DUBINA, Circuit Judge:
Petitioner, Torréy Twane McNabb, is currently serving a death sentence following his convictions for two counts of capital murder in connection with the murder of a Montgomery, Alabama, police officer. After unsuccessful state appeals and post-conviction proceedings, McNabb filed a federal habeas petition pursuant to 28 U.S.C. § 2254. The federal district court denied McNabb relief and also denied his motion to alter or amend the final judgment pursuant to Rule 59(e) of the Federal Rules of Civil Procedure. However, the district court did grant McNabb’s petition for a certificate of appealability (“COA”) on the issues that he raised in his Rule 59(e) motion. Upon review of the record, [1336]*1336including the briefs of the parties, and having the benefit of oral argument, we affirm the district court’s judgment denying McNabb’s federal habeas petition and his Rule 59(e) motion.
I. BACKGROUND
Facts
At trial, the State presented the testimony of numerous witnesses who were near the intersection of Rosa Parks Avenue and National Avenue in Montgomery, Alabama, on September 24, 1997, the day McNabb shot and killed Officer Anderson Gordon. Sanford Sharpe, a bail bondsman, testified that he was attempting to locate McNabb pursuant to a capias warrant because McNabb had failed to appear for two court appearances relating to charges of receiving stolen property and possession of a controlled substance. [R. Vol. 13 p. 1759-Vol. 14 p. 1857.] On this fateful day, Sharpe located McNabb sitting in an automobile parked on the street outside his grandmother’s residence. Sharpe attempted to pull his truck in front of McNabb’s vehicle to block McNabb, but McNabb sped away when he saw Sharpe. While pursuing McNabb, Sharpe saw McNabb run past a stop sign and strike another vehicle. As Sharpe approached the accident, McNabb got out of his vehicle, pulled a gun, and began shooting at Sharpe. Sharpe began to speed from the scene and telephoned 911. When he returned to the- scene of the vehicle accident, Sharpe parked next to a Montgomery police patrol car and saw that the officer in the patrol car had been shot several times.
Annie Gamble testified that she was driving on Rosa Parks Avenue when a white vehicle ran a stop sign and struck her car. [R. Vol. 14, p. 185871889.] She stated that a man, whom she later identified as McNabb, exited the white vehicle and waved a gun in her direction. Gamble pleaded with him not to shoot her. She saw a red truck drive by and McNabb began shooting at it. After the truck disappeared from sight, Gamble testified that McNabb walked to the patrol car with his gun hidden from the officer’s view. She noticed that “some words were passed” between McNabb and the officer, and when McNabb reached the rear of the patrol car, he began firing into the car. [Id. at 1871.] When the officer attempted to return fire, Gamble stated that McNabb fled, running behind a nearby church.
Christopher Best testified that he was walking toward the Beulah Baptist Church at the time of the vehicle accident involving McNabb and Gamble. [R. Vol. 14, p. 1894-1910.] He saw McNabb exit the white vehicle and begin shooting at a red truck that was driving down National Avenue. When Best heard the first shot, he ran behind the church for cover and later heard several gunshots in rapid succession. He then heard Gamble screaming for someone to call 911 so he entered the church and asked someone to call emergency. When he returned to the intersection, a crowd had gathered, and he noticed that both the front and back windows on the driver’s side of "the police car had been shot and were no longer intact.
The State also presented the testimony of Michael Johnson, who lived in a residence located at the intersection where the crime occurred. [Id. at .191171928.] Johnson testified that he heard what he thought were firecracker explosions about the time of the vehicle accident and looked out his front window. [Id. at 1912713.] From there, Johnson saw a Montgomery police patrol car stop in front of the church. He then saw a young black male, wearing dark-colored shorts and no shirt, approach the patrol car, holding a gun behind his back. After the police officer rolled down his window and spoke to the [1337]*1337young man, the man opened fire on the officer “out of .the blue.” [Id. at 1915.] Johnson testified that when the young man first fired at the police officer, he did not see a weapon in the hands of the police officer. Jeffrey Dyson testified that he was working on the cable near the corner of the intersection and saw the two wrecked vehicles. [Id. at 192871941.] He noticed a man with green shorts and no shirt walk toward a Montgomery police patrol car with his hands behind his back. Dyson testified that he returned-to work at this point, but almost immediately, heard gunshots. When he turned around, Dyson saw the man shooting at the officer in the patrol ear. [Id. at 1931.] John Reynolds testified that he was working behind Beulah Baptist Church on the day in question when he heard what sounded like a vehicle collision at the roadway intersection. [Id. at 194271945.] He then heard gunshots, ran for cover, then heard more gunshots, and saw a man wearing green shorts and no shirt run behind the church and “scale the fence.” [Id. at 1943.] Reynolds saw the man drop a gun on the ground, but he picked it up before he climbed the fence. The man then ran toward a ditch behind the church.
