John Robert Ellis appeals from the denial of his petition for writ of habeas corpus under 28 U.S.C. § 2254 (1976). He had been convicted of manslaughter in violation of Neb.Rev.Stat. § 28-403 (Reissue 1975). On appeal he reasserts each of the grounds argued before the district court:1 (1) that there was insufficient evidence to support a finding of guilt beyond a reasonable doubt, (2) that the cross-examination of a key witness was unduly restricted when the witness asserted a privilege against self-incrimination, (3) that the admission of evidence of other crimes, wrongs or bad acts committed by Ellis was improper, (4) that questions asked and arguments made by the prosecutor were inflammatory, and (5) that the cumulative effect of these errors requires reversal. All of these contentions were considered and rejected in the painstakingly detailed opinion of the district court, and we affirm.
Deborah Forycki, a University of Nebraska student, disappeared on October 3, 1974. She was last seen around 11:00 a.m. on her way to meet a friend for lunch. Skeletal remains, which were identified as hers, were found in an antique water wagon in a rural area near Elmwood, Nebraska, on September 13, 1978. Ellis was subsequently arrested and charged with first-degree murder in connection with her death. His trial lasted nearly three weeks. The jury acquitted Ellis of first-degree and second-degree murder but convicted him of manslaughter. The Nebraska Supreme Court affirmed the conviction, State v. Ellis, 208 Neb. 379, 303 N.W.2d 741 (1981), and because the testimony is thoroughly set forth in that opinion, we limit our discussion to those facts that are particularly material to the points raised on this appeal.
I.
We first consider the sufficiency of the evidence to sustain the manslaughter conviction. Under Nebraska law* a person commits manslaughter if he “kill[s] another without malice ... unintentionally, while ... in the commission of some unlawful act.” Neb.Rev.Stat. § 28-403 (Reissue 1975).2 The Supreme Court set forth the standard governing evidentiary sufficiency in Jackson v. Virginia, 443 U.S. 307, 324, 99 S.Ct. 2781, 2791-92, 61 L.Ed.2d 560 (1979):
[T]he applicant is entitled to habeas corpus relief if it is found that upon the record evidence adduced at the trial ho rational trier of fact could have found proof of guilt beyond a reasonable doubt.
We first applied this standard in Davis v. Campbell, 608 F.2d 317, 319-20 (8th Cir. 1979). In Lenza v. Wyrick, 665 F.2d 804, 812 (8th Cir.1981), we specifically applied it in a circumstantial evidence case, and observed that circumstantial evidence is to be. treated no differently than direct evidence.. Indeed, Jackson itself involved circumstantial evidence. 443 U.S. at 324-25, 99 S.Ct. at 2791-92. We further observed that to establish guilt such evidence need not be conclusive nor prove an absolute impossibility of innocence, and that we must consider the evidence in the light most favorable to the government. Lenza, 665 F.2d at 812.
The Supreme Court in Jackson also made clear that a state appellate decision as to the sufficiency of the evidence is entitled to deference. 443 U.S. at 323, 99 S.Ct. at 2791. In this case, both the Supreme Court of Nebraska and the district court, which expressly applied the Jackson standard, concluded that the evidence was sufficient to support the conviction. Upon reviewing the record, we conclude, in agreement with the district court, that under Jackson a rational trier of fact could have found proof of guilt beyond a reasonable doubt.
The skeleton was found in the water wagon, which was some ten feet long by three feet wide, lying on its back with the *653left arm along the side, the right hand at approximately where the right ear would be and the head turned slightly to the right. It was beneath three logs — each five feet long and four inches in diameter and apparently sawed at the ends — as well as two or three sticks four inches in diameter and a number of other sticks two inches in diameter. Wedged tightly in the water wagon’s opening, which measured two feet by two and a half feet, was a roll of woven wire fencing. No jewelry, fasteners, zippers, clasps, buckles or shoes were found in the water wagon. The skeleton showed no signs of trauma or force to fracture the bones, but according to a forensic scientist, the right thumb bone and right radius at the wrist end had defects consistent with being formed by a bullet. An anthropologist disputed this, and in any event the county coroner’s physician testified that such a wound would not be mortal. The water wagon had what were identified as bullet holes in its sides and a bullet was found under the skeleton at about where the kidney would have been.
