
807 P.2d 1379 (1991)
Stanley Wayne BROWN, Appellant,
v.
The STATE of Nevada, Respondent.
No. 21004.
Supreme Court of Nevada.
March 28, 1991.
*1380 Hager & Mausert, Reno, for appellant.
Frankie Sue Del Papa, Atty. Gen., Carson City, Kevin Pasquale, Dist. Atty., Paul Drakulich, and Robert V. Bogan, Deputy Dist. Attys., Fallon, for respondent.

OPINION
STEFFEN, Justice:
Appellant Stanley Wayne Brown was convicted by a jury of two counts of sexual assault and one count of attempted sexual assault. By amended judgment, he was consecutively sentenced to two life terms on the sexual assault counts and a ten-year term on the attempt count. As a result of Brown's first direct appeal to this court, we issued an Order of Remand on September 6, 1989 which vacated Brown's judgment of conviction and directed the district court to hold a hearing pursuant to Miller v. State, 105 Nev. 497, 779 P.2d 87 (1989). After holding the Miller hearing, the district court reinstated the jury verdict, an option accorded the court under our Order of Remand. Our review of the record persuades us that the district court was correct in its rulings concerning the Miller hearing. We therefore affirm the district court's reinstatement of the amended judgment.
During Brown's trial, the seventeen-year-old complaining witness testified that her uncle, Brown, repeatedly assaulted her sexually over an eight-year period. Several defense witnesses testified that the victim was a habitual liar, but the trial judge excluded testimony concerning the nature of her alleged falsehoods on the ground that it constituted allegations of sexual conduct. In the first appeal, this court was concerned that the result below may have been unreliable and that Brown may have been denied a fair trial. Moreover, after Brown's convictions, this court decided Millera decision that had direct application to the proceedings in the instant case.
Under Miller, we concluded that evidence of false accusations of prior sexual abuse or assaults attributable to a complaining witness do not constitute "previous sexual conduct" for purposes of Nevada's rape shield law, NRS 50.090. Miller, 105 Nev. at 501, 779 P.2d at 89. We also determined that complaining witnesses would be subject to cross-examination concerning such prior false accusations providing defendants were able to prove by a preponderance of the evidence, in a hearing outside the presence of the jury, that "(1) the accusation or accusations were in fact made; (2) that the accusation or accusations were in fact false; and (3) that the evidence is more probative than prejudicial." Id. at 502, 779 P.2d at 90.
In our Order of Remand, the trial judge was instructed to conduct a Miller hearing to determine by a preponderance of the evidence whether the complaining witness had made prior false accusations of sexual assault or molestation. The hearing was to involve consideration of the testimony of the five defense witnesses who were prepared to testify at trial. After the Miller hearing, the trial judge concluded that although there was evidence that the complaining witness had, in fact, made other allegations of sexual assaults and molestations, Brown did not meet his burden of proving that such allegations were, in fact, false.
The preponderance of the evidence test is not mechanistically satisfied according to "which side has produced the greater quantum, without regard to its effect in *1381 convincing [the trier of fact's] mind of the truth of the proposition asserted." In re Winship, 397 U.S. 358, 367-68, 90 S.Ct. 1068, 1074, 25 L.Ed.2d 368 (1970). The preponderance of the evidence burden "does not mean simple volume of evidence or number of witnesses." E. Cleary, McCormick on Evidence § 339 (3rd ed. 1984). In other words, proof by a preponderance of the evidence is not a standard that is satisfied merely by force of the greatest number of witnesses. The standard of proof should lead the trier of fact "to find that the existence of the contested fact is more probable than its nonexistence." Id.
Proof of falsity must be something more than a bare, unsupported opinion that the complaining witness is lying about certain events. Purported false allegations require some independent factual basis of falsity in order to be admissible in evidence.[1]
The trial judge did not simply resolve an issue of witness credibility, but in effect, albeit after the fact, decided the "probity of the evidence compared to its tendency to divert the trial and confuse the jury." Perry v. Rushen, 713 F.2d 1447, 1455 (9th Cir.1983), cert. denied, 469 U.S. 838, 105 S.Ct. 137, 83 L.Ed.2d 77 (1984). The proffered testimony did not prove falsity and was therefore irrelevant. The offers of proof relating to other witnesses waiting in the hall to testify indicated that the witnesses' statements were merely repetitive and of the same irrelevant nature as that of the other witnesses because of their insufficiency under the Miller standard.
