
576 F.3d 214 (2009)
Henry W. SKINNER, Petitioner-Appellant,
v.
Nathaniel QUARTERMAN, Director, Texas Department of Criminal Justice, Correctional Institutions Division, Respondent-Appellee.
No. 07-70017.
United States Court of Appeals, Fifth Circuit.
July 14, 2009.
*215 Douglas George Robinson, Skadden, Arps, Slate, Meagher & Flom, L.L.P., Washington, DC, Robert Charles Owen (Court-Appointed), Owen & Rountree, Austin, TX, for Skinner.
Katherine D. Hayes, Austin, TX, for Quarterman.
*216 Before SMITH, WIENER, and OWEN, Circuit Judges.
JERRY E. SMITH, Circuit Judge:
Henry Skinner, convicted of capital murder and sentenced to death, appeals the denial of his petition for writ of habeas corpus. We find no error and affirm.

I.

A.
We described the facts and procedural history in Skinner v. Quarterman, 528 F.3d 336, 339-40 (5th Cir.2008). In summary, Skinner lived with his girlfriend Twila Busby and her two mentally retarded sons, Randy Busby and Elwin Caler. Trial evidence showed that Twila left Skinner passed-out-drunk at home while she attended a New Year's Eve party from about 10:30 to 11:15 p.m.[1] At midnight, a police officer found Elwin on a neighbor's porch with multiple stab wounds; he died shortly thereafter in the hospital. The police found Twila's dead body in her living room, where she had been strangled to unconsciousness and beaten with a blunt object at least fourteen times. Randy lay dead in the upper bunk of his bedroom with three stab wounds in his back.
Three hours later, the police located Skinner at the home of an ex-girl-friend, Andrea Reed. Reed testified that Skinner arrived at midnight, appeared intoxicated, threatened to kill her if she called the police, and told her that he had kicked Twila to death. DNA testing showed that blood on Skinner's clothing belonged to Twila and Elwin, and he had a gash on the palm of his right hand.
Skinner presented evidence that he was too intoxicated, from alcohol and codeine, to have committed the murders. An expert testified that, based on blood-alcohol levels, Skinner should barely have been able to walk, let alone commit three murders. Skinner also argued that Robert Donnell, Twila's uncle, was the murderer.

B.
The jury sentenced Skinner to death, and the Texas Court of Criminal Appeals affirmed. Skinner filed a federal petition for writ of habeas corpus, raising a variety of ineffective-assistance-of-counsel claims that the district court rejected. We granted a certificate of appealability ("COA") on two of those claims. Id. at 345. Specifically, Skinner alleges that counsel should have made use of a blood-spatter report at trial and failed to discover and present testimony from a particular potential witness.

II.
"As a mixed question of law and fact, we review de novo the district court's resolution of [the petitioner's] ineffective assistance of counsel claims." Smith v. Quarterman, 515 F.3d 392, 403 (5th Cir. 2008). To prevail on such a claim, Skinner "must establish: (1) that counsel's representation fell below an objective standard of reasonableness and (2) that the deficient representation caused prejudice, which requires a showing that there is a reasonable probability that, but for counsel's unprofessional errors, the result of the proceeding would have been different." Coble v. Quarterman, 496 F.3d 430, 435 (5th Cir. *217 2007) (citations and internal quotation marks omitted). "Our scrutiny of counsel's performance is `highly deferential' and there is a `strong presumption' that any alleged deficiency `falls within the wide range of reasonable professional assistance.'" Id. (quoting Strickland v. Washington, 466 U.S. 668, 689, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984)). "The petitioner must `affirmatively prove,' not just allege, prejudice. If the petitioner fails to prove the prejudice component, the court need not address the question of counsel's performance." Day v. Quarterman, 566 F.3d 527, 536 (5th Cir.2009) (citing and quoting Washington, 466 U.S. at 693, 697, 104 S.Ct. 2052).