Forycki had told friends that she was to meet a man for lunch at 11:30 a.m. and then be at work at 1:00 p.m. She was last seen leaving her apartment and walking toward the downtown area around 11:00 a.m. After her disappearance the police found among her possessions a note which read, “Meet John Kondowski 10:30 at the Student Union.” Investigation failed to reveal the existence of a person with such a name in Lincoln.
Another young woman testified that in October of 1974 — about two weeks after Forycki disappeared — she had met a man using the name “John Tronzowski”, a name that was also not confirmed by investigators to be that of an existing person. She identified Ellis in the courtroom as this person. She stated that Ellis had arranged a date with her, cancelled it, and rescheduled it for a breakfast date. When she met him he was vague about where they were going, and he said that a friend had offered the use of his house where they could cook ham and eggs. This house in fact turned out to be rented by Ellis. At the house, he made sexual advances toward the young woman, who resisted them. He then grabbed and held her arm behind her back, held a butcher knife near her throat, and stuffed a handkerchief into her mouth. The handkerchief fell out and she managed to break loose. Although he threatened to break her arm if she screamed, she did scream and was eventually able to leave the house. The police were informed of the incident, but no charges were filed.
A second young woman testified about another incident involving Ellis that occurred two years later. On June 10, 1976, he called her and made a date for dinner at a restaurant that evening. After some discussion and another phone call involving changes of their meeting place, he told her that they would be going to a barbecue at a friend’s house in a rural area near Elm-wood instead. When he picked her up, she noticed that he had a hand-drawn map of the location with him. As they were driving near Elmwood, Ellis suddenly turned into a farm road screened by high weeds and trees. The car stopped, she felt a knife at her neck and Ellis grabbed her hair, pulling it tightly. He also tried to grab her left arm and pull it behind her. She struggled free and grabbed the blade of the knife. After somewhat calmer discussion, Ellis dropped the knife outside the car. When the woman suggested that they drive on to Elmwood, however, Ellis flew into a rage, again grabbed the top of her hair, clutched her arm and forced it behind her neck, forced her down on her knees to the floor of the car and tied her arms behind her back. He attempted to place masking tape over her mouth, but she screamed, which seemed to cause Ellis to change his mind and free her. The assault occurred within seventy-five feet of the location of the water wagon where the Forycki remains were found. Ellis was convicted and served time for this assault.
This witness testified on both direct and cross-examination that at the time of this assault Ellis stated that he knew he was sick, that he wanted to see a psychiatrist and that while in California he was in a *654group “that was in to inflicting pain on other people.” He said that he had enjoyed this. On cross-examination, she admitted that according to her prior deposition testimony, Ellis had said that he had experienced sex bondage or sadism or masochism and had probably said that he wanted to do it with her. She also testified on cross-examination that she had not believed all that he was telling her, that she thought he was play acting, but that her statement to this effect brought an angry response.
Ellis had driven his wife’s ear on this occasion. A later investigation of the car revealed the presence of certain hairs exhibiting the same characteristics as the hair of Deborah Porycki. There was testimony, however, that the hair could have come from a daughter of Ellis’ wife by a prior marriage.
A cellmate of Ellis’ during his incarceration for the 1976 assault testified that Ellis had described the rural area near Elmwood and had said that “if you ever kill somebody and wanted to hide the body, that would be a really good place to do it, that the police would never find it.” Ellis also told the cellmate that he had found a secluded place outside Elmwood to which he had taken persons from the college on occasion.
University records established that in the spring of 1974 Ellis and Forycki had classes which met the same three days of the week on the same floor of the same building and at the same time of day. The classrooms were about sixty to seventy feet apart. In the fall of 1974 the two had classes three days a week in the same building at the same time although on different floors. Ellis was listed as absent from his afternoon class on Thursday, October 3, 1974, the day Forycki disappeared. Evidence showed that Ellis had access to his wife’s car on Thursdays.
During interrogation just before his arrest, Ellis asked the police officers for an opportunity to meditate after he was told they wished to discuss the death of Deborah Forycki. After approximately twenty minutes they asked him about her death and whether he was present when she died. He stated that he could not do anything that brutal. At that time, though, nothing had been said concerning the discovery of her skeleton. When the officers told him they knew of the two incidents involving the other young women, he stated that he was “beginning a new life” and that he was putting that part of his life out of his mind and “would not remember that portion of his life.” When asked whether, if he had killed someone, he could put that out of his mind, he replied, “I think so.” Another officer, who interviewed Ellis separately, testified that Ellis did not respond to him when twice accused of Forycki’s slaying, but on the third time, Ellis replied that “he had put that part of his life out of his mind.”
