Doyle J. Williams, a Missouri prisoner convicted of capital murder, appeals the district court’s denial of his petition for a writ of habeas corpus. See 28 U.S.C. § 2254 (1982). We affirm.
I. BACKGROUND
Williams’s capital murder conviction arose out of a cold-blooded scheme to eliminate witnesses who might implicate him in the 1980 burglary of a doctor’s office in Auxvasse, Missouri. After the burglary, Williams attempted to pass a forged prescription using a form stolen in the burglary. Williams first murdered the doctor in the belief that by preventing the doctor from testifying that he had not signed the prescription form, the state’s charge against Williams for attempting to obtain a controlled substance by fraud would fail. Williams was eventually convicted of murdering the doctor. See generally Williams v. Armontrout, 877 F.2d 1376, 1378 (8th Cir.1989), cert. denied, — U.S. -, 110 S.Ct. 1140, 107 L.Ed.2d 1044 (1990). With the help of one of his girl friends and his accomplice in the burglary, Williams then set out to kill the accomplice’s roommate, who could also tie Williams to the crime. The girl friend was Betty Coleman, and the accomplice was John Morgan. The target of the murder scheme was Kerry Brum-mett.
To carry out the murder, Williams asked Coleman to arrange a date with Brummett late on October 9, 1980. Coleman met Brummett at a restaurant and drove Brum-mett to an isolated area near the Missouri River where Williams and Morgan were waiting. When Coleman and Brummett arrived, the men dragged Brummett from the car, brutally beat him, and handcuffed his hands behind his back. The men then put Brummett in the trunk of the car Coleman had arrived in and drove to a location where they could sink Brummett’s body in the river after they killed him. Finding their chosen location occupied by campers, the men drove on in search of another secluded location to complete their murderous scheme.
When they reached a deserted point at the river’s edge, Williams and Morgan removed Brummett from the trunk. While Morgan obtained a rope and weight to dispose of Brummett’s body, Williams brutally beat the handcuffed Brummett. No doubt sensing the men’s intentions, Brummett exercised his final option and fled toward the river with Williams in hot pursuit. Brum-mett ran into the water and immediately sank. After Brummett surfaced for the second time, Williams ordered Morgan to shoot him. Despite Williams’s order, Morgan later explained that he aimed and fired over Brummett’s head. Williams, who could have rescued Brummett if he was not bent on murder, entered the water only in an attempt to retrieve incriminating handcuffs from the body of a drowned man. When authorities discovered Brummett’s beaten and handcuffed body seven days later, they determined the cause of death was drowning. Other opinions further detail these facts. See Williams v. Armontrout, 679 F.Supp. 916, 922 (W.D.Mo.1988); State v. Williams, 652 S.W.2d 102, 106-07 (Mo.1983) (en banc).
*928Coleman was convicted at a separate trial of capital murder and sentenced to life imprisonment. Morgan received immunity from all charges in exchange for his testimony at Coleman’s and Williams’s trials. In 1981, a Missouri jury convicted Williams of capital murder. See Mo.Rev.Stat. § 565.001 (1978) (repealed 1984). After a sentencing hearing, the same jury recommended the death penalty based on the aggravating circumstance of murder for the purpose of preventing a witness from testifying in a judicial proceeding. See Mo. Rev.Stat. § 565.012.2(12) (Supp.1981) (repealed 1984). The state trial court sentenced Williams to death. The Missouri Supreme Court affirmed the conviction and sentence on direct appeal. See 652 S.W.2d at 117. Williams then sought a writ of habeas corpus in federal district court. We affirmed the district court’s dismissal of this writ for failure to exhaust state court remedies. See Williams v. Wyrick, 763 F.2d 363, 365 (8th Cir.1985) (per curiam).