Corporal E.B. White testified that he received a call about a shooting at the intersection of Rosa Parks Avenue and National Avenue on September 24, 1997. [R. Vol. 14, p. 1947-1956.] He saw Corporal Gordon “slumped over in the seat,” and he tried to revive him, but was unsuccessful. [Id. at 1949-50.] Officer Perkins testified that he responded to the emergency call regarding the gunshots and met Officer Danny Jackson at the Beulah Baptist Church. [R. Vol. 14, p. 1985-Vol. 15 p. 2011.] Wfiiile they surveyed the area around the ditch, a man who was in the vicinity alerted the officers to McNabb’s hiding place in the ditch. At that point, McNabb stood up in the ditch and fired at Officer Perkins, one time. Officer Jackson returned fire, wounding McNabb.
Procedural History
A grand jury indicted McNabb for the capital offense of murdering Montgomery County Police Officer Anderson Gordon, in violation of Alabama Code § 13A-5-40(a)(5) (1975) (murder of police officer on duty), and for the capital offense of murdering Officer Gordon while he was sitting in his patrol car, in violation of Alabama Code § 13A-5-40(a)(17) (1975) (murder committed by or through the use of a deadly weapon while the victim is in a vehicle). In separate indictments, the grand jury indicted McNabb for the offense of attempted murder of Montgomery County Police Officer William Perkins and the attempted murder of Sanford Sharpe, violations of Alabama Code § 13A-4-2 (1975). The trial court consolidated the charges for trial.
At trial, McNabb admitted that he shot and killed Officer Gordon and that he had fired at Sharpe' and Officer Perkins. However, he asserted two somewhat conflicting defenses. As to the charge of attempted murder of Sanford Sharpe, McNabb asserted that he acted in self-defense. As to both capital murder charges and both attempted murder charges, McNabb asserted that he did not have the intent to kill when he shot Officer Gordon and shot at the other two men because he had ingested so much cocaine on the morning of the shootings that he was in a cocaine-induced state of paranoia that left him unaware of his actions.
The jury found McNabb guilty of all charges. After a penalty phase proceeding, the jury recommended, by a vote of ten to two, that McNabb- be sentenced to death. The trial court followed the jury’s recommendation and imposed a death sentence. On direct appeal, the Alabama [1338]*1338Court of Criminal Appeals (“ACCA”) affirmed McNabb’s convictions but remanded the case to the trial court with instructions that the trial court make corrections to its sentencing order. McNabb v. State, 887 So.2d 929," 989 (Ala.Crim.App.2001). On return from remand, the ACCA affirmed McNabb’s convictions and sentence.
While McNabb’s case was pending in the ACCA on his application for rehearing, the United States Supreme Court issued its decision in Ring v. Arizona, 536 U.S. 584, 122 S.Ct. 2428, 153 L.Ed.2d 556 (2002). At the ACCA’s request, the parties filed supplemental briefs addressing the effect, if any, of this decision upon McNabb’s sentence. The ACCA denied McNabb’s application for rehearing, finding that his death sentence did not violate Ring. The Alabama Supreme Court affirmed his convictions and death sentence, Ex parte McNabb, 887 So.2d 998 (Ala.2004), and the United States Supreme Court denied his petition for certiorari review, McNabb v. Alabama, 543 U.S. 1005, 125 S.Ct. 606, 160 L.Ed.2d 466 (2004).
McNabb filed a petition for post-conviction relief, pursuant to Rule 32 of the Alabama Rules of Criminal Procedure. The state circuit court summarily dismissed his petition for post-conviction relief, and the ACCA affirmed. McNabb v. State, 991 So.2d 313, 335-36 (Ala.Crim.App.2007). The Alabama Supreme Court denied the petition for certiorari. Ex parte McNabb, 991 So.2d 336 (Ala.2008). Thereafter, McNabb filed a federal petition for writ of habeas corpus, which the district court denied. McNabb filed a motion to alter or amend the district court’s final judgment, pursuant to Rule 59(e), which the district court denied. The district court then granted McNabb’s request for a COA on the issues he raised in his Rule 59(e) motion.
II. ISSUES'
1. Whether the district court abused its discretion in dismissing McNabb’s habeas petition before the parties had filed additional briefs addressing the merits of his claims.
2. Whether the district court erred in denying relief on McNabb’s claims alleging that his counsel were ineffective for failing to investigate adequately and present mitigation evidence regarding his background.
