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GARWOOD, Circuit Judge: Robert Wallace West, Jr. (West) appeals the district court’s denial of his petition under 28 U.S.C. § 2254 challenging his February 1983 Texas conviction and death sentence for the August 1982 intentional murder of Deanna Klaus while in the course of committing or attempting to commit burglary of her motel room, contrary to Texas Penal Code § 19.03(a)(2). We previously granted a certificate of probable cause. We now affirm. Procedural Background West’s conviction and sentence were affirmed on direct appeal by the Texas Court of Criminal Appeals, West v. State, 720 S.W.2d 511 (Tex.Crim.App.1986) (en banc), and the United States Supreme Court denied certiorari. West v. Texas, 481 U.S. 1072, 107 S.Ct. 2470, 95 L.Ed.2d 878 (1987). West, represented by new counsel, filed state habe-as proceedings. The state trial court, the same judge who had presided at West’s 1983 trial, on August 25, 1987, entered findings and conclusions, based on the record and affidavits of West’s trial and direct appeal counsel, and recommended that the Court of Criminal Appeals deny all relief. The latter court on August 31, 1987, denied relief in a written order not stating reasons. West, through the same counsel who represented him in the state habeas proceedings, instituted the instant section 2254 proceedings in the district court below. Several months after West’s counsel filed his amended petition, the state filed its answer and motion for summary judgment. West never replied to the motion and some ten weeks after it was filed the magistrate judge issued a memorandum opinion recommending that the state’s motion be granted. After being granted several extensions, West filed an unverified “response to magistrate’s memorandum and recommendation.” On review of the record, the magistrate judge’s memorandum, and West’s response, the district court entered an order accepting the magistrate judge’s memorandum and recommendation, granting the state’s motion for summary judgment, and dismissing the petition. West filed a timely notice of appeal. Factual Background The state’s evidence showed that the victim, Deanna Klaus, lived alone in room 312 at the Memorial Park Motel in Houston, Texas, and worked as a waitress at the motel’s restaurant. Shortly after midnight on August 24, 1982, Vickie Stolz and two other residents of the motel were sitting in the motel’s breezeway and heard a commotion emanating from motel room 312. A fourth companion shortly joined these three. A few minutes later, West was observed exiting room 312; he walked within four to six feet of Stolz and her companions, then turned and walked up a flight of the motel’s stairs; the blue jeans he was wearing appeared to be soaked with blood. Stolz and her companions then looked into room 312, which was in total disarray, and observed the nude body of Deanna Klaus, bloody and bound, lying face down on the bed. Police officers arrived on the scene shortly thereafter, and one of the witnesses directed them to room 447 in the motel on the floor above room 312. Room 447 was occupied by West and a male transvestite companion, Gonzalo Tagle. The police asked both to step outside, and West was arrested when he did so. Tagle advised that the room was his and gave permission to search. The police observed a pair of wet, bloodstained blue jeans lying over a chair in the room. Stolz and her companions identified West as the individual they had observed leaving room 312. Police officers promptly examined room 312. Detective Lott testified that based on his examination of the door to room 312, in his opinion it had been forced open. Officer Richardson testified that the door “was separated from the seams as if broken into.” There was other similar testimony. There was police officer testimony that room 312 “was ransacked,” there was “stuff scattered around the floor” and “drawers have been pulled out, dumped on the floor.” Other testimony concerning the room was that there were “items on the floor” and it appeared “like somebody went through everything.” The pathologist testified that Klaus’ wrists and ankles were bound by cloth so tightly as to leave visible pressure grooves on her; her mouth and nose were gagged with a towel tied by a cloth binding that likewise left pressure grooves. Her head was covered by a bloody sheet tied by a leather belt wrapped twice around her neck. There was a stab wound in her neck and two on her left arm. A six-inch piece of wood protruded two inches from her back, being stuck four inches into her body. There was evidence of strangulation by hand, reflected by her broken hyoid bone. Death resulted from asphyxiation, caused by the belt and cloth ligatures around the neck and mouth as well as by manual strangulation, in combination with the wound from the stick penetrating four inches into her chest cavity. West, following repeated warnings as called for by Miranda v. Arizona, 384 U.S. 436, 86 S.Ct. 1602, 16 L.Ed.2d 694 (1966), gave a full written confession to the police in which he admitted killing Klaus. He said he forced his way into her room, pushing the door open with his shoulder. He disrobed Klaus, tied her up, and gagged her and put a belt around her neck. He thereafter beat her in the face with a “club” he found in the room; it broke, and he stabbed her with it. He hit her with a bottle, which broke, and then “gigged her in the neck with it.” Then, “[w]hen I got up she was still making noises, she was still alive. I knew that since I went that far that I couldn’t leave her like that. I grabbed the sheet and wrapped it around her neck and I strangled her. I pulled it until she didn’t move anymore.” West further stated that he took a gold necklace that he saw in her room, and when he returned to room 447 put the necklace in Tagle’s purse. West said that when he left room 312 “the door was hard to open because of when I had broke in” and “[t]here were two dudes and a girl outside when I came out and went to my room” and “I had blood all over me.” At the punishment stage of the trial, previously redacted portions of West’s confession were admitted in evidence. This portion of the confession reflected that West and Ta-gle — a “drag queen” female impersonator who used the first name Roxanne — had begun living together in Houston in April 1982. Roxanne had a job, and Roxanne and West “also made money by hustling tricks in the Montrose area of town.” One evening in May they went to the Montrose area “to make money any way we could.” Roxanne attracted a “trick” — whom West stated later turned out to be one William Longfellow whom West understood worked as a security guard — and West asked Roxanne “if she wanted me to roll him and she said yes.” West and Roxanne devised a plan whereby Longfellow would give West, as well as Roxanne, a ride home in Longfellow’s car and “I would do the rolling.” In the Montrose area, in front of the Chicken Coop Bar there, Longfellow, at the requests of Roxanne and West, agreed to give West a ride to his apartment, and all three got in the front seat of Longfellow’s red Mercury Zephyr and drove to the general vicinity of the apartments on Sage Street where Roxanne and West lived. Then Longfellow, at Roxanne’s request, stopped and let Roxanne out to urinate, and Longfellow followed her. West followed both of them. As they walked back to the car, West was behind Longfellow. West’s confession goes on to state: “... I