
528 F.3d 336 (2008)
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.
May 14, 2008.
*338 Douglas George Robinson, Skadden, Arps, Slate, Meagher & Flom, Washington, DC, Robert Charles Owen, Owen & Rountree, Austin, TX, for Petitioner-Appellant.
Katherine D. Hayes, Austin, TX, for Respondent-Appellee.
Before SMITH, WIENER, and OWEN, Circuit Judges.
*339 JERRY E. SMITH, Circuit Judge:
Henry Skinner was convicted of capital murder and sentenced to death. He seeks a certificate of appealability ("COA") from the denial of his petition for writ of habeas corpus. We deny in part and grant in part the application.

I.
In March 1995, a jury convicted Skinner of murdering his girlfriend, Twila Busby, and her two mentally retarded sons, Randy Busby and Elwin Caler, on New Year's Eve of 1993. Twila, Randy, and Elwin were strangled, bludgeoned, and stabbed in their house shortly before midnight.
At midnight, a police officer found Elwin, in bloodstained undershorts, sitting on the porch of a neighbor's house with stab wounds under his left arm and on his right hand and stomach. He was taken to a hospital and died shortly thereafter. Investigating Elwin's stabbing, the police went to the home where he lived with Twila, Randy, and Skinner. The police noticed a trail of blood on the ground running from the front porch to the fence line, a blood smear on the glass storm door, and a knife on the front porch. They found Twila dead on the living room floor. She had been strangled into unconsciousness, then beaten on the head with a blunt object at least fourteen times. A bloodstained axe handle and plastic trash bag containing a knife and bloody towel lay nearby. She exhibited signs of recent sexual intercourse. In a bedroom, officers found Randy dead in an upper bunk. His body was lying face down, and he had been stabbed three times in the back.
On the door frame between the bedroom and a utility room, officers found a bloody hand print roughly two feet above the floor. Bloody prints were also found on the door knob of the door connecting the utility room to the kitchen and on the doorknob of the utility room door opening to the backyard. The prints were Skinner's.
Suspecting Skinner, the police sought and found him at 3:00 a.m. in the house of Andrea Reed, his former girlfriend, standing in a closet wearing heavily bloodstained jeans and socks and bearing a gash on the palm of his right hand. DNA testing showed that blood on Skinner belonged to Twila and Elwin. Skinner appeared intoxicated, and a toxicology test taken at 5:48 a.m. revealed alcohol and codeine. Skinner was arrested, and in a statement to police he claimed not to recall much of what had transpired that evening.
At trial, the night's happenings were filled in by others. A friend, Howard Mitchell, went to Twila's and Skinner's home around 10:30 p.m. to give them a ride to his New Year's Eve party. When he arrived, Mitchell found Skinner passed out on the couch, apparently drunk. Unable to wake Skinner, Mitchell left with Twila for the party, where she was followed around by her drunken uncle, Robert Donnell, who made rude sexual advances toward her. Twila quickly became agitated by Donnell and had Mitchell take her back home. Mitchell dropped her off between 11:00 and 11:15 p.m. and left without going inside.
The trail of witnesses runs cold during the fateful hour before midnight but picks up thereafter. At midnight, roughly at the same time the police officer found Elwin, Reed answered a knock at the door of her trailer, which was about four blocks from Skinner's home. Skinner stood outside the door in blood-soaked shirt and pants and wearing socks but no shoes; he told Reed he had been stabbed and shot. He removed his shirt, but Reed could find no injuries except for the cut on the palm of his hand, which she bandaged for him. *340 Skinner stayed with Reed for roughly three hours until the police arrived to apprehend him.
Reed testified that Skinner appeared intoxicated and disoriented and made many inconsistent statements about the causes of his injury and the course of events. Reed tried to call police, but Skinner threatened to kill her if she did. Skinner eventually offered to tell Reed what really had happened if she would promise not to tell anyone; she promised, and Skinner told her he thought he had kicked Twila to death. In a later statement to police, he claimed he woke up on the couch to find someone standing over him with a knife and that he ran out of the house. He also guessed that Twila might have killed her sons and cut him with a knife, but he claimed not to remember plainly.[1]
At trial, Skinner sought first to show that, because of intoxication, he could not physically have committed the murders. An occupational therapist testified that an injury had deprived Skinner of the hand strength that would have been necessary to strangle Twila in the manner described by the medical examiner. A toxicologist testified that the alcohol and codeine in Skinner's system would have put him in a stupor, and he would not have had the physical coordination to overpower and inflict wounds on the three victims. In rebuttal, the prosecution suggested that Skinner's long history of drug and alcohol abuse gave him more tolerance for the substances than an average person would have, so he had a greater ability to function under the influence.
Skinner also suggested that Donnell was the murderer. Skinner presented evidence that Donnell was violent and hot-tempered. On the night of the murder, he was seen drunkenly harassing Twila at the party, and Mitchell claimed that Donnell had "a certain kind of hate" in his eyes. Mitchell also reported that when he returned to the party after driving Twila home, Donnell was no longer there. The defense, however, introduced no physical evidence indicating that anyone besides Skinner and the victims had been in the house at the time of the murder.[2]