3. Whether the district court erred in dismissing McNabb’s challenge to Alabama’s lethal injection protocol as unconstitutional because it determined that McNabb’s manner of execution claim would be more properly raised in a 42 U.S.C. § 1983 action.
4. Whether the district court erred in conducting a deferential review of McNabb’s ineffective assistance of counsel claims.
III. STANDARDS OF REVIEW
“We review de novo the denial of a petition for writ of habeas corpus.” Jamerson v. Sec’y for Dep’t of Corr., 410 F.3d 682, 687 (11th Cir.2005). The Antiterrorism and Effective Death Penalty Act (“AEDPA”) precludes federal courts from granting habeas relief on any claim adjudicated on the merits in state court unless the state court’s decision “was contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States.” 28 U.S.C. § 2254(d)(1); see also Berghuis v. Thompkins, 560 U.S. 370, -, 130 S.Ct. 2250, 2259, 176 L.Ed.2d 1098 (2010). This standard is “a highly deferential” one that “demands that state-court decisions be given the benefit of the doubt.” Renico v. Lett, 559 U.S. 766, 773, 130 S.Ct. 1855, 1862, 176 L.Ed.2d 678 (2010) (internal quotation marks omitted). [1339]*1339“A state court decision is ‘contrary to’ clearly established federal law if it applies a rule that contradicts the governing law set forth by the United States Supreme Court, or arrives at a result that differs from Supreme Court precedent when faced with materially- indistinguishable facts.” Ferguson v. Sec’y, Fla. Dep’t of Corr., 716 F.3d 1315, 1331 (11th Cir.2013). An “unreasonable application” of federal law occurs when a state court correctly identifies the governing legal principle from the relevant Supreme Court decisions but unreasonably applies that legal principle to the facts of the particular case. Id. “[A]n unreasonable application of federal law is different from an incorrect application of federal law.” Williams v. Taylor, 529 U.S. 362, 410, 120 S.Ct. 1495, 1522, 146 L.Ed.2d 389 (2000). “A state court’s application of clearly established federal law or its determination of the facts is unreasonable only if no ‘fairminded jurist’ could agree with the state court’s determination or conclusion.” Ferguson, 716 F.3d at 1332 (quoting Holsey v. Warden, Ga. Diagnostic Prison, 694 F.3d 1230, 1257 (11th Cir.2012)).
To prevail on his claim of ineffective assistance of counsel, McNabb must establish “both that trial counsel’s ‘performance was deficient, and that the deficiency prejudiced the defense’ ” during the penalty phase. Ponticelli v. Sec’y, Fla. Dep’t of Corr., 690 F.3d 1271, 1294 (11th Cir.2012) (quoting Wiggins v. Smith, 539 U.S. 510, 521, 123 S.Ct. 2527, 2535, 156 L.Ed.2d 471 (2003)), cert. denied, — U.S. -, 133 S.Ct. 2856, — L.Ed.2d -(2013). The performance prong is satisfied only if the petitioner “show[s] that counsel’s representation fell below an objective standard of reasonableness.” Strickland v. Washington, 466 U.S. 668, 688, 104 S.Ct. 2052, 2064, 80 L.Ed.2d 674 (1984). In other words, the petitioner “must establish that no competent counsel would have taken the action that his counsel did take.” Chandler v. United States, 218 F.3d 1305, 1315 (11th Cir.2000) (en banc). Under the prejudice prong, the petitioner must show a “reasonable probability” that, but for counsel’s errors, the outcome of his trial would have been different. Strickland, 466 U.S. at 694, 104 S.Ct. at 2068. “A reasonable probability is a probability sufficient to undermine confidence in the outcome.” Id. at 694, 104 S.Ct. at 2068. Furthermore, “[bjecause the failure to demonstrate either deficient performance or prejudice is dispositive ... there is no reason for a court deciding an ineffective assistance claim to address both components of the inquiry if the defendant makes an insufficient showing on one.” Windom v. Sec’y, Dep’t of Corr., 578 F.3d 1227, 1248 (11th Cir.2009) (internal quotation marks and alteration omitted).
IV. DISCUSSION
A. Dismissal of habeas petition
McNabb asserts that the district court violated his procedural due process rights when it decided the merits of his habeas claims without allowing him an opportunity to submit a brief in support of his claims. McNabb claims that he relied upon the magistrate judge’s scheduling order, which stated that the court would determine first whether any claims were procedurally barred from federal review and then order briefing on the merits of the remaining claims. We agree that McNabb should have been able to rely upon the court’s scheduling order; however, the failure of the district court to give notice to the parties that it would decide the merits of the claims without briefing does not rise to the level of a due process violation.