pulled out my knife and grabbed him by his hair and lifted him up off the ground and I stabbed him in the jugler vain [sic]. I stabbed him about six or seven times. As I was stabbing him I asked him where his money was. He told me that his money was in the trunk of his car. After he told me where his money was at I hit his head up against a tree and left him for dead. He wasn’t moving and he wasn’t saying anything and there was a lot of blood and I had blood all over my hands. I thought he was dead. As soon as I grabbed the guy and started stabbing him, Roxanne ran from there and ran to the apartments. The apartments are about two blocks away. After I stabbed him I got into his car and drove back to the apartments on Sage. I parked the car behind the WINDSOR PLAZA SHOPPING CENTER. I opened the trunk of the car and I found the guys money in a brown paper bag. I got the money and went to the apartment.... I thought I had killed the guy so the next morning we checked the newspapers to see if there was a story about him being found. We never seen nothing about the man being found. After a few weeks we just forgot about it. A couple of weeks later ROXANNE called me from the jail and she told me that she had been busted for prostitution. I went to the police station and found out that there was a hold on her for the stabbing. That’s when I found out that the man wasn’t dead.... Roxanne was in jail for about two weeks and she tried to call me several times but I was never there.... When Roxanne got out she told me that she had given Brett’s name as her lover and the police let her go.... A couple of weeks after Roxanne got out of jail we drove to McALLEN, TEXAS to her fathers ranch.... ” This portion of the confession also reflects that West and Tagle had returned to Houston and checked into the Memorial Park Motel on August 21. William Longfellow, a private security officer, testified at the punishment phase. His testimony related the May 15, 1982, brutal attack on him by West described in West’s confession, including taking Roxanne (Tagle) and West in his red Mercury Zephyr from the Chicken Coop Bar to an area near Sage Street, all three in the front seat, where they stopped so Roxanne could urinate, and West coming up behind Longfellow and knocking him down, slashing his throat with a knife several times. Longfellow told West his money was in a paper sack in the trunk of his ear. West hit Longfellow’s head several times against a tree stump, wound a roll of white cloth or gauze around his head and mouth several times, and held his head under water in a ditch. He took Longfellow’s car keys and driver’s license and other identification papers. After West and Tagle left, Longfellow managed to get help. He was taken to a hospital, underwent five and a half hours of surgery, and remained hospitalized for eight days. The state also introduced documentary evidence of West’s 1981 Florida conviction for felony grand theft. West introduced no evidence at the guilt-innocence or punishment stages of the trial. The main thrust of the defense, at trial and on direct appeal, was to attack the admissibility of West’s confession, as being the result of a warrantless arrest that was illegal under article 14.04 of the Texas Code of Criminal Procedure, and as having been taken in violation of his Miranda rights and his rights under the Fifth and Fourteenth Amendments and analogous provisions of Texas law. The state trial court held a Jackson v. Denno, 378 U.S. 368, 84 S.Ct. 1774, 12 L.Ed.2d 908 (1964), hearing out of the jury’s presence on the admissibility of the confession and found it admissible, and also instructed the jury not to consider the confession if it were not found to have been given freely and voluntarily after proper warnings. Discussion We turn now to the issues raised by West on this appeal. I. Sufficiency of the Evidence and Related Ineffective Assistance of Counsel West contends that the evidence is insufficient to support his capital murder conviction. His argument is that his confession as to the theft of the necklace was not corroborated, so accordingly there was no proof of the underlying felony of burglary that made the murder in question capital murder under Texas Penal Code § 19.03(a)(2). We reject this contention. Habeas relief under section 2254 on a claim of insufficient evidence is appropriate only “if it is found that upon the record evidence adduced at the trial no rational trier of fact could have found proof of guilt beyond a reasonable doubt.” Jackson v. Virginia, 443 U.S. 307, 322-26, 99 S.Ct. 2781, 2791-92, 61 L.Ed.2d 560 (1979). Even if we were to accept West’s premise that proof of theft was necessary to establish that the murder was committed “in the course of committing or attempting to commit ... burglary,” it is evident to us that, based on all the circumstances taken together with West’s confession, a rational trier of fact could have found theft proved beyond reasonable doubt. West’s confession was amply corroborated, and there was no evidence the theft did not occur. West relies on the “Corpus Delicti” rule. However, he cites no authority for the proposition that application of that rule is constitutionally mandated in a Jackson v. Virginia analysis, particularly as to an underlying felony in a felony murder or capital murder context. In any event, this Court, relying on, among other decisions, Smith v. United States, 348 U.S. 147, 75 S.Ct. 194, 99 L.Ed. 192 (1954), and Opper v. United States, 348 U.S. 84, 75 S.Ct. 158, 99 L.Ed. 101 (1954), long ago held that “corroborative evidence need not be sufficient, independent of a confession or admission of an accused, to establish all elements of a crime allegedly committed. Indeed, the Government fulfills its duty when it introduces substantial independent evidence which tends to establish the trustworthiness of an accused’s admissions.” United States v. Seckler, 431 F.2d 642, 643 (5th Cir.1970). See also id. at 644 n. 2; United States v. Abigando, 439 F.2d 827, 833 (5th Cir.1971) (“a confession can be corroborated by bolstering parts of it to show trustworthiness. Some elements can be proved by the confession alone”; footnote omitted); United States v. Gresham, 585 F.2d 103, 107 (5th Cir.1978) (same). Here it is plain that West’s confession was adequately corroborated — by evidence aliunde the confession — by bolstering parts of it to show its trustworthiness, and that the theft “element” of burglary could be adequately proved by the confession itself. West contends, at least implicitly, that the corroboration rule in Texas is otherwise. However, as we held in Schrader v. Whitley, 904 F.2d 282, 284 (5th Cir.), cert. denied, 498 U.S. 903, 111 S.Ct. 265, 112 L.Ed.2d 221 (1990), “in challenges to state convictions under 28 U.S.C. § 2254, only Jackson [v. Virginia] need be satisfied, even if state law would impose a more demanding standard of proof.” Accord Pemberton v. Collins, 991 F.2d 1218, 1227 (5th Cir.1993); Jones v. Butler, 864 F.2d 348, 361 (5th Cir.1988), cert. denied, 490 U.S. 1075, 109 S.Ct. 2090, 104 L.Ed.2d 653 (1989); Llewellyn v. Stynchcombe, 609 F.2d 194, 196 (5th Cir.1980). See also White v. Estelle, 669 F.2d 973, 978-79 (5th Cir.1982). West also claims ineffective assistance of counsel on the basis, inter alia, of counsel’s failure to raise the issue of alleged evidential insufficiency on direct appeal. For this purpose, the applicable state law standard is relevant. See Summit v. Blackburn, 795 F.2d 1237, 1244-45 (5th Cir.1986). We accordingly turn to Texas law. The most relevant authority at the time of West’s trial and appeal was reviewed in Wooldridge v. State, 653 S.W.2d 811 (Tex.Crim.App.1983), where the Court of Criminal Appeals affirmed a conviction for capital murder committed in the course of aggravated rape. Apart from the appellant’s confession, there was no evidence that the victim had been sexually molested, although there was ample corroboration of other parts of the confession. In rejecting appellant’s corpus delicti argument, the Court of Criminal Appeals wrote: “It is well settled that if there is some evidence corroborative of a confession, the confession may be used to establish the ‘corpus deleeti [sic].’ White v. State, 591 S.W.2d 851 (Tex.Cr.App.1979); Thomas v. State, 108 Tex.Cr.R. 131, 299 S.W. 408 (Tex.Cr.App.1927). In White, supra, the appellant admitted he participated in murders which occurred during the course of robbery. No independent evidence established a robbery had been committed. The Court held the confession was sufficiently corroborated by circumstances which coincided with details of the confession. In Thomas, supra, it was stated: ‘A confession is sufficient, if there be such extrinsic corroborative circumstances as will, taken in connection with the confession, produce conviction of the defendant’s guilt in the minds of the jury beyond a reasonable doubt. Such sup-pletory evidence need not be conclusive in its character. When a confession is made, and the circumstances therein related correspond in some points with those proven to have existed, this may be evidence sufficient to satisfy a jury in rendering a verdict asserting the guilt of the accused. Full proof of the body of the crime, the corpus delecti [sic], independently of the confession is not required by any of the cases.... [citations omitted].’ 299 S.W. at 410. Viewed in a light most favorable to the verdict, the evidence is ample to support it.” Id. at 816-817 (emphasis added). Under Wooldridge and White v. State, 591 S.W.2d 851 (Tex.Crim.App.1979), it is clear that the evidence of theft here is sufficient. Accordingly, the failure to argue the sufficiency of the evidence in this respect was not prejudicial and did not amount to constitutionally defective performance by counsel. Several years after West’s conviction was affirmed, the Court of Criminal Appeals handed down Gribble v. State, 808 S.W.2d 65 (Tex.Crim.App.1990), cert. denied, 501 U.S. 1232, 111 S.Ct. 2856, 115 L.Ed.2d 1023 (1991). The Court held the appellant was properly convicted for capital murder under § 19.03(a)(2) by murdering the victim in the course of kidnaping her, and rejected his twelfth point of error contending that the evidence was insufficient because, apart from his confession, there was insufficient evidence the victim had been kidnaped. Id. at 69-74 (the Court held, however, that a Penry v. Lynaugh, 492 U.S. 302, 109 S.Ct. 2934, 106 L.Ed.2d 256 (1989) error at the punishment stage mandated reversal of the conviction and sentence, id. at 75-76). There was no majority opinion. The opinion announcing the result in Gribble was written by Judge Teague and concurred in by two other judges. Although Judge Teague’s Gribble opinion states that “evidence independent of appellant’s confession was required to show that his victim had been kidnaped”, id. at 71 (emphasis omitted), it goes on to say that “[s]o long as there is some evidence which renders the corpus delicti more probable than it would be without the evidence, we believe that the essential purposes of the rule have been served”, id. at 72 [citing Wool-dridge and White], and “the evidence required for corroboration of an extrajudicial confession need only render the corpus de-licti more probable than it would be without the evidence”, id. at 73 (emphasis omitted). For this limited purpose, “circumstances ... ambiguous in some respects and far from adequate to support the conclusions they imply” provided the requisite corroboration. Id. These aspects of Judge Teague’s Gribble opinion were confirmed in Emery v. State, 881 S.W.2d 702 (Tex.Crim.App.1994), where the court sustained a conviction for capital murder committed in the course of a burglary, rejecting the contention that there was insufficient evidence aliunde the appellant’s confession to show there had been a burglary. In Emery there was “no sign of a forced entry or of anything missing from the apartment” the victim shared with a roommate and where her body, with its multiple stab wounds, was found. Id. at 704. In support of its affirmance, Emery noted that evidence aliunde the confession “need not be sufficient by itself to prove the [predicate] offense; it need only be ‘some evidence which renders the corpus delicti more probable than it would be without the evidence.’ ” Id. at 705 (quoting Gribble). Under this Gribble-Emery test there is sufficient corroboration here: the evidence of forced entry in the middle of the night into a single woman’s room which was then ransacked, with drawers pulled out and dumped on the floor, appearing as if somebody went through everything, certainly makes theft more probable than it would be without such evidence. Since the Gribble-Emery test was met in respect to theft, counsel’s failure to argue insufficiency of the evidence on appeal was neither defective performance nor prejudicial. But, even were the evidence insufficient in this respect under Gribble-Emery, we could not find that failure to raise that issue constituted defective performance, given that the evidence was clearly sufficient under the then current Texas case law exemplified by White v. State and Wooldridge. Counsel was not bound to foresee Gribble, much less Emery. Counsel is not obligated to urge on appeal every nonfrivolous issue that might be raised (not even those requested by defendant). Jones v. Barnes, 463 U.S. 745, 751-55, 103 S.Ct. 3308, 3313-14, 77 L.Ed.2d 987 (1983); Smith v. Murray, 477 U.S. 527, 535-37, 106 S.Ct. 2661, 2667, 91 L.Ed.2d 434 (1986); Mayo v. Lynaugh, 882 F.2d 134, 139 (5th Cir.1989), modified on other gr’ds, 893 F.2d 683 (5th Cir.1990); Wicker v. McCotter, 783 F.2d 487, 497 (5th Cir.), cert. denied, 478 U.S. 1010, 106 S.Ct. 3310, 92 L.Ed.2d 723 (1986). Nor is counsel obligated to anticipate changes in state appellate court rulings. Smith v. Murray, 477 U.S. at 535-37, 106 S.Ct. at 2667. Review of the record and of counsel’s Court of Criminal Appeals brief demonstrate a sound grasp of the case and reflect wholly competent and adequate representation. Our discussion of the sufficiency of the evidence — and of the related ineffective assistance of appellate counsel claim — has thus far proceeded on the arguendo assumption that proof of theft was necessary for proof of burglary and hence for capital murder. Actually, that is not so. Under section 30.02 of the Texas Penal Code burglary includes nonconsensual entry of a habitation either “with intent to commit a felony or theft,” or if the accused after such entry “commits or attempts to commit a felony or theft” (emphasis added). See note 8, supra. Here, not only theft, but attempted theft and also entry with intent to commit theft, would have been burglary. Moreover, burglary would be made out by murder after the nonconsensual entry, as indisputably occurred here. The indictment here charged that West did “while in the course of committing and attempting to commit burglary