The jury heard testimony that Deborah Forycki was an organized and very neat person. Testimony concerning her emotional state was inconsistent. While there was testimony that she was depressed in September, 1974, and could have committed suicide, there was also testimony that she was not suicidal and was functioning normally although she was having transient problems.
The district court reached the following conclusions concerning all of the evidence:
In examining the record in this case, I find adequate evidence under the Jackson standard. Ellis was portrayed as using a fairly consistent method of meeting young women and demanding certain conduct of them. He had a practice of making and altering engagements to lure the women to a place he had selected____ Ellis was shown to have a familiarity, complete to the extent that he had a map, of the very area where the remains of Deborah Forycki were hidden____ The name on the note found in Ms. Forycki’s possessions closely resembles a name used by Ellis when communicating to one of the witnesses____
Ellis was shown to have violent tendencies that could have reslted [sic] in the death of Deborah Forycki____
*655Ellis was also shown to have had the opportunity to commit the crime on the day Forycki disappeared____ As a final note, it should be remembered that Ellis stated to a fellow inmate at the Cass County jail that the exact place where Forycki’s remains were hidden was a good place to hide a body because no one would find it there.
While the evidence may not be overwhelming, I cannot say that a rational trier of fact could not find beyond a reasonable doubt that Ellis committed the crime. At each step of the process in the evidence, circumstance after circumstance eliminates others than the petitioner. The evidence points clearly to him as the one who committed the crime.
It is entirely consistent with the accounts of Ellis’ previous behavior with the two witnesses who testified at trial to find that the death of Forycki was unintentional while Ellis was in the commission of some unlawful act. There is, therefore, sufficient evidence under the Jackson standard.
Our careful review of the record leads us to conclude that the district court properly determined that the Jackson standard was satisfied and that there was sufficient evidence to sustain the conviction.
II.
Ellis argues that the district court, in limiting his cross-examination of the witness to the 1976 assault near the water wagon, violated his sixth amendment right to confront and cross-examine the witness. At trial Ellis had attempted to cross-examine this witness with respect to her sexual relationship with him in 1974. The witness, though, asserted a privilege against self-incrimination under both the fifth amendment and Neb.Rev.Stat. § 25-1210 (Reissue 1979), which provides that a witness is not compelled to answer “[wjhen the matter sought to be elicited would tend to render the witness criminally liable, or to expose him to public ignominy____” At the time of this earlier relationship the witness was married to another man, and adultery is a crime under Nebraska law. Neb.Rev.Stat. § 28-704 (Reissue 1979). The trial court refused to allow the cross-examination into the past sexual conduct between the witness and Ellis, saying that it was irrelevant, but did allow the introduction of other testimony that they had dated about five times over a period of a month and that she had answered Ellis’ advertisement seeking a roommate. The court admitted her cross-examination testimony as to their discussions concerning infliction of pain, sex bondage, sadism, and masochism; his stated desire to do these acts with her; and her perception that he was play acting. The district court concluded:
Under this standard, I believe that the state trial judge artfully and adequately balanced Ellis’ Sixth Amendment right to confrontation against the witness’ assertion of her Fifth Amendment and state statutory privilege against self-incrimination. By allowing questioning concerning the witness’ relationship with Ellis, short of inquiry into sex acts, the trial judge allowed the jury to have before it evidence it needed to assess the significance and meaning of the asserted attack near Elmwood and to understand the meaning of Ellis’ comment about inflicting pain on people. No cross-examination as to the witness’ pre-1974 sexual activities with Ellis was sought as bearing on the witness’ credibility, and evidence of such pre-1974 sexual activities was appropriately deemed by the trial judge to be irrelevant to any other issue. Ellis’ apparent meaning in making a statement about inflicting pain was adequately elicited on cross-examination as relating to sex bondage, sadism, or masochism, which evidently was the goal of defense counsel. Embellishing that with exploration of sexual relationships some two years previously between Ellis and the witness was not of such probative value that its absence amounts to a denial of a constitutional right of confrontation.