The due process right of an accused during a criminal trial is "the right to a fair opportunity to defend against the State's accusations." Chambers v. Mississippi, 410 U.S. 284, 294, 93 S.Ct. 1038, 1045, 35 L.Ed.2d 297 (1973). Through the in camera procedure of the Miller hearing, the trial judge must tread a delicate balance between the defendant's constitutional rights to a fair trial, and the State's policy of encouraging rape victims to testify without harassment and embarrassment stemming from public disclosure of irrelevant evidence concerning their private sexual experiences.
Although Chambers addresses assurances of a defendant's due process right to a fair trial, Brown, in emphasizing that aspect of Chambers, overlooks the important caveat in the opinion stating that "[i]n the exercise of this right, the accused, as is required of the State, must comply with established rules of procedure and evidence designed to assure both fairness and reliability in the ascertainment of guilt and innocence." Chambers, 410 U.S. at 302, 93 S.Ct. at 1049. The defendant's right to present witnesses in his own defense is subject to the rule of relevance and "does not require that the defendant be permitted to present every piece of evidence he wishes...." State v. Cassidy, 3 Conn. App. 374, 489 A.2d 386, 391 (1985).
The trial judge correctly ruled that the evidence presented at the Miller hearing was irrelevant because its probity was unpersuasive under the three Miller conditions.[2] The testimony of the witnesses did *1382 not satisfy the requirement of proof of falsity. The trial court thus appropriately ruled that the requisites of Miller had not been met and that the testimony of the Miller defense witnesses would not be relevant at trial. Such determinations of relevancy are within the discretion of the trial court. State v. Demos, 94 Wash.2d 733, 619 P.2d 968, 970 (1980). A minimal threshold of relevancy is a prerequisite to invoking the constitutional standard. People v. Hackett, 421 Mich. 338, 365 N.W.2d 120, 127 (1985).
An in camera hearing assures the defendant that the rules of evidence will not be applied in a mechanistic, unconstitutionally arbitrary fashion which might ultimately "defeat the ends of justice" if the evidence were material.[3]See Chambers, 410 U.S. at 302, 93 S.Ct. at 1049. At the same time, the procedural requirement for an in camera presentation of evidence of false allegations of rape or molestation is deferential to the broader state policy protecting alleged rape victims in open court "from unnecessary indignities and needless probing into their respective sexual histories." Summitt v. State, 101 Nev. 159, 161, 697 P.2d 1374, 1375 (1985); State v. Lemon, 456 A.2d 261, 264 (R.I.1983).
Brown also contends that he was not afforded a fair opportunity to cross-examine the complaining witness relative to her "numerous prior allegations of sexual assault." Cross-examination is a substantial right of the defendant and "the principal means by which the believability of a witness and the truth of his testimony are tested." Davis v. Alaska, 415 U.S. 308, 316, 94 S.Ct. 1105, 1110, 39 L.Ed.2d 347 (1974). Nevertheless, a defendant's "Sixth Amendment rights are subject to the same evidentiary rules as all other evidence. The threshold question for the admissibility of evidence is relevancy." State v. Blue, 225 Kan. 576, 592 P.2d 897, 901 (1979) (emphasis in text); see also, People v. Comes, 80 Ill.App.3d 166, 35 Ill.Dec. 818, 824, 399 N.E.2d 1346, 1352 (1980) (right to cross-examine witnesses does not extend to matters which are irrelevant and have little probative value).
An examination of the record also reveals that Brown availed himself of his right to cross-examine the complaining witness only when she testified at the preliminary hearing. Although asked by the court whether he wished to cross-examine the complaining witness both when she testified in camera and in open court, Brown declined to do so.
For the reasons stated above, we conclude that the district court properly determined, after the Miller hearing, that Brown did not carry his burden and that the original judgment entered against Brown pursuant to the jury's verdict be reinstated. The judgment is affirmed.
MOWBRAY, C.J., and YOUNG, J., concur.