of a habitation owned by DEANN KLAUS, intentionally cause the death of DEANN KLAUS” by hitting, stabbing and strangling her. The jury instructions here likewise allowed a finding of burglary on any of the theories authorized by section 30.02, including the commission of murder after unlawful entry into the room. The Texas Court of Criminal Appeals has several times upheld capital murder convictions on the basis of a burglary where the burglary was established by the murder of the victim following unlawful entry into his or her habitation. Fearance v. State, 771 S.W.2d 486, 492-494 (Tex.Crim.App.1988), cert. denied, 492 U.S. 927, 109 S.Ct. 3266, 106 L.Ed.2d 611 (1989); Beathard v. State, 767 S.W.2d 423, 427 & n. 6, 431 (Tex.Crim.App.1989) (under general burglary allegation); Matamoros v. State, 901 S.W.2d 470, 473, 474 (Tex.Crim.App.1995) (under general burglary allegation). The evidence here is plainly sufficient to show burglary by West’s forced entry into the victim’s room followed by his murder of her therein. Accordingly, for this reason also, West’s claim of insufficiency of the evidence and his related claim of ineffective assistance of counsel for failure to argue otherwise are both without merit. II. Brady and Related Ineffective Assistance of Counsel West argues that the prosecution suppressed evidence that his confession that he stole a necklace from Klaus’ room was fabricated and thus violated his rights under Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963). Relatedly, West argues, though in only the most conclusory manner, that counsel “failed to undertake reasonable investigation at guilt-innocence and to present evidence indicating that Mr. West was not guilty of the underlying felony of burglary.” The only thing in the record even arguably supporting these claims are the conelusory allegations of West’s federal and state habeas petitions. We reject these contentions. Brady proscribes “the suppression by the prosecution of evidence favorable to an accused.” Id. at 87, 83 S.Ct. at 1196. Certainly West knew whether or not he had taken the necklace, and necessarily knew that better than the prosecution could have. As we said in Lawrence v. Lensing, 42 F.3d 255, 257 (5th Cir.1994): “Brady claims involve ‘the discovery, after trial of information which had been known to the prosecution but unknown to the defense.’ United States v. Agurs, 427 U.S. 97, 103, 96 S.Ct. 2392, 2397, 49 L.Ed.2d 342 (1976).” And, in Lawrence we also quoted with approval the following passage from United States v. Zackson, 6 F.3d 911, 918 (2d Cir.1993): “Evidence is not ‘suppressed’ if the defendant either knew, or should have known, of the essential facts permitting him to take advantage of any exculpatory evidence.” Lawrence at 257 (citation and internal quotation marks omitted). See also, e.g., Williams v. Scott, 35 F.3d 159, 163 (5th Cir.1994), cert. denied, — U.S. —, 115 S.Ct. 959, 130 L.Ed.2d 901 (1995) (“A Brady violation does not arise if the defendant, using reasonable diligence, could have obtained the information”); Blackmon v. Scott, 22 F.3d 560, 564-65 (5th Cir.), cert. denied, — U.S. —, 115 S.Ct. 671, 130 L.Ed.2d 604 (1994) (“The state is not required to furnish a defendant with exculpatory evidence that is fully available to the defendant or that could be obtained through reasonable diligence”); Duff-Smith v. Collins, 973 F.2d 1175, 1181 (5th Cir.1992), cert. denied, 507 U.S. 1056, 113 S.Ct. 1958, 123 L.Ed.21d 661 (1993); May v. Collins, 904 F.2d 228, 231 (5th Cir.1990), cert. denied, 498 U.S. 1055, 111 S.Ct. 770, 112 L.Ed.2d 789 (1991); United States v. Marrero, 904 F.2d 251, 261 (5th Cir.1990), cert. denied, 498 U.S. 1000, 111 S.Ct. 561, 112 L.Ed.2d 567 (1990). Moreover, West cites no authority, and we have found none, supporting the conclusion that a Brady violation could be found in these circumstances. Accordingly, West would have to extend Brady beyond what is compelled by existing precedent, and relief is hence barred by Teague v. Lane, 489 U.S. 288, 109 S.Ct. 1060, 103 L.Ed.2d 334 (1989). Moreover, as the magistrate judge correctly observed in recommending that the state’s unopposed motion for summary judgment be granted, “[t]here is no evidence that the prosecution had any evidence relating to the fact that a burglary [by theft] never occurred.” The allegations of West’s amended section 2254 petition are wholly conelusory in this respect and do not assert that West ever informed (or even suggested to) anyone that he did not take the necklace. See note 19, supra. Such allegations do not suffice to entitle West to an evidentiary hearing. “The [habeas] petitioner must set forth specific allegations of fact, not mere conelusory allegations,” Johnson v. Scott, 68 F.3d 106, 112 (5th Cir.1995), and “[t]he court need not blindly accept speculative and inconcrete claims as the basis upon which to order a hearing,” Ellis v. Lynaugh, 873 F.2d 830, 840 (5th Cir.), cert. denied, 493 U.S. 970, 110 S.Ct. 419, 107 L.Ed.2d 384 (1989) (internal quotation marks omitted). “Conclusory allegations are not enough to warrant discovery under Rule 6 of the Federal Rules Governing Section 2254 Petitions; the petitioner must set forth specific allegations of fact; Rule 6, which permits the district court to order discovery on good cause shown, does not authorize fishing expeditions.” Ward v. Whitley, 21 F.3d 1355, 1367 (5th Cir.1994), cert. denied, — U.S. -, 115 S.Ct. 1257, 131 L.Ed.2d 137 (1995). West’s claim of ineffective assistance of counsel in this respect fails for similar reasons. It, too, is wholly conclusory. West’s confession states that he took the necklace, and he has never alleged that he ever informed his counsel that he had not done so, or ever gave counsel any reason to so believe (nor does West’s petition allege any facts that would have put counsel on notice under these circumstances, or specify any particular evidence that investigation in this respect would have revealed). There is simply no basis on which to conclude that counsel’s performance was constitutionally deficient in this respect. ‘We must strongly presume that trial counsel rendered adequate assistance and that the challenged conduct was the product of reasoned trial strategy,” Wilkerson v. Collins, 950 F.2d 1054, 1065 (5th Cir.1992), cert. denied, 509 U.S. 921, 113 S.Ct. 3035, 125 L.Ed.2d 722 (1993), and “[w]hen a defendant has given counsel reason to believe that pursuing certain investigations would be fruitless ... counsel’s failure to pursue those investigations may not later be challenged as unreasonable.” Id. (quoting Burger v. Kemp, 483 U.S. 776, 795, 107 S.Ct. 3114, 3126, 97 L.Ed.2d 638 (1987) [quoting Strickland v. Washington, 466 U.S. 668, 691, 104 S.Ct. 2052, 2066, 80 L.Ed.2d 674 (1984) ]; internal quotation marks omitted). West’s petition simply does not allege facts showing that counsel’s performance in this respect was constitutionally deficient. [18] Finally, we note that neither the Brady claim concerning the theft nor the related ineffective assistance of counsel claim demonstrate the requisite “ ‘reasonable probability’ of a different result” such as “ ‘undermines confidence in the result’ ” under Kyles v. Whitley, — U.S. -, -, 115 S.Ct. 1555, 1566, 131 L.Ed.2d 490 (1995), and Strickland v. Washington, 466 U.S. 668, 693-94, 104 S.Ct. 2052, 2068, 80 L.Ed.2d 674 (1984). The entire claimed importance of the necklace theft is based on the theory that without it there could be