Williams unsuccessfully sought state postconviction relief, and the Missouri Court of Appeals affirmed. Williams v. State, 712 S.W.2d 404, 411 (Mo.Ct.App.1986). Williams then brought this action in the district court seeking a second writ of habeas corpus under section 2254. In a comprehensive opinion, the district court denied the petition. See 679 F.Supp. at 949. Williams now appeals that denial to this court, claiming a number of errors we consider in turn.
II. LESSER INCLUDED OFFENSE INSTRUCTION
Williams asserts the state trial court denied him due process by refusing to instruct the jury on first-degree (felony) murder. See Mo.Rev.Stat. § 565.003 (1978) (repealed 1984). Williams argues he was entitled to the felony murder instruction because Brummett’s death occurred during a kidnapping. See id. § 565.110.1(4)-(5) (1978). Williams also argues he was denied his right to equal protection because the Missouri Supreme Court applied in his case a different rule on felony murder as a lesser included offense than'the Court applied in other eases.
In a capital case, due process requires a trial court to instruct the jury on. all lesser included offenses supported by the evidence. See Hopper v. Evans, 456 U.S. 605, 611, 102 S.Ct. 2049, 2052-53, 72 L.Ed.2d 367 (1982); Beck v. Alabama, 447 U.S. 625, 637-38, 100 S.Ct. 2382, 2389-90, 65 L.Ed.2d 392 (1980). At the time of Williams’s trial, felony murder was a lesser included offense of capital murder under Missouri law. See Mo.Rev.Stat. § 565.006.1 (1978); State v. Daugherty, 631 S.W.2d 637, 645 (Mo.1982); State v. Fuhr, 626 S.W.2d 379, 379 (Mo. 1982). The Missouri Supreme Court later held that felony murder is not a lesser included offense of capital murder in that state. See State v. Baker, 636 S.W.2d 902, 904-05 (Mo.1982) (en banc), cert. denied, 459 U.S. 1183, 103 S.Ct. 834, 74 L.Ed.2d 1027 (1983). The following year, the Missouri court ruled the Baker holding would be applied only prospectively. See State v. Goddard, 649 S.W.2d 882, 889 (Mo.) (en banc), cert. denied, 464 U.S. 997, 104 S.Ct. 495, 78 L.Ed.2d 689 (1983). Goddard is the basis for Williams’s equal protection argument and we recognize that some members of the Missouri Supreme Court have been critical of Goddard’s treatment of Baker. See, e.g., State v. Holland, 653 S.W.2d 670, 680 (Mo.1983) (en banc) (Welliver, J., dissenting) (“The majority ... has treated similarly situated defendants differently in a transparent effort to avoid granting them new trials.”); id. at 679-81; Williams, 652 S.W.2d at 117-18 (Welliver, J., dissenting); Goddard, 649 S.W.2d at 890-92 (Welliver, J., dissenting).
Williams’s federal due process and equal protection arguments depend on Williams’s contention the evidence at his trial supported giving the felony murder instruction as a lesser included offense of capital murder. See Hopper, 456 U.S. at 611, 102 S.Ct. at 2052-53; Beck, 447 U.S. at 635-37, 100 S.Ct. at 2388-90. We conclude the evidence does not provide the necessary support.
The federal district court in analyzing Williams’s lesser included offense argument first determined that lack of premeditation was an essential element of felony *929murder in Missouri. See 679 F.Supp. at 924-25. After reviewing the evidence in the case, the court concluded that “overwhelming evidence of premeditation was presented.” Id. at 924. Thus, the district court held the record did not support giving a felony murder instruction because “there was no evidence from which a reasonable jury could have concluded ... lack of premeditation was present.” Id.
The state trial court, however, had taken a different approach to Williams’s request for a felony murder instruction. The state court determined that under the evidence in this case no separate kidnapping occurred, and hence, no underlying felony was present to justify giving a felony murder instruction. We agree with the state court’s analysis.