Ellis argues that Davis v. Alaska, 415 U.S. 308, 94 S.Ct. 1105, 39 L.Ed.2d, 347 *656(1974), does not permit such a balancing and mandates reversal. In Davis, the trial court limited cross-examination of a prosecution witness as to that witness’ probation under juvenile delinquency laws. The Supreme Court held that this limitation violated the defendant’s right to cross-examination under the sixth amendment confrontation clause. In so holding the Court, quoting its earlier decision in Alford v. United States, 282 U.S. 687, 693, 51 S.Ct. 218, 220, 75 L.Ed. 624 (1931), declared
“[N]o obligation is imposed on the court, such as that suggested below, to protect a witness from being discredited on cross-examination, short of an attempted invasion of his constitutional protection from self incrimination, properly invoked. There is a duty to protect him from questions which go beyond the bounds of proper cross-examination merely to harass, annoy or humiliate him.”
Davis, 415 U.S. at 320, 94 S.Ct. at 1112 (emphasis supplied) (citation omitted).
Unlike the situation in Davis, here the cross-examination on past sexual conduct would have required the witness to subject herself to criminal prosecution. In Davis, the Court’s recognition of a trial court’s duty to protect a witness from “an attempted invasion of his constitutional protection from self-incrimination, properly invoked,” clearly mandates that a court balance the witness’ fifth amendment privilege on one hand against the defendant’s sixth amendment right to cross-examine on the other. See United States v. Nunez, 668 F.2d 1116, 1121-23 (10th Cir.1981); United States v. Seifert, 648 F.2d 557, 562-63 (9th Cir.1980). We recognized the necessity for such balancing in United States v. Humphrey, 696 F.2d 72, 75 (8th Cir.1982), cert. denied, 459 U.S. 1222, 103 S.Ct. 1230, 75 L.Ed.2d 463 (1983), and United States v. Gould, 536 F.2d 216, 222 (8th Cir.1976). Thus, where the witness’ invocation of the fifth amendment privilege precludes the defendant from inquiring merely as to collateral matters such as credibility, as opposed to substantive matters about which the witness testified on direct examination, the defendant’s sixth amendment right is not violated. Humphrey, 696 F.2d at 75; Nunez, 668 F.2d at 1122; Gould, 536 F.2d at 222. A critical inquiry is whether the witness’ invocation of the testimonial privilege materially prejudices the defendant, United States v. Diecidue, 603 F.2d 535, 552 (5th Cir.1979), cert. denied, 445 U.S. 946, 100 S.Ct. 1345, 63 L.Ed.2d 781, 446 U.S. 912, 100 S.Ct. 1842, 64 L.Ed.2d 266 (1980); see Humphrey, 696 F.2d at 75. Thus, if the defendant has effective alternative means of exploring relevant matters on cross-examination, there is no sixth amendment violation. Nunez, 668 F.2d at 1123; Seifert, 648 F.2d at 563.
Here the witness was cross-examined concerning her testimony on direct examination. As the district court concluded, cross-examination was allowed in sufficient detail to demonstrate the relationship between Ellis and the witness and to illuminate the issues of substance and credibility before the jury; the failure to allow cross-examination on their sexual relationship did not violate the principles set forth in Davis. We conclude that the district court in its careful analysis of this issue did not err.
III.
Ellis claims that testimony from the two young women concerning the other incidents involving Ellis deprived him of a fundamentally fair trial, unconstitutionally deprived him of his presumption of innocence and prejudiced his right to due process of law. He points out that the Supreme Court of Nebraska was closely divided, four to three, on the admissibility of this evidence.
Neb.Rev.Stat. § 27-404(2) (Reissue 1979) permits evidence of other crimes, wrongs or acts “as proof of motive, opportunity, intent, preparation, plan, knowledge, identity, or absence of mistake or accident.” It is essentially identical to Federal Rule of Evidence 404(b). The Supreme Court of Nebraska stated: “The evidence was introduced, it would seem, to prove the identity of the assailant of Miss Forycki, *657knowledge by the defendant of the scheduled area where the victim’s body was found, and plan or schemes or modus operandi.”