no burglary and hence no capital murder. As demonstrated above, this is simply not so. It is uncontested and beyond dispute that West forced his way into Klaus’ motel room where Klaus lived and then and there murdered her. This constitutes burglary and establishes West’s guilt of capital murder. We reject the Brady claim and related claim of ineffective assistance of counsel. III. Admissibility of Confession West argues that the admission in evidence of his written confession violated his rights under the Fifth Amendment in that his Miranda right to cut off questioning was not scrupulously honored, relying on Charles v. Smith, 894 F.2d 718 (5th Cir.1990). The evidence shows that when West was arrested and placed in a patrol car at the motel Officer Rogers read him his Miranda rights. He did not appear to be intoxicated or on drugs. After being read his rights West told Officer Rogers that “he already knew his rights anyway”. West was thereafter taken to the police station about 3:30 A.M. and was there interviewed by detective Kent after Kent had again read West his Miranda rights. West advised Kent that he understood those rights. West did not appear intoxicated or under the influence of drugs. West talked to Kent about 30 to 45 minutes, and gave no indication that he wished to exercise or invoke any of the rights read to him, nor did he discuss those rights. Kent made no promises or threats to West, and there was no coercion. At the end of this interview Kent took West to the jail to be booked in. Kent talked to West again from about 9:20 to 10:40 A.M. Kent testified that West was “coherent,” “in control of his faculties,” and “seemed calm, was responsive to my questions and talked freely.” Kent testified that no promises or threats were made and there was no coercion. West did not indicate he wished to invoke any of the rights previously read to him. He was taken back to the jail about 10:40 A.M. About noon that day murder charges were filed. Slightly over thirteen hours later, at about 11:50 P.M. that night, West was again questioned by Kent. Kent read West his rights, and told him he had been charged with murder and could get the death penalty. During the questioning Kent informed West that Tagle had implicated him by saying West had returned to their motel room with his clothes bloody and then washed them off. West responded that “he didn’t believe Tagle would say that” and said he wanted to talk with Tagle. Officer Rogers was sent to get Tagle, who Kent mistakenly thought was at the police station. About an hour later Rogers returned without Tagle. Kent at that time, approximately 1:00 A.M. August 25, decided to terminate the interview with West and take him back to the jail, which had called advising they wanted West back so he could be transferred to the county. Kent so advised West. Up until that time, West in all discussions with Kent had denied any involvement in the murder. Kent testified “I was getting ready to put him in jail. He decided to start telling me the story.” West was not intoxicated, he “was alert,” and he “talked freely” and was “responsive to” questions. West never stated he did not want to talk and never asked for a lawyer or otherwise sought to invoke his Miranda rights. No threats or promises were made, and there was no coercion. After telling his story, West indicated that he would make a written statement. Kent then again read West the warnings printed on a statement form (identical to those on West’s written statement, see note 27, infra) and again asked him if he understood them and if he wanted to make a written statement. West said he understood his rights and would give a written statement. Kent then proceeded to type on the statement form what West told him. Kent would from time to time ask questions and type what West said in response. The statement is seven pages long, Kent was a slow typist, and several coffee breaks were taken. The entire process took several hours. When the statement was finished, Kent handed it to West who read it, the first sentence aloud, and made several corrections. West then read silently the printed warnings, said he understood them, and initialed them. He then signed each page of the statement. The entire process was completed at about 7:45 A.M., and West was then returned to the jail. Summarizing his three separate interviews with West, detective Kent testified there were never any promises or threats made to West, nor any coercion applied. He further testified that on each of these three occasions West had never sought to exercise or raise a question about any of the rights he had been read. Kent also testified: “He never once at all stated that he didn’t want to talk to me” or “that he wanted a lawyer,” and “he continued to talk with me. He would answer my questions. He would talk freely with me.” West did not testify at the Jackson v. Denno hearing, and no evidence was presented contradicting the testimony of the police officers called by the prosecution. The trial court entered detailed written findings that the confession was in all respects voluntary and properly warned. The court found, inter alia, that the warnings as testified to were given West, that he never advised the officers that he wanted an attorney present, that “at no time ... did the defendant request police officers to cease interrogating him,” that “defendant, after repeated warnings, knowingly, intelligently and voluntarily waived his rights under Article 38.22, V.A.C.C.P., including his right to assistance of counsel,” and that “the defendant’s confession was not the product of force, threats, persuasion, intimidation or promises, but was freely and voluntarily given.” On direct appeal, the Court of Criminal Appeals rejected challenges to the confession, holding that the trial court’s “findings of fact are supported by the record” and “we find ample support for the finding-that appellant never requested the interrogation cease.” West, 720 S.W.2d at 518. Where the question presented in a section 2254 proceeding is whether a confession admitted at trial was voluntary and in compliance with Miranda, with respect to issues of underlying or historic facts, the state court findings, if fairly supported in the record, are conclusive, but there is independent federal determination of the ultimate question whether, under the totality of the circumstances, the challenged confession was obtained in a manner compatible with the requirements of the Constitution. Miller v. Fenton, 474 U.S. 104, 110-14, 116-18, 106 S.Ct. 445, 450-51, 453, 88 L.Ed.2d 405 (1985). West challenges the finding of the state courts that he never invoked his right to remain silent, relying on the testimony of detective St. John that between 9:00 and 10:00 A.M. on August 24 West told the officers he “didn’t want to tell us anything about it.” This testimony is best understood, however, as saying not that West refused to talk or exercised his right to silence, but rather that, denying any involvement in the murder, he refused to talk about what he would only know if he were involved. This construction .is consistent with St. John’s testimony that during this interview West was “very arrogant in that interview. He was denying his involvement in the episode” and that West never indicated in his presence any desire to invoke the rights of which he had been advised. Moreover, Kent was doing the interviewing, and St. John was in and out of the room. Kent likewise