Missouri law does not recognize as a separate offense an abduction that otherwise meets the elements of a kidnapping when the abduction is “merely incidental to another offense.” State v. Erby, 735 S.W.2d 148, 149 (Mo.Ct.App.1987); see, e.g., State v. Jackson, 703 S.W.2d 30, 32-33 (Mo.Ct.App.1985); State v. Jackson, 703 S.W.2d 23, 24-25 (Mo.Ct.App.1985); State v. Stewart, 615 S.W.2d 600, 602-04 (Mo.Ct.App.1981); State v. Johnson, 549 S.W.2d 627, 630-33 (Mo.Ct.App.1977); see also State v. Coleman, 660 S.W.2d 201, 209-10 (Mo.Ct.App.1983). In determining if the abduction is merely incidental for these purposes, the state trial court must consider whether the abduction substantially increased the risk of harm to the victim beyond the risk inherent in the principal crime. See, e.g., Erby, 735 S.W.2d at 149; Jackson, 703 S.W.2d at 31-33; Jackson, 703 S.W.2d at 24-25; Stewart, 615 S.W.2d at 604; Johnson, 549 S.W.2d at 631-33. Under these controlling legal principles, a victim who is marked for murder and transported to carry out the killing does not experience an “increased risk of harm or danger ... from the movement itself or from the potential of more serious criminal activity because of the remoteness ... of the area to which the victim is moved.” Jackson, 703 S.W.2d at 25. Thus, Missouri would not recognize an abduction that is part and parcel of a premeditated murder plan as a separate kidnapping offense.
The state trial court was aware of these critical principles of Missouri law and clearly appreciated their significance in Williams’s case. In refusing to give the kidnapping-based felony murder instruction requested by Williams, the trial court stated:
The [c]ourt ... does not feel ... there is evidence sufficient to submit on the felony murder theory. The ... only evidence ... is that [Williams], together with one John Morgan, set about with an intent and design to cause the death of the deceased in this case, Kerry Brum-mett.
The plan was ... that [Brummett] would be killed and his body thrown in the Missouri River.
The [c]ourt feels that the kidnapping that took place ... was merely one link in the chain of events that had been planned by [Williams] and John Morgan in committing the offense of murder.
Now, the [c]ourt feels ... there is no evidence to the contrary. [Thus,] ... there is no independent collateral felony to draw upon to create the crime of felony murder. And ... the kidnapping ... would just be one of the circumstances planned by the two conspirators to cause the death of Kerry Brummett.
State Trial Tr. at 613-14. Based on the evidence in this case, we agree with the state trial court that under controlling principles of Missouri law Williams’s conduct did not rise to the level of a separate kidnapping. Thus, the evidence did not establish a separate felony to support Williams’s requested felony murder instruction.
From the outset Brummett was slated to be killed. This was because Williams was bent on eliminating witnesses who might implicate him in the burglary of a doctor’s office. To this end, Williams had already murdered the unfortunate doctor. Brum-mett’s abduction and movement in the trunk of the car did nothing to intensify the risk he faced from the beginning. Instead, Brummett’s abduction was Williams’s chosen method to accomplish his plan to mur*930der Brummett and dispose of the body secretly.
Indeed, in Coleman’s prosecution for Brummett’s murder, Williams’s girlfriend claimed she was entitled to a felony murder instruction because Brummett’s abduction was a kidnapping. See Coleman, 660 S.W.2d at 208. The Missouri Court of Appeals recognized at once that “there [was] no evidence that Brummett was kidnapped ... within the meaning of the [kidnapping] statute.” Id. at 210. Instead, the court held the evidence showed “[Coleman], Morgan, and Williams planned the ‘luring’ of Brummett to a predetermined location for the express purpose of murdering him.... The transportation of Brummett without his consent was merely the physical means to complete the murder.” Id. We completely agree.