II.
Skinner was convicted of capital murder and sentenced to death, and the conviction was affirmed by the Texas Court of Criminal Appeals.[3] Skinner sought federal habeas relief, raising a number of due process, Sixth Amendment, and ineffective assistance claims. Adopting the magistrate judge's findings after an evidentiary hearing, the district court denied relief and denied Skinner's application for a COA on his ineffective assistance claims.

III.
Under the Antiterrorism and Effective Death Penalty Act of 1996, a petitioner must secure a COA as a "jurisdictional prerequisite" to appealing the denial of habeas relief. Miller-El v. Cockrell, 537 U.S. 322, 336, 123 S.Ct. 1029, 154 L.Ed.2d 931 (2003); see also 28 U.S.C. § 2253(c)(2). A COA will be granted only if the petitioner makes "a substantial showing of the denial of a constitutional right." Id. We conduct only a "threshold inquiry" and must issue a COA if "reasonable jurists would find the district court's *341 assessment of the constitutional claims debatable or wrong." Miller-El, 537 U.S. at 336, 338, 123 S.Ct. 1029. "Indeed, a claim can be debatable even though every jurist of reason might agree, after the COA has been granted and the case has received full consideration, that petitioner will not prevail." Id. In death penalty cases, we resolve in the petitioner's favor any doubt about whether a COA should issue. Pippin v. Dretke, 434 F.3d 782, 787 (5th Cir. 2005). Nevertheless, "issuance of a COA must not be pro forma or a matter of course," and "a prisoner seeking a COA must prove `something more than the absence of frivolity.'" Miller-El, 537 U.S. at 337-38, 123 S.Ct. 1029 (quoting Barefoot v. Estelle, 463 U.S. 880, 893, 103 S.Ct. 3383, 77 L.Ed.2d 1090 (1983)).
To prevail on an ineffective assistance of counsel claim, Skinner must show that trial counsel's performance was deficient and that the deficiency prejudiced his defense. Strickland v. Washington, 466 U.S. 668, 687, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984). Performance is deficient where counsel's representation falls "outside the wide range of professionally competent assistance" expected of him. Id. at 690, 104 S.Ct. 2052. Prejudice occurs only if "there is a reasonable probability that, but for counsel's unprofessional errors, the result of the proceeding would have been different." Id. at 694, 104 S.Ct. 2052.

IV.

A.
Skinner contends that trial counsel should have conducted DNA tests of crime scene evidence not tested by the state, including hairs clutched in Twila's right hand, material found under her fingernails, vaginal swabs taken at her autopsy, blood found on two knifes, and hair and perspiration on a man's jacket found near her body. The district court held that counsel was not deficient in failing to test that evidence and that the failure was not prejudicial.
It is not debatable among jurists of reason that counsel was not deficient in failing to test the evidence. "A conscious and informed decision on trial tactics and strategy cannot be the basis for constitutionally ineffective assistance of counsel unless it is so ill chosen that it permeates the entire trial with obvious unfairness."[4]
At the evidentiary hearing, counsel explained that he did not request DNA testing of the additional evidence because of the risk that such testing would reveal that the DNA was Skinner's instead of Donnell's or some other person's. Contrary to Skinner's contention that counsel had "nothing to lose" and "everything to gain" from DNA testing, evidence of Skinner's DNA, such as on a knife handle or under Twila's fingernails, would have been highly probative, incriminating evidence for the prosecution.[5] Conducting its own DNA test would also have deprived the defense of its primary argument at trial that the government conducted a shoddy investigation. Not knowing what more thorough DNA testing would have uncovered, a jury *342 might have found reasonable doubt in such uncertainty.
Skinner's counsel made an informed, strategic decision that DNA testing was at least as likely to incriminate Skinner as to exonerate him and that additional testing was a gamble not worth taking. Given the "double-edged" nature of that choice, ineffectiveness cannot be established by second-guessing.[6]