A.
Skinner asserts that his attorney should have used a police report that analyzed photographs of a blood spatter on Elwin's body. Based on the spatter pattern, the report concluded that Elwin was "in the immediate vicinity of the victim Twila Busby at the time of her assault."[2]
Skinner alleges that failure to use the report was prejudicial in two regards. First, one of the defense's expert trial witnesses, Dr. Lowry, testified that Skinner would have been in a "stuporous state" at the time of the murders and could not have committed them on account of the amount of alcohol and codeine in his system. Skinner now avers that counsel was deficient for not giving Lowry the report, because it would have bolstered the intoxication defense by demonstrating, for the first time, that the murderer would have needed the dexterity to contend with Twila and Elwin simultaneously.
Second, counsel explained, in closing argument, that a bloody hand print found low on the door frame of Elwin and Randy's bedroom was consistent with "somebody who's prone and trying to get up on their feet and having trouble navigating...." The prosecution rebutted with the theory that the print was left when Skinner entered the room and "Elwin Caler came out of [the] bottom bunk." Skinner contends that his attorney should have objected to that theory, because the report showed that any altercation between Skinner and Elwin would have occurred in the living room.[3]
*218 We agree with the district court that Skinner has failed to demonstrate that the omission of the report was sufficiently prejudicial. Even taking the report at face value,[4] Skinner overstates its implications.
As the district court pointed out, the forensic evidence showed that Twila "would have been unconscious from strangulation before she was beaten," and therefore, Skinner "would not have had two live, active victims in the same room." Instead, Twila "would have been unconscious or already dead when [Elwin] appeared." Skinner concedes the point but argues that "the killer must have stopped beating Twila, put down the ax handle, found a knife, and stabbed Elwin repeatedly," which would require more "strength, mindfulness and coordination ... than Skinner likely possessed and more than would have been required for the killer to go from room to room, attacking his victims seriatim."
That situation, however, is not significantly different from the one that the state presented to the jury. The prosecution's closing-argument theory was that Skinner killed Twila alone in the living room and then dealt with Elwin and Randy in the bedroom, where Elwin knocked Skinner to the ground, causing him to leave the bloody hand print. The inference from the report only changes the location of any confrontation with Elwin from the bedroom to the living room. If anything, it would be easier for an intoxicated Skinner to stab Elwin when he walked in on the beating of an unconscious Twila than for Skinner to overcome Elwin after being knocked to the ground in the same room as Randy.[5] It is therefore not reasonably probable that the blood spatter evidence would have caused the jury to acquit Skinner.
Counsel's failure to object during closing argument is similarly nonprejudicial. Had an objection prevented the prosecution from introducing its theory that Elwin came out of the bottom bunk, that would have left unrebutted the defense's speculation that the print was consistent with a stuporous Skinner's trying to get to his feet. The value of that speculation is attenuated, however, because it provided only circumstantial corroboration for Lowry's already-extensive testimony about Skinner's intoxication.
Moreover, most of Skinner's activities during the evening of the murder were inconsistent with the defense that he was in a "stuporous state." For example, Lowry testified that someone in such a state should have been unable to stand up or walk and that it was "highly unlikely" that Skinner would have been awake at midnight. Yet, Skinner walked four blocks in the dark to Reed's house shortly after midnight.[6]
Lowry also admitted his "surprise" at Skinner's ability to perform a number of *219 actions upon arriving at Reed's house, including taking his shirt off, asking Reed to sew up a cut on his hand, and threatening to kill her when he caught her on the phone. In short, had counsel objected to the prosecution's explanation for the hand print, the best Skinner could have hoped for was that the defense's circumstantial speculation would have lent small support to an already-weak intoxication theory.
Finally, there was ample evidence that Skinner was the murderer: He confessed to Reed that he had killed Twila; there was no physical evidence of anyone else's having entered the house the night of the murders; and DNA testing demonstrated that the blood on Skinner's shirt belonged to Twila and Elwin. We find no "reasonable probability that, but for counsel's [failure to use the blood spatter report], the result of the proceeding would" have been acquittal. Wiggins v. Smith, 539 U.S. 510, 534, 123 S.Ct. 2527, 156 L.Ed.2d 471 (2003) (quoting Washington, 466 U.S. at 694, 104 S.Ct. 2052).