Because the evidence did not support Williams’s claim that Brummett’s abduction was a separate felony, the state trial court’s refusal to give the requested instruction on the lesser included offense of felony murder did not violate due process. See Hopper, 456 U.S. at 611, 102 S.Ct. at 2052-53; Beck, 447 U.S. at 637-38, 100 S.Ct. at 2389-90. Similarly, despite the Missouri Supreme Court’s arguably inconsistent application of its felony murder precedents on this point, supra at 928, Williams’s equal protection claim necessarily fails because the evidence presented in his case did not fall within the state law principles entitling him to the felony murder instruction in the first instance.
III. OTHER CRIMES EVIDENCE
Williams contends the trial court improperly admitted evidence of Williams’s involvement in burglarizing the doctor’s office, killing the doctor, and attempting to obtain controlled substances using forged prescriptions. Williams argues that because this evidence “bore only a tenuous relationship to the Brummett matter,” it should have been excluded. At a minimum, Williams argues the trial court should have given a limiting instruction to the jury on the evidence’s permissible uses, despite his counsel’s failure to request one, see 679 F.Supp. at 928. We disagree.
This evidence was highly relevant to show both Williams’s motive for the Brum-mett murder (witness elimination) and a common scheme or plan (to kill the doctor first, then Brummett). See id. at 927; 652 S.W.2d at 110. In light of all the other evidence at trial, we agree with the district court that admission of this evidence does not show the type of prejudice resulting in a fundamentally unfair trial. See 679 F.Supp. at 927. See also Mercer v. Armontrout, 844 F.2d 582, 586-87 (8th Cir.), cert. denied, 488 U.S. 900, 109 S.Ct. 249, 102 L.Ed.2d 238 (1988); Manning-El v. Wyrick, 738 F.2d 321, 323 (8th Cir.) (per curiam), cert. denied, 469 U.S. 919, 105 S.Ct. 298, 83 L.Ed.2d 233 (1984); Britton v. Rogers, 631 F.2d 572, 575 (8th Cir.1980), cert. denied, 451 U.S. 939, 101 S.Ct. 2021, 68 L.Ed.2d 327 (1981). In addition, we find no due process error in the trial court's failure to give a limiting instruction on its own motion. See Amos v. Minnesota, 849 F.2d 1070, 1073-74 (8th Cir.), cert. denied, 488 U.S. 861, 109 S.Ct. 159, 102 L.Ed.2d 130 (1988); Williams, 679 F.Supp. at 928.
IV. PROSECUTOR’S CONDUCT AND COUNSELS’ PERFORMANCE
Before discussing the issues considered in this part of our opinion, we note several principles concerning the state court proceedings in Williams’s case. The factual findings made by the state courts are presumptively correct. See Sumner v. Mata, 449 U.S. 539, 550, 101 S.Ct. 764, 770-71, 66 L.Ed.2d 722 (1981); Frank v. Brookhart, 877 F.2d 671, 674-75 (8th Cir.1989), cert. denied, — U.S. -, 110 S.Ct. 736, 107 L.Ed.2d 754 (1990); 28 U.S.C. § 2254(d) (1982). These findings are presumptively binding on determinations in federal habeas proceedings when they are fairly supported by evidence in the record. See Marshall v. Lonberger, 459 U.S. 422, 432, 435, 103 S.Ct. 843, 851, 74 L.Ed.2d 646 (1983); 28 U.S.C. § 2254(d). Williams bears the burden of establishing that these factual determinations are erroneous. Sumner, 449 U.S. at 550, 101 S.Ct. at 770-71; Frank, 877 F.2d at 675. After carefully examining the record, we believe all of the state court findings are adequately supported, and to the extent they apply to the *931claims Williams raises in this appeal, we adopt them.
We also note the district court occasionally took alternate or additional positions on Williams’s claims, including in some instances Williams’s procedural default. Williams, however, insists we are in a position to reach the merits of all of his contentions, and we have taken this opportunity to do so. Thus, we have not considered the district court’s alternate reasoning.