testified that at this interview he discussed the case with West and West “still denied having anything to do with it,” but “was responsive to my questions and talked freely.” And, as noted, Kent testified that West did not invoke his rights at this meeting, or any other, never said he did not want to talk with Kent, and always “would talk freely with me.” The construction West now seeks to place on St. John’s testimony would make it contradictory to that of Kent. The record fairly supports the underlying factual determination of the Texas courts that West did not invoke his right to silence. Even if West had invoked his right to silence at the 9:20-10:00 A.M. interview, this would not render his resumed questioning more than thirteen hours later a failure to scrupulously honor his right to silence. In Charles v. Smith, supra, the resumed questioning took place “just a few minutes after” the defendant had exercised his right to silence. Id. at 726. Similarly, we found a Miranda violation where questioning was resumed thirty or forty-five minutes after invocation of the right to silence. United States v. Hernandez, 574 F.2d 1362 (5th Cir.1978). Here, questioning was not resumed until after a lapse of thirteen hours. Thus, the present case is controlled by Kelly v. Lynaugh, 862 F.2d 1126 (5th Cir.1988), cert. denied, 492 U.S. 925, 109 S.Ct. 3263, 106 L.Ed.2d 608 (1984), likewise a capital ease in which we affirmed a summary judgment denial of habeas relief. There, Kelly, about 11:00 A.M. the day of his arrest, having been advised of his Miranda rights, was asked if he wanted to talk, and he responded “no,” and was taken to the jail. About 4:00 P.M. the same day, he was taken out of the jail and given his Miranda warnings, but he again refused to answer questions, and was returned to the jail. He was yet again removed from the jail for questioning some four and a half to six hours later (at some time between 8:30 and 10:00 P.M. the same day), and then, after being shown a co-defendant’s statement and “without new Miranda warnings, Kelly orally confessed. When the confession was reduced to writing [and signed by Kelly], the Miranda warnings were stated at the top of the first page” and were followed by a statement that the signer had read, understood, and voluntarily waived those rights. Kelly at 1130. Reviewing Michigan v. Mosley, 423 U.S. 96, 96 S.Ct. 321, 46 L.Ed.2d 313 (1975), and other relevant authorities, we held that the written confession was admissible, that Miranda had been complied with, and “Kelly’s right to cut off questioning was scrupulously honored.” Kelly at 1130-31. Our thorough examination of the record here leads to the same conclusion. We reject West’s contentions to the contrary. We likewise reject West’s claim that the confession was taken in violation of his Sixth Amendment right to counsel. Although West’s Sixth Amendment rights attached when charges were filed, West had never requested (or retained) counsel and none had been appointed for him. In those circumstances, his waiver of counsel pursuant to his Miranda warnings waived his Sixth Amendment right not to be interrogated or give a statement without the presence or guidance of counsel. This is made clear by Patterson v. Illinois, 487 U.S. 285, 108 S.Ct. 2389, 101 L.Ed.2d 261 (1989), and its progeny. See United States v. Gaytan, 74 F.3d 545, 555 (5th Cir.1996) (“As long as the defendant is given Miranda warnings, his voluntary decision to answer questions without invoking the right to counsel constitutes waiver [of the Sixth Amendment right]”); Wilcher v. Hargett, 978 F.2d 872, 876 (5th Cir.1992); Montoya v. Collins, 955 F.2d 279, 282 (5th Cir.), cert. denied, 506 U.S. 1036, 113 S.Ct. 820, 121 L.Ed.2d 692 (1992) (“As long as the police administer Miranda warnings before proceeding, a defendant’s voluntary decision to answer questions without claiming his right to have a lawyer present to advise him constitutes a ‘knowing and intelligent,’ and therefore valid, waiver of his Sixth Amendment right”; citing Patterson). Finally, West complains of violation of his rights under Tex.Code.Crim.Proe. art. 15.17, requiring that a person arrested be taken before a magistrate “without unnecessary delay.” However, asserted violations of state law do not constitute a basis for federal habeas relief. West’s written confession was completed approximately thirty hours after his arrest, and there is no showing that he was not taken before a magistrate well before the forty-eight hour presumptive maximum delay of County of Riverside v. McLaughlin, 500 U.S. 44, 111 S.Ct. 1661, 114 L.Ed.2d 49 (1991) “Even assuming that the time gap between arrest and initial appearance was unreasonable, the claim does not rise to constitutional significance.” De La Rosa v. State of Texas, 743 F.2d 299, 303 (5th Cir.1984), cert. denied, 470 U.S. 1065, 105 S.Ct. 1781, 84 L.Ed.2d 840 (1985). “The rule in McNabb v. United States, 318 U.S. 332, 63 S.Ct. 608, 87 L.Ed. 819 (1943) [which] prohibits the use in [federal] criminal cases of confessions ... where there was a failure to bring the accused before a committing magistrate without unnecessary delay ... has not been extended to state prosecutions as a requirement of the Fourteenth Amendment.” Smith v. Heard, 315 F.2d 692, 694 (5th Cir.), cert. denied, 375 U.S. 883, 84 S.Ct. 154, 11 L.Ed.2d 113 (1963), citing Brown v. Allen, 344 U.S. 443, 73 S.Ct. 397, 97 L.Ed. 469 (1953), and Gallegos v. Nebraska, 342 U.S. 55, 72 S.Ct. 141, 96 L.Ed. 86 (1951). “Failure to [timely] take an accused before a magistrate ... bear[s] only upon the issue of voluntariness” of the confession, and is only one of several factors to be considered in that respect. Smith v. Heard at 694 (emphasis added), citing Culombe v. Connecticut, 367 U.S. 568, 81 S.Ct. 1860, 6 L.Ed.2d 1037 (1961). In De La Rosa, relying on Culombe; Brown; Gallegos; and Smith v. Heard, we upheld the admissibility of the confession, despite its having been given before the arrested accused was taken to a magistrate and following what we assumed was an unreasonable delay in doing so, because “[i]n our reading of the record we find nothing to indicate that De La Rosa’s confession was anything other than the product of his free and voluntary choice." De La Rosa at 303. Our review of the entire record here leads to the same conclusion as to West's confession. Notwithstanding the delay between arrest and arraignment, under all the circumstances reflected by the record here, West's confession is shown to be the product of his free and voluntary choice. We reject all the contentions West raised on appeal in respect to the admissibifity of his confession. IV. Penry Claim, and Challenges to Texas Capital Sentencing Scheme West argues that his rights under Penry v. Lynaugh, 492 U.s. 302, 109 S.Ct. 2934, 106 L.Ed.2d 256 (1989), were violated because under the Texas sentencing special issues the jury could not give full effect to the allegedly mitigating circumstances of his case. Insofar as West relies on allegedly mitigating circumstances not reflected by evidence introduced or tendered at his trial, his claim is without merit as we have repeatedly held that a Penry claim may be based only on evidence introduced or offered at trial. Briddle v. Scott, 63 F.Sd 364, 377 (5th Cir.), cert. denied, — U.S. — 116 S.Ct. 687, 133 L.Ed.2d 531 (1995); Anderson v. Collins, 18 F.3d 1208, 1214-15 (5th Cir.1994); Allridge v. Scott, 41 F.3d 213, 223 (5th