B.
Skinner argues that trial counsel should have impeached Reed with a prior written statement during cross-examination. On re-direct examination, Reed testified that Skinner made her "swear to God" not to tell anyone that he thought he had kicked Twila to death. Skinner posits that counsel should have impeached Reed with her statement to the police in which she stated that Skinner made her promise not to tell numerous stories, and not just the one about killing Twila. The district court held that counsel was not deficient in failing to impeach Reed on this point and that the failure was not prejudicial.
It is undebatable among jurists of reason that counsel was not deficient in failing to impeach Reed, nor was the failure prejudicial. Skinner's lawyer conducted an effective cross-examination of Reed, eliciting much to suggest that Skinner's "confession" to Reed was unreliable. Reed admitted that Skinner appeared drunk and confused, that much of the time Skinner did not even seem to know who Reed was, that Skinner told Reed many things Reed knew to be untrue or that were demonstrably untrue, and that despite the untruths, Skinner swore every story was true. Against this background, the fact that Skinner made Reed promise not to tell many of his stories, and not just the story about killing Twila, adds only marginally to the general picture of unreliability.
Counsel's failure to elicit this additional point hardly amounts to "error[] so serious that counsel was not functioning as the `counsel' guaranteed ... by the Sixth Amendment." Washington, 466 U.S. at 687, 104 S.Ct. 2052. Furthermore, the failure to elicit the fact from Reed could not have constituted prejudice, because counsel later placed that same fact into evidence through another witness, defense expert Dr. William Lowry. Counsel also reminded the jury during closing argument that Skinner had not emphasized the story about killing Twila over any of the other stories told to Reed.

C.
Skinner avers that counsel should have presented evidence that Skinner believed he was allergic to codeine. If Skinner had not taken much codeine in the past, he would not have had a high tolerance for it. This might have bolstered the defense theory that, having taken three times the therapeutic dose of codeine on the night of the murders, Skinner was too incapacitated to have committed them. Trial counsel did not recall the codeine allergy evidence, despite the fact that it was contained in counsel's files, but the district court held that even if counsel was deficient, the failure to present evidence of a codeine allergy caused no prejudice.
It is undebatable among jurists of reason that counsel's failure to present evidence of Skinner's perceived codeine allergy does not amount to prejudice.[7] If *343 counsel had introduced evidence suggesting that Skinner did not have a tolerance for codeine, the prosecution could have countered with evidence showing that it was still possible for Skinner to have had such a tolerance.
Skinner did not show signs of an allergic reaction to the codeine in his blood on the night of the murder, and it is likely that he was not allergic to it. Although he argues that evidence he self-reported a codeine allergy to doctors proves he at least believed he was allergic, the prosecution could have put on witnesses to show that drug users often falsely self-report allergies to get prescriptions for other, stronger drugs. Counsel therefore could not have undisputedly established that Skinner had avoided codeine in the past and had developed no tolerance for it.
Even if counsel could have used the evidence to prove that Skinner had no tolerance for codeine, that marginal supporting evidence would have done nothing to overcome the greatest weakness of the defense's intoxication theory. The defense's toxicologist admitted at trial that if Skinner was as incapacitated as an ordinary person would have been after taking the alcohol and codeine, Skinner would not have been able to do many things he was known to have done on the night of the murder, such as walking four blocks to Reed's house.[8]
This anomaly could have been explained by a high tolerance for alcohol and codeine.[9] And even without a high tolerance, it could have been explained by the possibility that Skinner took the codeine after committing the murders, perhaps to soothe the pain from his injured hand. Indeed, his expert witness admitted it was possible the codeine had been taken after the murders had been committed at midnight and that this would have explained the high concentration of it in his blood.
Presenting the codeine allergy evidence would have bolstered the defense theory of the case only marginally and would not have overcome the theory's greatest weakness. Accordingly, jurists of reason would not debate that the evidence supplied no reasonable probability of acquittal. Counsel's failure to present it at trial caused no prejudice. Washington, 466 U.S. at 694, 104 S.Ct. 2052.