A. PROSECUTORIAL MISCONDUCT
Williams makes numerous claims that the prosecution failed to disclose requested, material evidence favorable to his case. See United States v. Bagley, 473 U.S. 667, 682, 105 S.Ct. 3375, 3383-84, 87 L.Ed.2d 481 (1985); Brady v. Maryland, 373 U.S. 83, 87, 83 S.Ct. 1194, 1196-97, 10 L.Ed.2d 215 (1963); Daniels v. Wood, 819 F.2d 195, 198 (8th Cir.), cert. denied, 484 U.S. 861, 108 S.Ct. 177, 98 L.Ed.2d 131 (1987). In addition, Williams claims the prosecution failed to advise the defense of the extent of Morgan’s immunity and allowed Morgan to testify falsely concerning that immunity. To promote continuity with the other proceedings since Williams’s trial, we refer to these claims by the names of the individuals involved.
1.Larry Pirner and Pamela Mealey
Pirner was the night manager at the restaurant where Coleman met Brum-mett on the night of the murder. Mealey asserts she was a customer in the restaurant that evening. At a hearing on Williams’s motion for new trial, Mealey testified she had given a report to law enforcement authorities that she saw Brummett at the restaurant on the night he was killed, but that he left with a woman who was not Coleman. After Williams’s trial, Pirner also testified that police had interviewed him, and he gave them a report similar to Mealey’s.
On direct appeal, the Missouri Supreme Court adopted the state trial court’s determination that there was no credible evidence showing Mealey actually made the report. See 652 S.W.2d at 116-17; 712 S.W.2d at 408; see also 679 F.Supp. at 934. The state trial court also found there was no credible evidence Pirner made any report to authorities. See 679 F.Supp. at 933. The district court thus held that Williams “failed to establish the first prong of the Brady test ... because the state cannot suppress evidence ... it does not possess.” Id. We agree.
2.Debbi Salmons
Williams contends Salmons convinced his lawyers not to call Robert Day as a defense witness. Williams’s lawyers had considered calling Day to testify that Day had gone to Williams’s home to borrow money on the night Brummett was murdered. This testimony might have corroborated Williams’s contention that he spent the night at home with another of his girl friends. According to Williams, Salmons made a statement to authorities that Day was confused about the date of the loan transaction and that the prosecution withheld this statement from Williams.
The district court correctly determined Williams had failed to show Salmons’s statement would have been helpful because both she and Day were uncertain about the critical times and dates. See id. at 938-39. Williams nevertheless argues the defense would have called Day as a witness had it known of Salmons’s statement. As we point out later, however, assuming Day testified accurately about the date he saw Williams, that testimony would not have been helpful to Williams’s defense. See infra at 933. Under these circumstances, we do not believe Williams has shown the prosecution withheld evidence that was either favorable or material to Williams’s case. See Bagley, 473 U.S. at 674-75, 682, 105 S.Ct. at 3383-84; Brady, 373 U.S. at 87-88, 83 S.Ct. at 1196-97.
3.Barbara Rea
Rea, who was Coleman’s roommate, loaned her car to Coleman for the fatal rendezvous with Brummett. Williams claims the prosecution knew police had coerced Rea’s testimony by threatening to take her child from her and had failed to disclose the existence of this coercion. The district court, however, adopted the state *932court’s finding that Williams had not shown Rea testified under threat of any kind. See 679 F.Supp. at 937; 712 S.W.2d at 409. In addition, the district court determined Williams had not established the prosecution knew of the threat even if it existed and that had any coercion been disclosed, it would not have altered the trial’s result. See 679 F.Supp. at 937. We find nothing in the record to contradict these determinations, and thus, Williams’s argument on this point is without merit.
4. John Morgan
Williams asserts the prosecution failed to disclose that the immunity Morgan received in exchange for his testimony was not as broad as the defense had been led to believe it was. Williams also contends the prosecution allowed Morgan to testify falsely that the broader immunity was in place.