B.
Skinner complains of his attorney's failure to uncover additional evidence to support the theory that Twila's uncle, Robert Donnell, was the murderer. Specifically, Skinner argues that counsel should have discovered and presented the testimony of Debra Ellis, Donnell's neighbor. In our grant of COA, we summarized the relevant sections of Ellis's proposed testimony:
[A] couple of days after the murders, she saw Donnell thoroughly clean the carpets and inside of his truck and paint the outside; she had never seen him clean the truck before. She noted, however, that when she went out to the truck as he was cleaning it, she did not see blood or anything else unusual. Ellis also testified that Donnell carried a knife and that she observed him when police told him his niece and her two sons had been murdered, and he said "okay" without emotion.
Skinner, 528 F.3d at 345.[7]
Skinner does not contend that his counsel failed to conduct any investigation of Donnell.[8] Instead, he alleges that counsel did not investigate Donnell enough. He says that "[a]ny reasonably thorough investigation... would have included a canvass of Donnell's neighborhood and an inquiry into how Donnell reacted to news of *220 the murders, and either of those lines of inquiry would have led directly to Ellis."
"A fair assessment of attorney performance requires that every effort be made to eliminate the distorting effects of hindsight... and to evaluate the conduct from counsel's perspective at the time." Washington, 466 U.S. at 689, 104 S.Ct. 2052. Accordingly, "[w]e must be particularly wary of arguments that essentially come down to a matter of degrees. Did counsel investigate enough? Did counsel present enough mitigating evidence? Those questions are even less susceptible to judicial second-guessing." Dowthitt v. Johnson, 230 F.3d 733, 743 (5th Cir.2000) (citation and internal quotation marks omitted).
We agree with the district court that trial counsel's representation was constitutionally adequate. Notably, in the opinions Skinner cites for the proposition that his lawyer should have investigated further, the deficient counsel failed to pursue known leads.[9] Nothing in this record indicates that counsel knew (or should have known) about Ellis, let alone that he ignored evidence that suggested she might have useful information.[10]
Further, despite criticizing the district court for not "identify[ing] the method by which it assessed trial counsel's actions" and "completely fail[ing] to attend explicitly to prevailing norms of representation," Skinner provides no useful countervailing evidence. He refers several times to the 1989 edition of the "American Bar Association Guidelines for the Appointment and Performance of Counsel in Death Penalty Cases," but nothing in the ABA Guidelines indicates that canvassing a neighborhood is a prevailing norm of representation. And although Skinner's attorney expert testified generally that he thought trial counsel should have investigated more, he did not suggest any specific further steps that should have been taken.
Skinner has not established that his counsel's failure to go knocking door-to-door fell outside the "wide range of reasonable professional assistance." Washington, 466 U.S. at 689, 104 S.Ct. 2052. Having determined that counsel's performance was not constitutionally infirm, we do not address the issue of prejudice.
The denial of habeas corpus relief is therefore AFFIRMED.
NOTES
[1]  She left early because her drunken uncle, Robert Donnell, was making rude sexual advances toward her.
[2]  The report states in part,

