.” Appellant App. at 177;
see
Appellant Br. at 67. Like the claim described above, however, this claim was included in Middlebrooks’s initial post-conviction motion in state trial court: Middlebrooks labeled this claim in his state-court petition as Claim (9)(m). Appellee App. at 9. As with the claim discussed above, this claim was considered and rejected on the merits by the initial post-conviction court, and
Martinez
and
Trevino
do not apply to the failure to preserve this claim on appeal.
vi.Claim Relating to Trial Counsel’s Failure to Request Jury Instruction
. Claim 9mm(6) of Middlebrooks’s habeas petition alleges that trial counsel was ineffective in failing to request a contemporaneous jury instruction regarding Middle-brooks’s lack of remorse. Appellant App. at 182;
see
Appellant Br. at 68. A review of the record demonstrates that Middle-brooks included this claim in his initial post-conviction petition in state trial court, labeled as Claim (9)(hh)(vi).
Appellee App. at 14. Like the two claims above, this claim is not affected by
Martinez-Trevino.
vii.Claims Relating to Trial Counsel’s Failure to Strike Jurors or Appropriately Charge Jurors
Middlebrooks’s habeas petition also raises several claims relating to trial counsel’s ineffectiveness for failing to strike various jurors, including Claims 9w
and 9y,
in
addition to both claims labeled 9x.
Appellant App. at 178;
see
Appellant Br. at 71. These claims were presented in his initial post-conviction petition in state-trial court, however, as Claims (9)(r)
and (9)(hh)(viii).
Appellee App. at 9, 14. The same is true for Claim 9t of Middle-brooks’s federal habeas petition, which asserts that “[tjrial counsel failed to object to charging the jury pursuant to the statutory language regarding mitigating circumstances.” Appellant App. at 177;
see
Appellant Br. at 74. This was presented in Middlebrooks’s initial petition as (9)(o),
see
Appellee App. at 9. Like the claims discussed above, this claim is not saved by
Martinez-Trevino.
Significantly, in concluding its initial post-conviction opinion, the state court stated, “[t]he Court has considered all the other grounds set forth in the petition and finds them without merit. They are grounds previously determined or grounds upon which no proof was offered," State Ct. Mem. & Order at 28,
Accordingly, after careful review of the record, we find that Middlebrooks’s remaining claims were either resolved on the merits, defaulted in post-conviction appeal, or defaulted on appeal to this court, and thus Middlebrooks is not entitled to habeas relief pursuant to
Martinez
and
Trevino.
B. Middlebrooks is Not Entitled to Relief Under the Eighth Amendment
Middlebrooks next contends that our prior opinion failed to address his Eighth Amendment argument — Claim 13(c) in his federal habeas petition — that the prosecution violated
Booth v. Maryland,
482 U.S. 496, 107 S.Ct. 2529, 96 L.Ed.2d 440 (1987), and
Payne v. Tennessee,
501 U.S. 808, 830 n.2, 111 S.Ct, 2597, 115 L.Ed.2d 720 (1991), by arguing in its closing argument for the jury to impose the death penalty “based upon the wishes of the victim’s mother.” Appellant Br. at 82. We note that this is the third time that Middlebrooks has presented his
Booth
argument to our panel. Middlebrooks argued that
Booth
entitled him to relief in his appeal from the district court’s initial denial of his habeas petition.
See
2009 Appellant Br. at 64; 2009 Reply Br. at 19. Following our 2010 opinion, Mid-dlebrooks argued in a petition for panel rehearing that we incorrectly addressed his Eighth Amendment claim. We denied Middlebrooks’s petition for panel rehearing on February 1, 2011.
See Middlebrooks
v. Bell,
619 F.3d 526 (6th Cir.2011) (unpublished order). We find no error in our prior panel decision.
On direct appeal in state court, Middle-brooks argued that the prosecutor improperly “emphasized] the victim’s family’s desire that the death penalty be returned,”
State v. Middlebrooks,
995 S.W.2d at 557. Middlebrooks contended “that the misconduct violated his right to due process and led to arbitrary and unreliable sentencing in violation of the Eighth and Fourteenth Amendments to the United States Constitution,” in addition to the Tennessee Constitution.
Id.
“[T]he Tennessee Supreme Court concluded that [the prosecutor’s] statements were improper but that they did not require reversal because they did not affect the jury’s verdict.”
Middlebrooks,
619 F.3d at 543 (citing
Middlebrooks,
995 S.W.2d at 557-61). Our prior opinion reviewed whether the state court unreasonably applied
Darden v. Wainwright,
477 U.S. 168, 106 S.Ct. 2464, 91 L.Ed.2d 144 (1986), which establishes the standard for determining whether a prosecutor’s “comments were flagrant enough to violate” the defendant’s due-process rights.