First, the Rules Governing Section 2251 Cases do not specifically provide for [1340]*1340briefing before a district court disposes of a habeas petition. Rule 2(c) provides that the petition must specify all grounds for relief, state the facts supporting ■ all grounds, and state the relief requested. See Jones v. Sec’y, Dep’t of Corr., 607 F.3d 1346, 1354 (11th Cir.2010) (“By rule, in the district court, a petition for a writ of habeas corpus must specify all the grounds for relief available to the petitioner.” (internal quotation marks omitted)). Rule 4 provides that a district court must examine promptly a petition and must dismiss it “[i]f it plainly appears from the petition and any attached exhibits that the petitioner is not entitled to relief in the district court.” Rules Governing Section 2254 Cases, Rule 4. Rule 5 governs the filing of the respondent’s answer, and it specifies the specific material the respondent must include with its filing. Rule 6, 7, and 8 address discovery, expansion of the record, and procedure for an evidentiary hearing, respectively. None of the remaining rules address briefing. Thus, there is no provision in the habeas rules that contemplates that a district court should grant the parties leave to file briefs addressing the merits of the claims that are contained in the habeas petition. See, e.g., Maynard v. Dixon, 943 F.2d 407, 411-12 (4th Cir.1991) (affirming a district court’s order adjudicating a habeas petition without briefing and stating that “the district court acted consistently with the rules in deciding on its own that no evidentiary hearing was required and that briefing was unnecessary”). Although adversarial briefing is vital to the court’s decision-making process, a petitioner has no right to briefing in his habeas proceeding. Accordingly, we conclude that the district court did not violate McNabb’s due process rights in this circumstance.
We are hard-pressed, however, to understand why the district court permitted the case to languish for approximately four years without any determination on which issues were procedurally barred from federal review. It was the State who brought the matter to the district court’s attention by filing a motion requesting a ruling on the issues that were procedurally barred. Of course, at that time, McNabb could have requested leave of court to file a brief on the merits of his petition before the district court ruled, or he could have filed a brief because the scheduling order provided a time table for such filing. Instead, McNabb remained silent and did not raise any challenge to this procedure until he filed his Rule 59(e) motion. The district court did address the challenge in its order denying McNabb’s Rule 59(e) motion, stating that the court had exhaustively reviewed the record and concluded that because no evidentiary hearing was necessary, the court was within its discretion to dispose of the habeas petition without merits briefing. We may not fully condone this procedure, but neither can we say it amounted to a due process violation. Accordingly, McNabb is not entitled to relief on this claim.
B. Ineffective assistance of penalty phase counsel
McNabb contends that the district court erred in determining that the state courts reasonably applied Strickland to his claims of ineffective assistance of penalty phase counsel because there was no evidence that his counsel conducted an adequate mitigation investigation and his counsel failed to introduce any mitigation evidence at his sentencing proceeding. McNabb also asserts that the state courts unreasonably applied Strickland’s prejudice prong because there was significant mitigation evidence that counsel failed to present that would have changed the outcome of his sentencing. The specific mitigation evidence that McNabb claims would have [1341]*1341changed the outcome of his sentence was the fact that he grew up' in a housing project living with ten people in. a two-bedroom apartment; -that his mother was a sexual abuse victim and longrterni drug addict who prostituted herself for drugs; that McNabb had no contact with his father during his formative years because his father was in prison; that McNabb was very attached to his grandmother, the only stable influence in his life, who moved away when he was 14 years old; and that his mother had a relationship with a drug dealer who enlisted McNabb to deal drugs for him.
In his state post-conviction . petition, McNabb argued that his trial counsel performed deficiently because they did not investigate his family life and social history, did not locate and interview family members, teachers, and social workers who knew him, and did not request any health or education records. In rejecting his claim, the state circuit court reasoned as follows:
This claim is dismissed because McNabb has not met his burden of pleading with specificity. Ala.'R.Crim. P. 82.6(b). Although McNabb alleges that his trial counsel were ineffective for failing to investigate mitigation evidence, he has not alleged in his petition any mitigation evidence that trial counsel should have uncovered-.... In fact, at the September 30, 2005, hearing held on the State’s motion to dismiss McNabb’s petition, his counsel admitted that he does not know whether trial counsel investigated any mitigation evidence or to what extent they may have investigated claims. Furthermore, McNabb has not named any witness that counsel should have called in the penalty phase. Nor has he pleaded what those witnesses’ testimony would be or pleaded how it would have affected the outcome of that phase of the trial. Additionally, McNabb has not pleaded what specific records were not obtained by trial counsel, what information is contained in those records, or how their contents would have affected the outcome of the penalty phase. Finally,' McNabb has not named any “medical or mental health expert,” that should have been called to testify or stated what their testimony would have been had they been called to testify. Thus, McNabb has utterly failed to satisfy Rule 32.6(b)’s requirement of full factual pleading, and this claim is summarily dismissed.