Photograph 5 is a close-up of the abdomen and stomach of the victim, Elwin [Caler]. There is an overall blood flow pattern which is consistent with the wound this victim suffered. Also noted was medium velocity impact spatter on the front of the victim's underwear, stomach, left side and left forearm. The spatters on the right forearm indicate that they originated somewhere in the front of the victim's hand. The spatters on the front of the victim's undershorts appear to be nearly circular in shape with some indication that they were traveling right to left on impact. There are two nearly circular shaped spatter [sic] on the left side of the victim which indicate they originated somewhere to the victim's left side and were in the immediate vicinity of the victim Twila Busby at the time of her assault.
[3]  The government contends that that argument "exceeds the scope of the COA grant and must be dismissed." See, e.g., Ott v. Johnson, 192 F.3d 510, 512 n. 6 (5th Cir. 1999) ("Without an express request to broaden the COA, one which we approved, we will not consider issues on which a COA was denied."). Although our grant of COA did not specifically mention counsel's failure to object to the prosecution's theory, we did acknowledge the impact proper use of the blood spatter report could have had on the prosecution's closing. Skinner, 528 F.3d at 344 (The reports "would undermine the prosecution's theory that Skinner's bloody hand print on the low part of the bedroom door frame was caused by Elwin's knocking Skinner to the ground in a struggle as Skinner attacked him in the bedroom."). The closing argument issue is therefore plainly within the scope of our COA, and out of an abundance of caution, we also address Skinner's failure-to-object argument.
[4]  The district court and this court noted that "[t]he report does not establish, beyond mere speculation, that the blood on Elwin was Twila's." Skinner, 528 F.3d at 344 n. 10. Skinner responds that "[o]f the four persons known to have been bleeding in the house that night (the three victims and Skinner), only Twila was attacked in such a way as to cause the type of cast-off blood spatter observed by" the police report. He does not, however, provide a citation to the record or any other source that supports that contention.
[5]  Elwin was more than 6-1/2 feet tall and weighed 225 pounds.
[6]  Reed remembers the time, because neighbors were celebrating the new year by firing shotguns.
[7]  Skinner adds that Ellis also could have testified about Donnell's violent behavior toward his wife. We already found the omission of that evidence to be non-prejudicial, however. Skinner, 528 F.3d at 345 n. 11 ("No reasonable jurist would debate whether counsel's failure to present the evidence deemed cumulative by the district court was prejudicial.... [A]lthough Skinner points to new evidence that Donnell was violent toward his wife, trial testimony of Donnell's violent nature had already established that.").

Skinner also says that Ellis could have testified that "Donnell owned and often wore a windbreaker jacket," and "a jacket of that type was found next to Twila Busby's body." As the state points out, however, "Ellis testified that Donnell always wore a tan windbreaker jacket, [and] the jacket found near Twila's bludgeoned body at the crime scene was grey, not tan." Thus, Ellis's testimony on the jacket may not have been helpful to Skinner and possibly could have suggested that Donnell was not the killer. Given the marginal probative value of the testimony, its omission was not prejudicial.
[8]  In fact, counsel did investigate Donnell and presented the testimony of Sarah Mitchell the daughter of Howard Mitchell, who hosted the party that Twila and Donnell attended on the night of the murderand Sherry Baker, a good friend of Twila's. Sarah testified about events at the party, including that Donnell followed Twila around; Baker testified that Donnell had previously sexually assaulted her and that Donnell was hot-tempered, belligerent, and demanding toward Twila.
[9]  See, e.g., Rompilla v. Beard, 545 U.S. 374, 389, 125 S.Ct. 2456, 162 L.Ed.2d 360 (2005) (finding counsel deficient for failing to examine easily accessible court file on defendant's prior conviction "despite knowing that the prosecution intended to introduce [defendant]'s prior conviction"); Wiggins v. Smith, 539 U.S. 510, 523-29, 123 S.Ct. 2527, 156 L.Ed.2d 471 (2003) (finding counsel deficient for failing to follow up on leads found in a presentence investigation report and a department of social services report); Draughon v. Dretke, 427 F.3d 286, 294-96 (5th Cir.2005) (finding counsel deficient for failing to obtain a forensics report to substantiate defendant's testimony about bullet flight path); Miller v. Dretke, 420 F.3d 356, 361-62 (5th Cir.2005) (finding counsel deficient for "fail[ing] to contact [defendant's] treating physicians" despite counsel's knowledge that "[defendant] had suffered mental and emotional injuries" and that "these injuries comprised mitigating evidence"); Soffar v. Dretke, 368 F.3d 441, 473-74 (5th Cir.2004) (finding counsel deficient for "fail[ing] to take the most elementary step of attempting to interview the single known eyewitness to the crime with which their client was charged") (emphasis added), amended, 391 F.3d 703 (5th Cir.2004) (per curiam); Bigelow v. Williams, 367 F.3d 562, 571-74 (6th Cir.2004) (remanding for hearing on ineffective assistance where counsel failed to perform any investigation after learning about a new alibi witness days before trial).
[10]  Although Ellis reported her observations to the police, they were not included in any report.