Cir.1994), cert. denied, — U.S. — 115 S.Ct. 1959, 131 L.Ed.2d 851 (1995); Crank v. Collins, 19 F.3d 172, 176 (5th Cir.), cert. denied, — U.S. —, 114 S.Ct. 2699, 129 L.Ed.2d 825 (1994); Callins v. Collins, 998 F.2d 269, 275 (5th Cir.1993), cert. denied, 510 U.S. 1141, 114 S.Ct. 1127, 127 L.Ed.2d 435 (1994). The only evidence actually introduced (or offered, conditionally or otherwise) at trial that West claims is mitigating evidence that could not adequately be taken into account under the sentencing special issue, consists of statements in his confession that he had been drinking heavily the afternoon and evening of the murder and that he "boiled up" or "blew up" at things the victim said to him after he had forced his way into her room and attacked her. As to the drinking and inference of intoxication, we have many times held that this may be adequately taken into account under both the first and second punishment issues (deliberateness and future dangerousnes~). Briddle at 377; Anderson at 1214-15 n. 5; Nethery v. Collins, 993 F.2d 1154, 1161 (5th Cir.1993), cert. denied, — U.S. —, 114 S.Ct. 1416, 128 L.Ed.2d 87 (1994); James v. Collins, 987 F.2d 1116, 1121 (5th Cir.1993); Cordova v. Collins, 953 F.2d 167, 170 (5th Cir.), cert. denied, 502 U.S. 1067, 112 S.Ct. 959, 117 L.Ed.2d 125 (1992). See also Lackey v. Scott, 28 F.3d 486, 487 (5th Cir.1994), cert. denied, — U.S. —, 115 S.Ct. 743, 130 L.Ed.2d 644 (1995). As to West's having "blown up" or the like, any mitigating quality of this evidence could be adequately taken into account under both the punishment issues. Blackmon at 564; Marquez v. Collins 11 F.3d 1241, 1248 (5th Cir.1994). West also makes what appears to be both an as applied and a facial challenge to the Texas sentencing scheme on the basis that it chills counsels’ presentation and/or development of mitigating evidence. We have repeatedly rejected such claims. Briddle at 378; Lackey at 490; Crank at 176; Black v. Collins, 962 F.2d 394, 407 (5th Cir.), cert. denied, 504 U.S. 992, 112 S.Ct. 2983, 119 L.Ed.2d 601 (1992). West advances a further facial challenge to the Texas sentencing scheme on the basis that the second special issue improperly functions as an aggravating circumstance and is invalid in the absence of appropriate narrowing definitions or instructions. We rejected essentially the same contention in James at 1119-20, and, more recently, in Woods v. Johnson, 75 F.3d 1017, 1033-34 (5th Cir.1996). See also Nethery at 1162; Thompson v. Lynaugh, 821 F.2d 1054, 1059-60 (5th Cir.), cert. denied, 483 U.S. 1035, 108 S.Ct. 5, 97 L.Ed.2d 794 (1987); Milton v. Procunier, 744 F.2d 1091, 1095-96 (5th Cir.1984), cert. denied, 471 U.S. 1030, 105 S.Ct. 2050, 85 L.Ed.2d 323 (1985). In Jurek v. Texas, 428 U.S. 262, 96 S.Ct. 2950, 49 L.Ed.2d 929 (1976), the facial validity of the Texas capital sentencing scheme was sustained. There the Court held that the constitutionally required narrowing function was performed at the guilt-innocence stage, and further narrowing at the sentencing stage was not required. Id. at 268-75, 96 S.Ct. at 2955-57. This was confirmed by Lowenfield v. Phelps, 484 U.S. 231, 243-47, 108 S.Ct. 546, 554-55, 98 L.Ed.2d 568 (1988). Jurek likewise expressly rejects the contention that the second punishment issue is impermissibly vague. Id. at 272-75, 96 S.Ct. at 2957-58. See also Pulley v. Harris, 465 U.S. 37, 49 n. 10, 104 S.Ct. 871, 879 n. 10, 79 L.Ed.2d 29 (1984) (Texas punishment issues not imper-missibly vague). We reject West’s claims based on Penry, as well as his challenges to the Texas capital sentencing scheme. V. Ineffective Assistance of Counsel at Sentencing West claims counsel was ineffective in failing to present mitigating evidence at sentencing and in failing to adequately investigate in that respect. West’s amended federal petition alleged in general terms that his counsel was ineffective because he failed to adequately investigate West’s “social, educational, health, and medical background and failed to discover facts which, if provided to a psychologist or psychiatrist, would have rendered relevant and significant evidence regarding the defendant’s responsibility for the crime as well as his deliberateness and future dangerousness.” It is alleged that West’s mother abandoned him to her parents shortly after his birth, and his grandparents (described as “very good people” whom West “loved” and was “close to”) raised West, who believed they were his real parents until he was approximately twelve years old. He did well in school until he was twelve, and then began having problems, including alcohol and drug abuse. He suffered a head injury of a wholly unspecified sort. After his grandfather died when West was fifteen, West was placed in various juvenile facilities. Attached to West’s amended federal habeas petition was an affidavit by psychologist Dr. Brown, who examined West in July 1987 and performed three psychological tests on him. Brown also examined West’s school and juvenile facility records, as well as his records after his conviction at the Texas Department of Corrections. This affidavit states that West’s “social, educational and athletic development were excellent until the age of twelve.” Some time thereafter he was involved in a series of juvenile offenses and was eventually placed in the Illinois Department of Corrections, where he remained until age eighteen. He received some psychological testing there, which reflected an I.Q. of 100. It was also “regularly noted that he had anger and hostility within and poor impulse control” but “seemed typically to respond well to supervision.” After release he “continued his drug use as an adult, primarily using angel dust, often combining it with alcohol.” In Houston, West and his friends “spent most of their time in bars and on the streets hustling for their money.” Brown reports West “has long suffered from headaches” which “are getting worse now” so he “now takes aspirin by the handful”; he “currently suffers from blurred vision and, on at least one occasion, passed out and fell without explanation.” Brown did not make any diagnosis of insanity, incompetence, psychosis, or any particular psychological malady. However, he did opine that “some type of organic brain syndrome” “may exist,” confirmation of which would require “a complete neurological examination, CAT scan, and EEG sleep tracing.” In support of his “may exist” opinion, Brown stated that the drugs West had been abusing “when taken in significant dosages over a period of years, can be causative to brain tissue pathology” and also referred to West’s “history of headaches, flashbacks, blurred vision, multiple head injuries ... one episode of passing out without explanation and ... rocking himself prior to sleep.” Brown opined that West’s murder of Klaus Was “a singular event” and it was “highly unlikely” West would “commit such an offense again.” In support of this opinion, Brown principally stressed West’s “history of drug abuse and excessive consumption of alcohol the day of the crime”; that the victim was a woman and West, who “experienced problematic relationships with women” harbored “deep-seated anger at women”; that “the killing was done out of loyalty to a friend rather than other criminal behavior like robbery or burglary”; and that West “did not enter the victim’s room with the idea of killing her, but did so afterwards in an unusual rage state which was out of character for him.” The affidavit of West’s trial