D.
Skinner avers that trial counsel should have made use of a blood spatter report prepared by Officer Morse Burroughs. The report documents blood spots on Elwin's underwear and speculates that the circular shape of the spots indicate Elwin was in the immediate vicinity of Twila at the time of Twila's assault. In other words, the blood spots could have *344 resulted from Twila's blood flying onto Elwin as she was beaten. Counsel offered no strategic reason for failing to utilize the report, but the district court held that, even if counsel was deficient, the failure caused no prejudice.
Because jurists of reason could debate whether failure to present the blood spatter report caused prejudice, this claim merits a COA. Skinner argues that the blood spatter report proves Elwin was in the same room as Twila while Twila was being assaulted and that the murderer therefore would have had to fend off two live victims at the same time. If true, this would bolster the primary defense theory that Skinner was too incapacitated to commit the murders and 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. It would thereby bolster the defense theory that the hand print resulted instead from the fact that Skinner was "falling-down drunk."
Despite the relevance of the blood spatter report to the defense's theory of the case, however, it requires considerable speculation to conclude that counsel's use of the blood spatter report would have created a "reasonable probability" of acquittal. Washington, 466 U.S. at 694, 104 S.Ct. 2052.[10] Nevertheless, to grant a COA we "need not decide the ultimate merits of the underlying issue in the petitioner's favor." Jackson v. Dretke, 450 F.3d 614, 616 (5th Cir.2006), cert. denied, ___ U.S. ___, 127 S.Ct. 935, 166 L.Ed.2d 717 (2007). Because jurists of reason might disagree about the impact of the blood spatter report, we grant a COA on this issue.