[R. Vol. 27, Tab R-61, p. 21?22 (internal citations omitted).] The ACCA affirmed the circuit court’s order dismissing McNabb’s Rule 32 post-conviction petition on this ground.
Furthermore, the state court adjudicated McNabb’s claim that his trial counsel failed to present valuable, readily-available-, mitigation evidence at his sentencing proceeding. The state circuit court first dismissed the claim because it found no material issue of law or fact to exist that would entitle McNabb to relief. ' [Id., p. 23 (citing Ala. R.Crim. P. 32.7(d)).] The state court then found that the information McNabb alleged his family members or former teachers could have provided to the jury were, in fact, presented through his own testimony. Specifically,, the court stated:
McNabb testified that he was addicted to cocaine at the time of the murder and that he had been addicted- to cocaine for one to two years prior to the murder. (R. 2184) He thoroughly and vividly described his drug use and his uses progression to addiction. (R. 2196-98) He testified that his mother had been addicted to drugs for as long as he could remember, and he began using drugs [1342]*1342when he was fourteen or fifteen years old. (R. 2185)
McNabb testified that he lived in Gibbs Village with his grandmother, mother, siblings, aunts, and cousins. (R. 2186) He informed the jury that there were nine to ten people living in the two-bedroom apartment in Gibbs Village. (R. 2186)
McNabb informed the jury that his father was in prison during his childhood. (R. 2189) He also testified that his paternal family would take him to visit his father in prison when he was a child. (R. 2189)
McNabb thoroughly explained to the jury that his mother was rarely around, that she received welfare checks, and that she probably wasted the welfare money on drugs. (R. 2186-87) He also explain[ed] that as a child he would find his mother in various crack houses. (R. 2186-87) McNabb further testified that his mother did not provide for the family and that she spent all of the money that she received on drugs. (R. 2186-87, 2193) Through his testimony, McNabb informed the jury that he, himself, had to provide for the family, using the money he earned from selling drugs to buy food for his siblings and to buy drugs to feed his own habit. (R. 2193-94)
[R. Vol. 27, Tab R-61, p. 23-24.]
The state circuit court further noted that McNabb explained to the jury that his family was evicted from their government subsidized home because. Keith Chainey, who had moved into their apartment after McNabb’s grandmother moved to Florida, was selling drugs from their apartment. After their eviction, McNabb’s mother and siblings moved into Chainey’s apartment, but Chainey did not allow McNabb to live with them. Thus, McNabb moved' often, living with different family members, including his father. McNabb also informed the jury about his emotional and educational difficulties in school, and that he quit school while in the ninth grade. McNabb testified to numerous encounters with law enforcement, and how one encounter led the county court to order that he attend a rehabilitation program similar to boot camp.
The state circuit court then concluded by stating:
Clearly, both this Court and the jury were well aware that McNabb experienced a deprived childhood. McNabb thoroughly informed this Court and the jury of the mitigation evidence that he now alleges his trial counsel were ineffective for failing to present. Furthermore, this Court found to exist the non-statutory mitigation evidence that McNabb now claims was not presented, balanced that information with the aggravating circumstances, and found that the aggravating circumstances far outweighed the mitigation circumstances in his case.
[Id. at 25.]
On appeal, the ACCA affirmed, noting that the record indicated that the very mitigating evidence McNabb contended was not presented to the jury was, in fact, before the jury via McNabb’s own testimony during the guilt phase. McNabb, 991 So.2d at 331-32. The ACCA also noted that the record showed that the trial court instructed the jury at the penalty phase to consider not only the evidence presented at the sentencing phase, but also any evidence presented during the guilt phase that was relevant to the existence of any aggravating or mitigating circumstance. Id. at 331. In addition, the ACCA commented that the trial court instructed the jury on a number of mitigating circumstances, and defense counsel stated during closing argument that McNabb’s cocaine usage and deprived childhood were miti[1343]*1343gating factors that outweighed the aggravating circumstances. Id. at 331-32.
On federal habeas review, the district court first found that the state courts’ adjudication of this claim of ineffective assistance of counsel was neither contrary to, nor an unreasonable application of, Strickland because McNabb failed to plead the claim with specificity and failed to show how his attorneys’ deficient investigation into his background prejudiced him. - The district court then found that the state courts’ adjudication was reasonable in light of the evidence presented to the state courts. The district court noted that there is no clearly established federal law holding that counsel’s failure to present evidence during the penalty phase that was offered at the guilt phase establishes deficient performance. Moreover, the district court found that the state trial court weighed the three statutory aggravating circumstances with the non-statutory mitigating circumstances and found that the aggravating circumstances outweighed the mitigating ones. On appeal, the ACCA independently weighed the two and -concurred with the trial court.