The district court aptly observed that Williams was not prejudiced by Morgan’s testimony about his overstated immunity because, if anything, it opened Morgan to wider attack on cross-examination by making him appear to have a greater reward for testifying against Williams. See id. at 933. We are convinced by the district court’s reasoning that any miscommunication regarding Morgan’s immunity did not prejudice Williams and would not have affected the outcome of his trial. See United States v. Foster, 874 F.2d 491, 494-95 (8th Cir.1988). Furthermore, the crux of Williams’s argument is that the prosecution in his case did not have authority under Missouri law to grant Morgan immunity from prosecution for offenses committed in other counties. See 679 F.Supp. at 932. This argument has already been considered and rejected in Williams’s prosecution for murdering the doctor. See Williams, 877 F.2d at 1383 & n. 2.
B. INEFFECTIVE ASSISTANCE OF COUNSEL
A public defender represented Williams throughout the course of the state prosecution. In addition, Williams’s family retained private counsel who entered the case approximately one month before trial. The two lawyers worked together on the case and hired two investigators to assist them. Williams asserts numerous instances of ineffective assistance by these counsel. Bearing in mind the general controlling standards for these types of claims, see Strickland v. Washington, 466 U.S. 668, 687-88, 691, 694, 104 S.Ct. 2052, 2064-65, 2066-67, 2068 (1984); Laws v. Armontrout, 863 F.2d 1377, 1381-82, 1386, 1389-94 (8th Cir.1988) (en banc), cert. denied, — U.S. -, 109 S.Ct. 1944, 104 L.Ed.2d 415 (1989), we examine each claim in turn.
1. Pretrial Investigation
Williams first argues his trial counsel should have discovered three potentially favorable witnesses who provided evidence after the trial concerning Brummett’s murder. These witnesses are: (1) Larry Pir-ner; (2) Pamela Mealey; and (3) Jesse Maxwell.
Pirner, the night restaurant manager, fled the state in February 1981 to avoid arrest on criminal charges. The district court, relying on the state trial court’s findings, found that after Williams’s attorneys entered the case, both they and their investigators went to the restaurant seeking to discover information about the night of the murder. See 679 F.Supp. at 943. They were told Pirner no longer worked there and that no one knew how to contact him. See id. at 943; see also 712 S.W.2d at 407-08. In addition, the district court determined “ ‘defense counsel had no reason to believe from the facts in their possession that Pirner had any information [that] was helpful or favorable to the defense.’ ” 679 F.Supp. at 943 (quoted citation omitted). Thus, when authorities eventually apprehended Pirner and extradited him from California to Missouri later in 1981, Pir-ner’s return was of no significance to the case.
Williams contends his lawyers should nonetheless have attempted to locate Pir-ner by using restaurant records to contact Pirner’s parents. Williams, however, did not show Pirner’s parents knew where he *933was or that they would have revealed that information to Williams’s attorneys in view of Pirner’s fugitive status. In the case of a fugitive of unknown whereabouts with no known useful information, we agree with the district court that Williams’s counsel conducted a reasonable investigation regarding Pirner.
Mealey did not work at the restaurant, but was merely a customer. Although Williams did not tell his lawyers Mealey was at the restaurant that night, he contends they “should have found her in time to use her at trial.” When Williams’s lawyers and investigators went to the restaurant, however, Mealey’s name was not mentioned as a customer. At his postcon-viction hearing, Williams testified he gave his lawyers the names and addresses of people he “associated with almost on a daily basis,” including Mealey, Nina Potts, and other acquaintances. This list was to aid Williams in accounting for his activities on the night of October 9 and the early morning of October 10 and to identify people who might be called as alibi witnesses. According to Williams, he told his lawyers to contact these people.
From the lawyers’ perspective, the difficulty with Williams's alibi defense was that Williams gave them five possible alibis. See 712 S.W.2d at 406. Eventually, Williams told his lawyers “his alibi would be that he was in bed with his girl friend Nina Potts.” Id. Once Williams established Potts as the basis for his alibi, there was no reason for the lawyers to contact Mealey as a crucial alibi witness. See United States v. Cockrell, 720 F.2d 1423, 1428 (5th Cir.1983) (“failure to investigate everyone whose name happens to be mentioned by [a] defendant does not suggest ineffective assistance”). In these circumstances, we agree with the Missouri Court of Appeals that “[t]here is no basis shown to indicate ineffectiveness concerning the discovery or production of Mealey.” 712 S.W.2d at 408.