Middlebrooks,
619 F.3d at 543. We held that the Tennessee Supreme Court did not unreasonably apply federal law.
Id.
at 544.
Middlebrooks contends that the Tennessee Supreme Court’s decision was contrary to
Booth
and
Payne
and that our opinion erroneously ignored the Eighth Amendment in applying
Darden
and the due-process clause. Apellant Br. at 82, 86-87. We disagree. The Supreme Court in
Booth
evaluated the constitutionality of admitting a “Victim Impact Statement” into evidence at a capital sentencing hearing; the impact statement at issue contained two types of information: “[f]irst, it described the personal characteristics of the victims and the emotional impact of the crimes on the family,” and “[s]econd, it set forth the family members’ opinions and characterizations of the crimes and the defendant.”
Booth,
482 U.S. at 502, 107 S.Ct. 2529. The Supreme Court held that the admission into evidence of both types of information violated the Eighth Amendment.
Id.,
at 507-09, 107 S.Ct. 2529. The Court revisited its holding in
Booth
a few years later in
Payne v. Tennessee,
501 U.S. 808, 827, 111 S.Ct. 2597, 115 L.Ed.2d 720 (1991), holding that “if the State chooses to permit the admission of victim impact evidence ..,, the Eighth Amendment erects no
per se
bar.” Instead, “[i]n -the event that evidence is introduced that is so unduly prejudicial that it renders the trial fundamentally unfair, the Due Process Clause of the Fourteenth Amendment provides a mechanism for relief.”
Id.
at 825, 111 S.Ct. 2597 (citing to
Darden,
477 U.S. at 179-83, 106 S.Ct. 2464). We have observed that the Court noted that its decision in
Payne
“overturned only that part of
Booth
that disallowed ‘evidence ... relating to the victim and the impact of the victim’s death on the victim’s family,’ ” but thai; it was not disturbing the “portion of
Booth
that forbids ‘a victim’s family members’ characterization and opinions about the crime, the defendant, and the appropriate sentence’ ” from being admitted into evidence.
Fautenberry v. Mitchell,
515 F.3d 614, 638 (6th Cir. 2008) (quoting
Payne,
501 U.S. at 830 n.2, 111 S.Ct. 2697).
Middlebrooks argues that because
Payne
did not disturb
Booth’s
holding that the Eighth Amendment prohibits evidence of “a victim’s family members’ characterization and opinions about ... the appropriate sentence,” our earlier opinion in
Middlebrooks
failed to evaluate whether the Tennessee Supreme Court’s decision is contrary to
Booth.
Contrary to Middle-brooks’s argument, however, we appropriately applied
Darden
to the state court’s decision. In evaluating Middlebrooks’s argument on direct appeal, the Tennessee Supreme Court cited
Booth
and
Payne,
but recognized that
evidence
of the victim’s opinions about the crime was not admitted at Middlebrooks’s sentencing hearing, as was the case in Booth; instead, the prosecutor in Middlebrooks’s trial made improper statements during closing arguments.
Middlebrooks,
995 S.W.2d at 558. The Tennessee Supreme Court evaluated Middlebrooks’s argument under a heading entitled “prosecutorial misconduct” and ultimately “conclude[d] that the prosecutor’s misconduct did not prejudicially affect the jury’s verdict” after applying its five-factor test for evaluating a prosecutor’s remarks.
Id.
at 557-60 (citing
State v. Bigbee,
885 S.W.2d 797, 809 (Tenn. 1994)). We did not overlook or erroneously evaluate Claim 13(c) in our prior opinion; rather, because the prosecution had not introduced evidence at sentencing in violation of
Booth,
we dismissed Middlebrooks’s claims on the merits under AEDPA after determining that the state court did not unreasonably apply
Darden, see Middlebrooks,
619 F.3d at 543-44, which is the relevant “clearly established Federal law” for evaluating whether a prosecutor’s improper statements during closing arguments “so infected the trial with unfairness so as to make the resulting conviction a denial of due process.”
See Parker v. Matthews,
567 U.S. 37, 132 S.Ct. 2148, 2153, 183 L.Ed.2d 32 (2012) (quoting
Darden,
477 U.S. at 181, 106 S.Ct. 2464). Middlebrooks is not entitled to relief on this claim.
III. CONCLUSION
For the foregoing reasons, we AFFIRM the district court’s judgment denying Mid-dlebrooks’s petition for a writ of habeas corpus.