The district court properly denied relief to McNabb on this claim. The state courts reasonably rejected the claims of ineffective assistance of counsel because, first, McNabb failed to plead specific facts to support his claim. The ACCA affirmed on appeal, and this adjudication is a ruling on the merits. See Borden v. Allen, 646 F.3d 785, 815 (11th Cir.2011) (reviewing claims under AEDPA deference because state court “plainly utilized Rule 32.6(b) as a tool with which to address the merits” of the petitioner’s claims), cert. denied, — U.S.-, 132 S.Ct. 1910, 182 L.Ed.2d 778 (2012). Second, even if McNabb pled specific facts to demonstrate that his counsel performed deficiently, he cannot satisfy the prejudice prong of Strickland. McNabb failed to plead any specific facts or provide any specific names or information about his horrific childhood that would mitigate his sentence, or in other words, that would have lessened his culpability for the crimes. See Price v. Allen, 679 F.3d 1315, 1325 (11th Cir.2012) (finding that the allegations in petitioner’s Rule 32 petition regarding the evidence that his friends, family members, and school records would have revealed was “too general and conclusory to be able to say that there is a reasonable probability that this evidence would have changed the outcome of the petitioner’s sentencing.”), cert. denied, — U.S.-, 133 S.Ct. 1493, 185 L.Ed.2d 548 (2013). Moreover, the mitigation evidence McNabb contends should have been presented during the penalty phase was provided during the guilt phase via his own testimony; thus, this evidence would have been cumulative. See, e.g., Cullen v. Pinholster, — U.S. -, 131 S.Ct. 1388, 1409, 179 L.Ed.2d 557 (2011) (finding no reasonable probability that the additional evidence presented in state habeas proceeding would have changed jury’s verdict because the “new” evidence largely duplicated the mitigation evidence at trial); Wong v. Belmontes, 558 U.S. 15, 22, 130 S.Ct. 383, 387, 175 L.Ed.2d 328 (2009) (finding no prejudice in part where portion of the evidence “was merely cumulative of the humanizing evidence” that defendant presented at trial); Holsey, 694 F.3d at 1271 (“The cumulative nature of [the mitigating] evidence weakens its usefulness to [the capital habeas petitioner] on the prejudice inquiry.”); Rose v. McNeil, 634 F.3d 1224, 1243 (11th Cir.2011) (“[A] petitioner cannot satisfy the prejudice prong of the Strickland test with evidence that is merely cumulative of evidence already presented at trial.”). Hence, McNabb cannot demonstrate prejudice.
[1344]*1344Additionally,, the trial court found the existence of three ■ aggravating circumstances: (1) McNabb knowingly created a great risk of death to many persons, pursuant to Alabama Code § 13A-5-49(3); (2) the capital offense was committed for the purpose of avoiding or preventing a lawful arrest or effecting an escape from custody, pursuant to Alabama Code § 13A-5-49(5); and (3) the capital offense was committed to disrupt or hinder the lawful exercise of any government function or the enforcement of laws, pursuant to Alabama Code § 13A-5-49(7). After considering these aggravating circumstances, and the non-statutory mitigating evidence that McNabb presented during his guilt phase, the trial court found that the aggravating circumstances outweighed the mitigating circumstances and sentenced McNabb to death. In light of the nature of his crimes and the specific findings of the trial court and McNabb’s own testimony about his deprived childhood, we conclude that there is no reasonable probability that the presentation of further, mainly cumulative, evidence regarding McNabb’s horrific home life would have changed the outcome of his sentence. Accordingly, the district court properly denied relief on this claim, and we affirm its judgment with respect to this issue.
C. Lethal injection
McNabb contends that the district court erred in dismissing his claim that Alabama’s lethal injection protocol is unconstitutional. He asserts that because his claim challenges the entire method of execution — an ineffective first drug or improper administration of a first drug in a three- . drug protocol would violate the constitution — the district court erred in dismissing his claim because it determined that the claim was more properly cognizable in a 42 U.S.C. § 1983 action. His contention fails.