According to Williams, Maxwell would have been able to testify that he saw Morgan at a bait and tackle shop in the early morning hours on the date Brummett was murdered. At Williams’s postconviction hearing, however, Maxwell testified “he could not remember if he had seen Morgan at 1:00 a.m. on October 9 or October 10.” . Id. In addition, there was no evidence of .how Williams’s lawyers could have been expected to discover Maxwell’s identity because he did not come forward until ten months after Williams was convicted. See 679 F.Supp. at 944. Further, Maxwell had not mentioned the asserted encounter with Morgan during his interview with the prosecutor before Williams’s trial. See id.; 712 S.W.2d at 408. We agree with the district court that “[u]nder these circumstances, Williams has not established that counsel’s investigation was professionally unreasonable.” 679 F.Supp. at 944.
2. Trial Performance
Williams’s claims of ineffective assistance related to his trial fall into three categories, which wé discuss in turn.
a. Witness Selection
Williams claims his lawyers should have called Roger Hazlett and Robert Day as defense witnesses.' According to Morgan’s testimony, he and Williams' went to Hazlett’s house after the murder and burned their bloody clothing in the front yard. The state postconviction court found Hazlett told Williams’s lawyer that he was drunk that night and did not remember anything. See 712 S.W.2d at 408. The district court found Williams’s lawyer made a reasonable decision not to call Haz-lett after determining he had no solid recollection of the events and no other useful information. See 679 F.Supp. at 947. We agree.
Day’s recollection of the date and circumstances regarding his borrowing money from Williams was unsure. In addition, even his best version failed “to demonstrate how it would have been impossible for [Williams] to have been at home at 9:30 p.m. and still have been involved in a murder that occurred [around 1:45 a.m.] just a short distance away.” 712 S.W.2d at 408; see also 679 F.Supp. at 947.
*934Decisions relating to witness selection are normally left to counsel’s judgment, and' “this judgment will not be' second-guessed by hindsight.” See Frank, 877 F.2d at 674. In this situation, we observe no inadequate performance by Williams’s attorneys in failing to call either Hazlett or Day as witnesses.
b. Witness Cross-Examination
As we discussed earlier, Williams’s accomplice, Morgan, testified against Williams under a grant of immunity. Williams claims his lawyers did not fully discredit Morgan’s testimony by further probing into the extent of this immunity. In addition, Williams claims his counsel should have more vigorously cross-examined Morgan about his prior inconsistent statements to police. On postconviction review, the Missouri Court of Appeals determined these matters were fully put before the jury to determine Morgan’s credibility. See 712 S.W.2d at 409; see also 679 F.Supp. at 945.
Similarly, Williams asserts his counsel did not properly cross-examine Kay Lepley about her immunity to testify. Williams believes this cross-examination would have undermined Lepley’s testimony that she had seen Williams with a pair of handcuffs five days before the murder. We disagree. Lepley testified she had no immunity. See 679 F.Supp. at 945; 652 S.W.2d at 111; 712 S.W.2d at 409. In any event, her testimony concerning the handcuffs was cumulative. See 679 F.Supp. at 935; 712 S.W.2d at 409. We find no shortcomings of a constitutional dimension in the cross-examination of Morgan or Lepley.