In addition, such evidence must meet the standard we set forth in Maggitt v. Wyrick, 533 F.2d 383, 385 (8th Cir.), cert. denied, 429 U.S. 898, 97 S.Ct. 264, 50 L.Ed.2d 183 (1976):
In order to establish a denial of due process the petitioner must prove that the asserted error was so “gross”, Taylor v. Minnesota, supra [466 F.2d 1119] at 1121 [8th Cir.1972], “conspicuously prejudicial”, United States ex rel. Cannon v. Maroney, 373 F.2d 908, 910 (3d Cir.1967), or otherwise of such magnitude that it fatally infected the trial and failed to afford petitioner the fundamental fairness which is the essence of due process. Lisenba v. California, 314 U.S. 219, 236, 62 S.Ct. 280, 289, 86 L.Ed. 166, 179 (1941). In making this determination courts must review the totality of the facts in the ease pending before them and analyze the fairness of the particular trial under consideration.
As the district court observed, the testimony of the two witnesses was crucial to the prosecution of the case, establishing a discernible pattern and tying Ellis to the very location where the Forycki remains were found. We agree with the district court that the totality of the events may have been critically harmful to Ellis but that the admission of these acts could not be characterized as gross or conspicuously prejudicial or of such magnitude as to deprive him of fundamental fairness. States traditionally have been afforded substantial latitude in fashioning their own rules of evidence. Maggitt, 533 F.2d at 385. In Hogan v. State of Nebraska, 535 F.2d 458, 460 (8th Cir.1976), we expressed similar thoughts and observed that only where the trial errors or irregularities infringe upon a specific constitutional protection or are so prejudicial as to amount to denial of due process that a justiciable federal issue is presented in a habeas corpus proceeding.
The Supreme Court of Nebraska gave careful consideration to the admission of this evidence and pointed to the strong competing interests at play as well as the substantial discretion of the trial judge. The Nebraska Supreme Court concluded:
Nevertheless, as stated in 70 Yale L.J. 763, 773 (1961): “[W]here the highly prejudicial evidence also has great probative worth and plays a crucial role in the prosecutor’s case, exclusion of the evidence may destroy his case and result in an unjustified acquittal.” In this instance, we cannot say that the trial court abused its discretion when it determined that the probative value of the evidence of other crimes in the facts and circumstances of this ease was not outweighed by the prejudicial effect. The evidence was properly received.
208 Neb. at 393-94, 303 N.W.2d 741.
We cannot conclude that the district court erred in its ruling that there was no constitutional error in the admission of this evidence.
IV.
Ellis argues that instances of inflammatory prosecutorial misconduct in the examination of witnesses and in comments to the jury amounted to constitutional error. We must determine whether such conduct deprived Ellis of due process under the Maggitt standard, supra. The first instance involved a question posed to Dr. McWilliams, a prosecution witness who had testified that it would have been difficult to place the body in the tank through the hatch and extend the arms and legs and that the position of the body was not inconsistent with the individual having crawled into the water tank and assumed that position. The prosecutor then asked him: “And of course, you are not trying to say what might have caused somebody to crawl into a tank such as having a gun pointed at them.” An objection was sustained with the comment, “That was a very bad question.”
In closing argument the prosecutor commented about the necessity to prove *658every element, a comment that defendant argues was improper because it suggested that by vigorously defending himself, Ellis was admitting guilt. The prosecutor also commented about a little “noose” formed by a piece of copper found with the skeleton, a characterization unsupported by evidence. Finally, the prosecutor lauded the marvelous work of the very fine police department. As we observed in Rhodes v. Foster, 682 F.2d 711, 714 (8th Cir.1982), a prosecutorial irregularities can only be challenged in federal habeas corpus proceedings if they rise to the status of a constitutional violation or deprive the defendant of due process under the Maggitt standard. The district court carefully considered each of these arguments under the Maggitt standard. We agree with its conclusion that in each of these respects sufficient prejudice could not be found under that standard.
Our review of the record discloses that this was a trial of nearly three weeks and from beginning to the end, it was hard fought with many rulings of the trial court unfavorable both to the state and to the defendant. These claimed errors have been discussed in detail by the Supreme Court of Nebraska and in the district court’s painstaking analysis. We have nothing further to add to the district court’s opinion with respect to these issues; the rulings of the district court that these were not errors of constitutional dimension were correct and should be affirmed.
We have carefully reviewed the record and have addressed and rejected each of Ellis’ contentions individually. Furthermore, we cannot say that viewed in the aggregate his claims establish constitutional error so as to justify reversal. We affirm the denial of the writ.
. The Honorable Warren K.’ Urbom, Chief Judge, United States District Court for the District of Nebraska.
. Section 28-403 has subsequently been recodified as Neb.Rev.Stat. § 28-305 (Reissue 1979). Its provisions remain essentially unchanged.