Issues sounding in habeas are mutually exclusive from those sounding in a § 1983 action. See Hutcherson v. Riley, 468 F.3d 750, 754 (11th Cir.2006) (“An inmate convicted and sentenced under state law may seek federal relief under, two primary avenues:” a petition for habeas corpus or a complaint under 42 U.S.C. § 1983.). “The line of. demarcation between a § 1983 civil rights action and a § 2254 habeas claim is based on the effect, of the claim on the inmate’s conviction and/or sentence.” Id. A claim is properly raised under § 1983 when “an inmate challenges the circumstances of his confinement but not the validity of his conviction and/or sentence.” Id. (internal quotation marks omitted). By contrast, “habeas corpus law exists to provide a prisoner an avenue to attack the fact or duration of physical imprisonment and to obtain immediate or speedier release.” Valle v. Sec’y, Fla. Dep’t of Corr., 654 F.3d 1266, 1267 (11th Cir.2011), cert. denied, — U.S.-, 132 S.Ct. 73, 180 L.Ed.2d 942 (2011).
Usually, an inmate who challenges a state’s method of execution is attacking the means by which the State intends to execute hi m, which is a circumstance of his confinement. It is not an attack on the validity of his conviction and/or sentence. For that reason, “[a] § 1983 lawsuit, not a habeas proceeding, is the proper way to challenge lethal injection procedures.” Tompkins v. Sec’y, Dep’t of Corr., 557 F.3d 1257, 1261 (11th Cir.2009). Hence, we conclude that the district court did not err in dismissing McNabb’s lethal injection challenge in his federal habeas petition. That avenue of relief is still available to him in a § 1983 actipn.
D. District court’s application ofAEDPA standard of review
' McNabb challenges the district court’s resolution of three of his claims alleging [1345]*1345that his counsel were ineffective at the penalty phase of his trial and one of his claims alleging that his counsel were ineffective at the guilt phase of his trial. In particular, McNabb claims that the district court should not have applied AEDPA’s deferential standard of review in disposing of these claims because the state courts did not adjudicate these claims on the merits. He requests that this court vacate the district court’s order and remand the case with directions that the district court conduct a de novo review of these claims.1
1. Mitigation expert
McNabb asserts that the district court erred in denying him relief, under the deferential standard of review, on his claim that his counsel were ineffective for failing to secure the services of a mitigation expert. He contends that because the state court did not adjudicate this claim on the merits, the district court should have reviewed the claim de novo. We agree with the district court, however, and find no error in its deferential review of this claim.
The state circuit court dismissed this specific claim, holding that McNabb failed to plead any specific facts to support it and, thus, failed to comply with the requirements of Rule 32.6(b) of the Alabama Rules of Criminal Procedure. Then, the state circuit court made an alternative ruling. .It dismissed the claim because no material issue of fact or law existed that entitled McNabb to relief. [R. Vol. 27, Tab. R-61, p. 17.] The court found that “McNabb, himself, thoroughly testified regarding the mitigation evidence to which he now claims a mitigation expert should have testified. Further, trial counsel did hire an expert, John Holbrook, who testified directly to the defense’s claim of cocaine paranoia.” [Id.] The court concluded that any further testimony regarding McNabb’s deprived childhood and addictions would have been cumulative, and that counsel cannot be deemed ineffective for failing to present cumulative evidence. [Id.] In affirming the state trial court’s denial of this particular claim, the ACCA adopted the trial court’s findings. See McNabb, 991 So.2d at 321-23, 327-28.
The district court properly conducted a deferential review and correctly determined that the state courts’ merits adjudication of this claim was neither contrary to, nor an unreasonable application of, clearly established Supreme Court precedent. As the district court noted, there is no clearly established federal law holding that trial counsel’s performance is deficient when counsel fails to repeat evidence at the penalty phase that has already been offered at the guilt phase. Moreover, contrary to McNabb’s contention, counsel did hire an expert who testified regarding McNabb’s defense of cocaine paranoia. The fact that this expert was not a mitigation expert and did not opine on specific mitigating factors does not, by itself, demonstrate that McNabb’s trial counsel were deficient in failing to procure such a particular expert. McNabb cannot meet his burden of showing that counsel’s failure to hire a mitigation expert fell below an objective standard of professional reasonableness and that, but for this failure to hire a mitigation expert, the result of McNabb’s trial would have been different. [1346]*1346Accordingly, we affirm the district court’s judgment as to this claim.
2. Closing argument at penalty stage
McNabb contends that the district court erred in conducting a deferential review of his claim that the attorney who presented the closing argument at the penalty phase of his trial was ineffective. Finding that the state courts conducted a merits adjudication of this particular claim, the district court determined that its adjudication was neither contrary to, nor an unreasonable application of, clearly established federal law. The district court did not err.