c. Jury Instructions
Williams also contends his lawyers should have requested a limiting instruction on the other crimes evidence, see supra at 930, and a cautionary instruction on Morgan’s credibility as an accomplice and a drug addict. We agree that the decision not to request the first instruction was a reasonable, strategic choice designed to avoid highlighting Williams’s other undesirable activities. See 679 F.Supp. at 945; 712 S.W.2d at 407. Concerning the credibility instruction, both the district court and the state trial court held the jury received the only instruction permitted under Missouri law. See 679 F.Supp. at 946; 712 S.W.2d at 407. Furthermore, any errors in state law instructions must have fundamentally infected the fairness of Williams’s trial in order to justify federal habeas corpus relief. See Berrisford v. Wood, 826 F.2d 747, 752 (8th Cir.1987), cert. denied, 484 U.S. 1016, 108 S.Ct. 722, 98 L.Ed.2d 671 (1988). Thus, we find no error regarding counsel’s decision not to request these instructions.
3. Cumulative Effect of Counsel’s Errors
We have found no ineffective assistance by Williams’s lawyers in any of the pretrial investigation or trial performance matters raised in this appeal. We agree with the Missouri Court of Appeals that “Williams was represented by two experienced lawyers who spent many hours in preparation for trial and who had the assistance of two investigators.... [These lawyers] gave Williams effective representation and did all any attorney could have done to insure that all of Williams’[s] constitutional rights ... were protected.” 712 S.W.2d at 411. Thus, we necessarily reject Williams’s additional argument that the cumulative effect of these asserted errors amounted to ineffective assistance. See 679 F.Supp. at 949; 712 S.W.2d at 410-11.
V. SUFFICIENCY OF EVIDENCE AND CAPITAL MURDER INSTRUCTION
Finally, Williams contends there was insufficient evidence to support his conviction. Williams’s sufficiency argument is closely tied to his attack on the jury instruction containing the elements of capital murder. The jury was instructed that in order to convict Williams it was required to find, among other things, that he had “caused the death of Kerry Brummett by beating him and drowning him.” Williams contends this instruction was flawed because: (1) the medical evidence showed Brummett drowned, and there was no evidence to support a finding that he died from the beating; and (2) the applicable capital murder statute required the jury to find Williams caused Brummett’s killing and, thus, the trial court lowered the standard of proof required for conviction when it instructed the jury it had to find Williams caused Brummett’s death.
The Missouri Supreme Court has rejected Williams’s first argument in an analogous context involving an instruction that referred to death by striking and suffocating. See Daugherty, 631 S.W.2d at 639-41; see also Williams, 652 S.W.2d at 114-15. In Daugherty, the court held that even when “the medical expert’s opinion *935included suffocation and hemorrhage as causes of death[,] [that] does not invalidate other aspects of the attack as a contributing factor.” 631 S.W.2d at 640. In view of this holding and our agreement with the state court that “[t]here was ample evidence at trial showing ... [Brummett] was beaten, handcuffed[,] and drowned,” 652 S.W.2d at 114, Williams’s first contention is without merit, see 679 F.Supp. at 928-29.
Williams’s further attempt to draw significance from a difference between “causing Brummett’s killing” and “causing his death” amounts to little more than a play on words. Standard dictionaries equate the two. See Webster’s Third New International Dictionary 1242 (1981). We agree with the district court that this difference, if any, did not fundamentally misdirect the jury in violation of due process. See 679 F.Supp. at 928; see also Berrisford, 826 F.2d at 752. We also agree with each of the courts to consider Williams’s cause thus far that the record contains more than ample evidence for a rational jury to find Williams guilty of capital murder beyond a reasonable doubt. See Jackson v. Virginia, 443 U.S. 307, 319, 99 S.Ct. 2781, 2789, 61 L.Ed.2d 560 (1979); see also 679 F.Supp. at 928-29; 652 S.W.2d at 115; 712 S.W.2d at 410. As the Missouri Supreme Court observed, “[t]he fact ... [Brummett] ran into the river to escape his attackers does not alter [Williams’s] liability for the death.” 652 S.W.2d at 112.
VI. CONCLUSION
We have examined the record and applicable legal principles with great care. Having done so, we find no error warranting habeas corpus relief. Accordingly, we affirm the district court’s denial of Williams’s petition.