E.
Skinner reasons that counsel should have further investigated Donnell, whom they presented as an alternative suspect, and should have called further witnesses supporting the defense theory that Donnell was the real killer. At trial, counsel called witnesses Howard Mitchell, Sara Mitchell, and Sherry Baker to testify about Donnell. That testimony established that Donnell was violent and quick-tempered, that Donnell and Twila did not always get along, that Donnell had harassed Twila at Howard Mitchell's party, that Donnell had left the party before Mitchell returned from taking Twila home, and that Donnell had previously sexually assaulted Baker.
At his hearing in federal district court, Skinner called three additional witnesses, James Hayes, Vicki Broadstreet, and Debra Ellis. The district court held that counsel was not deficient in failing to present these additional witnesses and that the failure was not prejudicial. As the district court explained in detail, much of this new testimony was either unhelpful to Skinner *345 or cumulative of testimony already given by others.[11]
It is undebatable among jurists of reason that counsel's failure to present the testimony of Hayes and Broadstreet was not prejudicial. The only new evidence that was not cumulative or unhelpful was testimony from Ellis. Reasonable jurists could debate whether failure to present her testimony was deficient or prejudicial.
Ellis was Donnell's neighbor and a friend of his wife's. At the federal hearing, Ellis testified that 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.
Ellis's testimony offered strong circumstantial evidence to corroborate the defense theory that Donnell was the murderer. Although the significance of that evidence is tempered by the fact that Donnell exhibited no injuries, and no bloody clothes of Donnell were ever found, jurists of reason could debate whether the failure to present Ellis's testimony caused prejudice.
Jurists of reason could also debate whether counsel was deficient in failing to seek out Ellis and present her testimony. Effectiveness in failing to investigate turns on "whether the known evidence would lead a reasonable attorney to investigate further." Wiggins v. Smith, 539 U.S. 510, 527, 123 S.Ct. 2527, 156 L.Ed.2d 471 (2003). Counsel had decided to blame Donnell for the murder and had investigated enough to unearth evidence from witnesses to suggest his guilt. Ellis did report her observations to the police, but they never noted them in a report. Skinner's claim thus amounts to a contention that a reasonable lawyer, knowing that suspicion of Donnell would be important at trial, would have knocked on Donnell's neighbor's door. Although we are "wary of `arguments that essentially come down to a matter of degrees'"[12] in the scope of an investigation, reasonable jurists could debate whether a reasonable attorney would have investigated further.
In summary, the application for a COA is GRANTED with regard to the claim of failure to make use of the blood spatter report and with regard to the claim of failure to discover and present Ellis's testimony; the application for a COA is DENIED with regard to all other claims. We express no view on how any claims should *346 ultimately be resolved; we conclude only that the mild standard for granting a COA has been met as to the two claims mentioned above.
NOTES
[1]  He stated, "I think that Twila came home drunk and had a knife. I don't know if she stabbed the boys and then we got into a fight or [she] tried to stab me or what the hell happened. I just don't know. But I think she's the one that cut my hand. I think that."
[2]  See Skinner v. State, 956 S.W.2d 532, 536-37 (Tex.Crim.App.1997) (reviewing sufficiency of the evidence).
[3]  Id.
[4]  Cotton v. Cockrell, 343 F.3d 746, 752-53 (5th Cir.2003) (quoting United States v. Jones, 287 F.3d 325, 331 (5th Cir.2002)); see also Williams v. Cain, 125 F.3d 269, 278 (5th Cir. 1997) (observing that failure to present evidence does "not constitute `deficient' performance within the meaning of [Washington] if [counsel] could have concluded, for tactical reasons, that attempting to present such evidence would be unwise.").
[5]  Even if the defense would have been able to keep the results of its tests secret, the state had custody of the evidence and would have known which additional items the defense had selected for testing and then could have tested those items itself.
[6]  See Kitchens v. Johnson, 190 F.3d 698, 703 (5th Cir.1999) (deeming failure to present evidence not ineffective because of "double-edged nature of the evidence involved"); Boyle v. Johnson, 93 F.3d 180 (5th Cir.1996) (same).
[7]  We reject Skinner's argument that all the failings of counsel nevertheless add up to cumulative prejudice. There is no reasonably debatable cumulative prejudice in this case.
[8]  Skinner argues that although he had enough functioning to walk to Reed's house, he was in too "stuporous" a state to commit the murder. But this possibility does not change the fact that Skinner was more mobile than an ordinary person would have been under the circumstances. This fact is more substantial evidence of a high tolerance for codeine and alcohol than is the fact that Skinner had reported in the past that he was allergic to codeine.
[9]  Although deeming it "highly improbable" that Skinner could have committed the murders in his "stuporous" state, Skinner's toxicologist seemed to admit the prosecution's tolerance theory, explaining, "A person with drug and alcohol [abuse] would be able to [walk to Reed's home]. So the history of drug and alcohol abuse is very self-explanatory of events how he was capable of being mobile under those conditions."
[10]  The report does not establish, beyond mere speculation, that the blood on Elwin was Twila's. Even assuming it was and that the spots were caused in the manner envisioned by the report, the report does not establish that the murderer would have had to contend with two live victims in the room at the same time.

Forensic evidence showed that Twila was strangled before she was beaten and thus could have been unconscious at the time Elwin was also in the room. Finally, even if the murderer would have had to contend with two victims, it is not evident that Skinner was too intoxicated to have done it. The defense's toxicologist admitted that, according to his assessment, an ordinary person in Skinner's position should not have been able to do most of the things he did on the night of the murder, such as walking four blocks to Reed's house.
[11]  Skinner argues that counsel may be ineffective even for failing to develop "enough evidence of a certain type," see Smith v. Dretke, 422 F.3d 269, 283-84 (5th Cir.2005), but any ineffective assistance claim must falter where the evidence to be discovered is so similar and cumulative that failure to find and present it would not prejudice the result. Washington, 466 U.S. at 694, 104 S.Ct. 2052. No reasonable jurist would debate whether counsel's failure to present the evidence deemed cumulative by the district court was prejudicial. Although Skinner points to new evidence that Twila was having a sexual relationship with Donnell, trial testimony that Donnell lewdly followed Twila around the party had already established a sexual or jealous motive for murder. Likewise, although Skinner points to new evidence that Donnell was violent toward his wife, trial testimony of Donnell's violent nature had already established that.
[12]  Smith v. Cockrell, 311 F.3d 661, 669 (5th Cir.2002) (quoting Dowthitt v. Johnson, 230 F.3d 733, 743 (5th Cir.2000), abrogated on other grounds by Tennard v. Dretke, 542 U.S. 274, 124 S.Ct. 2562, 159 L.Ed.2d 384 (2004)).