counsel, which is wholly uncontradicted on this record, states in part as follows: “On August 22, 1982, Mr. West was present in the courtroom of the 182nd District Court and Roy Ashe and I had an opportunity to talk with him. Mr. West appeared lucid and coherent; he was able to and did respond appropriately to the questions that we asked. During the course of our case preparation, both Roy Ashe [co-counsel] and I visited with Mr. West on numerous occasions. At no time during the course of the investigation, trial preparation, or trial itself did Mr. West give any indication that he was anything other than sane at the time he committed the offense and competent to stand trial. He was able to relate details of the offense and justified the killing on the basis that the victim was at least partially responsible for his friend Brett getting killed. Mr. West communicated freely with Roy Ashe and me during the course of the trial, often asking pertinent questions or providing additional information. In the course of my preparation I asked Mr. West whether he had ever had any psychiatric/psychological problems. While I do not recall his exact response, I feel certain that his response, coupled with my personal observations of Mr. West, foreclosed any potential insanity defense. In my professional opinion I saw no need to have Mr. West undergo a psychiatric examination. ****** In preparation for trial, including the punishment phase, I had Mr. West prepare a background summary of his work history and school history. Unfortunately for the defense, the information provided by Mr. West was not at all helpful and generally damaging. Neither conversations with Mr. West nor his summary provided us with names of people (employers, roommates, schoolmates) who might testify in his behalf at punishment. I personally contacted the grandmother who had raised Mr. West. She refused to testify for him and did not tell me anything that compelled me to subpoena her in spite of her refusal.” As we have many times held, “[t]he failure to present a case in mitigation during the sentencing phase of a capital murder trial is not, per se, ineffective assistance of counsel.” Stringer v. Jackson, 862 F.2d 1108, 1116 (5th Cir.1988), vacated and remanded on other grounds, 503 U.S. 222, 112 S.Ct. 1130, 117 L.Ed.2d 367 (1992), following remand, 979 F.2d 38 (5th Cir.1992) (modifying original opinion in other respects). See also, e.g., Woods at 1034-35; Andrews v. Collins, 21 F.3d 612, 623-25 (5th Cir.1994); Duff-Smith at 1183; Lincecum v. Collins, 958 F.2d 1271, 1278-80 (5th Cir.), cert. denied, 506 U.S. 957, 113 S.Ct. 417, 121 L.Ed.2d 340 (1992); Wilkerson at 1065; DeLuna v. Lynaugh, 873 F.2d 757, 758-60 (5th Cir.), cert. denied, 493 U.S. 900, 110 S.Ct. 259, 107 L.Ed.2d 208 (1989). West’s counsel, from his observations of and discussions with West, and his inquiry of him as to whether “he had ever had any psychiatric/psychological problems,” was given no reason to suspect anything significant in that regard, much less any organic brain syndrome. Nothing in Dr. Brown’s affidavit even suggests otherwise. There is no allegation—much less any affidavit or other evidence—that West had ever been hospitalized for a head injury or for a mental condition or had ever been diagnosed as having any sort of brain damage or psychosis, or that West ever gave counsel any reason to believe that he had ever suffered a head injury or suffered from any psychiatric or psychological problems. Counsel likewise talked to West’s grandmother, who refused to testify for West and provided no useful information. West provided no names of potential witnesses for the punishment hearing, and the information he did provide “was not at all helpful and generally damaging.” West has not even alleged—much less provided any affidavit or other evidence of— anything tending to contradict these statements. Accordingly, counsel was not ineffective for failing to further investigate in these respects. See, e.g., Andrews at 623 (“Because counsel had no reason to believe that pursuing further investigation into Andrews’ mental capacity or his background would be useful, ‘counsel’s failure to pursue those investigations may not ... be challenged as unreasonable’ ”) (quoting Burger v. Kemp, 483 U.S. 776, 795, 107 S.Ct. 3114, 3126, 97 L.Ed.2d 638 (1987)); Wilkerson at 1065. See also Cantu v. Collins, 967 F.2d 1006, 1016 (5th Cir.1992), cert. denied, 509 U.S. 926, 113 S.Ct. 3045, 125 L.Ed.2d 730 (1993). Moreover, “[w]e must ‘indulge a strong presumption that counsel’s conduct falls within the wide range of reasonable professional assistance’ and that the ‘challenged action might be considered sound trial strategy.’ ” Belyeu v. Scott, 67 F.3d 535, 538 (5th Cir.1995) (emphasis added; quoting Strickland, 466 U.S. at 689, 104 S.Ct. at 2065), cert. denied, — U.S. —, 116 S.Ct. 1438, 134 L.Ed.2d 559 (1996). See also Wilkerson at 1065. “The defendant must overcome the presumption that, under the circumstances, the ‘challenged action might be considered sound trial strategy.’ ” Strickland, 466 U.S. at 689, 104 S.Ct. at 2065. In light of the record as a whole, West has neither alleged nor tendered evidence of concrete facts sufficient to overcome those presumptions. Evidence of West’s drinking on the afternoon and evening of the offense was before'the jury, and evidence that he customarily abused alcohol or drugs or had a juvenile record would be — especially in the pre-Penry setting of this trial — at best a two-edged sword. See Woods at 1034; King v. Lynaugh, 868 F.2d 1400, 1405 (5th Cir.) (“ ‘jurors are generally unsympathetic toward drug abusers’ ”), cert. denied, 489 U.S. 1099, 109 S.Ct. 1576, 103 L.Ed.2d 942 (1989); DeLuna v. Lynaugh, 873 F.2d 757, 759 (5th Cir.), cert. denied, 493 U.S. 900, 110 S.Ct. 259, 107 L.Ed.2d 208 (1989). We observed in Smith v. Black, 904 F.2d 950, 977 (5th Cir.1990), vacated and remanded on other grounds, 503 U.S. 930, 112 S.Ct. 1463, 117 L.Ed.2d 609 (1992), aff'd in relevant part, 970 F.2d 1383 (5th Cir.1992), that although certain “mitigating evidence might have been presented” but was not, nevertheless “it is equally possible that Smith’s trial counsel had sound strategic reasons for not presenting it, and we cannot speculate that Smith was unconstitutionally impaired by any ineffective assistance on such an allegation.” West has not shown that his counsel was constitutionally defective. Moreover, not only has West failed to show that his counsel’s performance was defective, he has also failed to show the requisite Strickland prejudice. Even if Dr. Brown had testified as stated in his affidavit, and even if it were shown that West had a history of drug and alcohol abuse, and had some character of organic brain syndrome that diminished his “ability to control his impulses and behavior,” and even if his grandmother and counselors were to have testified to his good behavior in grade school (see note 43, supra), we are convinced that there is no reasonable probability — no probability sufficient to undermine our confidence in the sentencing (or the guilty) verdict — that the outcome would have been different. Strickland, 466 U.S. at 693-95, 104 S.Ct. at 2068. West forced his way into the room of the victim — a woman he barely knew — in the middle of the night, and admitted that he had gone there with intent to kill her. He did so in a most brutal and savage manner, but only after putting her through a horrifying and degrading series