The state circuit court reviewed McNabb’s post-conviction claim alleging that his counsel was ineffective in the penalty-phase closing argument and dismissed it because McNabb failed to plead any specific facts to support it. [R. Vol. 27, Tab R-61, p. 26?27.] Alternatively, the court found that in light of the overwhelming evidence presented by the State and “the cold-blooded manner in which McNabb murdered Officer Gordon, trial counsel’s closing argument was not only coherent, but effective.” [Id.] The state court noted that during the closing argument, trial counsel argued several mitigating circumstances that surrounded the crime, such as McNabb’s use of, and addiction to, cocaine and McNabb’s difficult childhood. Additionally, the state court noted that trial counsel thoroughly argued that the State had not met its burden of proving beyond a reasonable doubt any of the three proffered aggravating circumstances. On review, the ACCA stated that McNabb did not present any argument on appeal in support of this particular claim, but did address the claim on the merits. See McNabb, 991 So.2d at 327-29. The ACCA adopted the state circuit court’s findings and affirmed its judgment. Id.
The district court correctly found that the state courts’ merits adjudication of this claim was neither contrary to, nor an unreasonable application of, clearly established federal law. McNabb cannot meet his burden of showing that his counsel performed deficiently and that this deficient performance prejudiced him. Considering the overwhelming evidence the State presented against McNabb, trial counsel provided an effective closing argument highlighting McNabb’s deprived childhood, lack of parental influence, cocaine addiction, and absence of past violence, in an attempt to save McNabb’s life. Under AEDPA, we cannot say that this closing argument was objectively unreasonable. Accordingly, we affirm the district court’s judgment as to this claim.
3. Expert witnesses at guilt stage
McNabb contends that the district court erred in denying relief, under the deferential standard of review, on his claim that counsel were ineffective for failing to procure an appropriate expert witness to testify on his behalf at the guilt phase of his trial. Specifically, McNabb claims that his counsel were deficient for not obtaining the assistance of a forensic social worker to conduct an extensive social history and background to cull relevant information about his childhood. On review, the district court determined that the state courts made an adjudication on the merits of this claim, and under its deferential review, denied relief on this claim. The district court did not err.
On post-conviction review, the state circuit court dismissed the claim, finding that McNabb failed to plead any specific facts to support it. [R. Vol. 27, Tab R-61, p. 14.] The state court noted that McNabb did not plead the name of any forensic social worker who would have testified at trial, and that McNabb did not [1347]*1347state specifically what evidence the forensic social worker would have uncovered. The state court further noted that McNabb did not allege how the employment of a forensic social worker would have changed or enhanced the defense’s trial strategy. [Id,.]
The state court also dismissed the claim because there was no material issue of law or fact that would have entitled McNabb to relief, citing Alabama Rule of Criminal Procedure 32.7(d). It found “that the information McNabb alleges a forensic social worker would have uncovered — ‘a childhood that included drug addiction, violence and abandonment’ — was known by trial counsel and presented at trial.” [Id. at 15.] Thus, it reasoned that there was “no probability, much less a reasonable probability, that discovering the same information from two different sources would have enhanced trial counsels’ ability ‘to make important decisions about the defense strategy’ as McNabb claims.” [Id.] The court further found that any testimony by a forensic social worker about McNabb’s deprived childhood would have been cumulative to McNabb’s own testimony. The ACCA affirmed the state circuit court’s denial of post-conviction' relief, adopting the circuit court’s findings as part of its opinion. See McNabb, 991 So.2d at 321-22, 327-28.
The district court correctly determined that the state courts’ merits adjudication of McNabb’s claim was neither contrary to, nor an unreasonable application of, clearly established federal law. The district court noted that Dr. Holbrook, a Professor of Pharmacology at Mercer University, whose specialty was psychopharmacology, testified immediately after McNabb and buttressed McNabb’s testimony regarding his cocaine use and the extreme fear it caused him during the crime. [R. Vol. 16, Tab R-12, p. 2312.] After highlighting much of Dr. Holbrook’s testimony, the district court found that the doctor was a strong witness in support of McNabb’s cocaine-paranoia defense. The district court then addressed McNabb’s claim that counsel were also ineffective because they did not call Dr. Stanley Brodsky, who actually examined McNabb, to testify. The district court found that, without McNabb presenting any evidence to the contrary, his trial counsel had a reason for not calling Dr. Brodsky to testify. Regardless, the district court concluded that any information Dr. Brodsky would have provided would have been cumulative to the information already presented to the jury. As such, we conclude that McNabb was not prejudiced by his counsel’s alleged deficiency for failing to call Dr. Brodsky to testify.
The district court did not err in denying relief to McNabb on this claim of ineffective assistance of counsel. Accordingly, we affirm its judgment as to this claim.
V. CONCLUSION
The district court correctly determined that McNabb was not entitled to relief on his federal habeas petition. Accordingly, we affirm its judgment denying McNabb’s § 2254 petition for habeas relief and his Rule 59(e) motion to alter or amend the judgment.
AFFIRMED.