ROSE, Justice, dissenting, with whom SPRINGER, Justice, agrees:
I believe the cumulative events that occurred in this case and the rulings of the district court have prevented the appellant Stanley Brown (Brown) from receiving a fair trial. At trial, Brown was not permitted to present evidence of the complaining witness's propensity to make false accusations of sexual assault. At the Miller hearing subsequent to trial, the district court found that the allegations of sexual assault by others were not proven to be false and denied Brown a new trial. From the evidence presented, this finding was erroneous and a new trial should have been granted.
*1383 The complaining witness was Brown's niece, Janet Rains. However, there was no blood relationship between the victim and appellant because Brown had been adopted by Rains' grandparents. At the time of the alleged sexual assaults, Brown was 21 and Rains was five years younger.
The victim's account of the two sexual assaults and one attempted assault are unusual. Rains testified that on November 21, 1986, Brown asked her to accompany him to a movie and dinner. After Rains' mother agreed, the pair left Rains' house. Rains claimed that instead of going to a movie, Brown took her to a party and sexually assaulted her thereafter. Brown denies this charge. Rains returned to her home without any visible signs of having been assaulted and made no mention of the alleged incident.
On November 26, 1986, Rains claims that Brown entered her home, proceeded to her bedroom and began to threaten her with an unloaded shotgun. She claims that Brown pushed her around with the butt of the gun and then ordered her to pull her pants down. In response, she pulled her pants down to her knees. At that moment, the phone rang and Rains' mother came home. Brown ran out of Rains' room, Rains pulled up her pants and her mother came into the house. Brown also denied this allegation and no complaint was made by Rains at the time.
On the night of December 4, 1986, Rains testified that she was in her bedroom asleep. She was awakened by a knock on her window and discovered it was Brown, who apparently needed some clothes. Rains let Brown in the house and then she claims that he sexually assaulted her. She claims that she tried to scream, but couldn't. She testified, "whenever I would go to scream, I can't scream. I don't have that voice when I am scared." Rains maintained that Brown threatened to injure her if she told anyone. Brown also denied this charge and no immediate complaint was made by Rains.
About a month later, Rains told her mother about the assaults. She claimed that she waited that long because she was not sure how her mother would react.
At trial, Brown's attorney wanted to present numerous witnesses to establish that Rains had made many false accusations of sexual assault against other men. Rather than cross-examine Rains about these incidents, Brown's attorney attempted to call witnesses to testify to these other false accusations. The district court precluded Brown from introducing these witnesses based on NRS 50.085(3), the rape shield law. Brown was permitted to call five witnesses who testified that Rains' reputation for truth and veracity was bad. The jury found Brown guilty of the two sexual assaults and one attempted sexual assault and the court then sentenced Brown to the maximum possible sentence, two life sentences on the sexual assaults and ten years on the attempted sexual assault, all to run consecutive.
When appealed to this court, we remanded the case back to district court for a hearing to determine whether Rains had made prior false sexual assault and molestation accusations. In doing this, we stated:
Given Miller and the facts and circumstances of this case, we are concerned that the result below may be unreliable and that Brown may have been denied a fair trial. Therefore, we elect to vacate the judgment below and remand this case to the district court for further consideration. Specifically, on remand, the district court shall hold a Miller hearing to determine, by a preponderance of the evidence, whether the complaining witness made prior false sexual assault and molestation accusations. In the event that fabrication is established, the district court shall grant Brown a new trial. Assuming falsity is not shown, the original judgment shall be reinstated.
On remand, the district court held a Miller hearing as we had directed, but refused to hear any witnesses Brown had not tried to offer at trial. This precluded five witnesses who were present and prepared to testify. Such a restriction was not imposed by this court and I see no good reason why *1384 these additional witnesses should have been precluded from testifying at a hearing premised on a search for truth.
At the Miller hearing, Brown was permitted to call three witnesses who testified about Rains making false allegations of sexual assault. The testimony of these witnesses was compelling and there is no question in my mind that they established that Rains had made such false statements. The first witness was a Mr. Sperlak who currently lives in Denver but had met Rains when he was serving in the Navy near Fallon. He dated her for about one month. Sperlak testified that Rains told him that her father had raped her and that he used to beat her. She also accused her ex-boyfriend of having raped her. To establish the falsity of these two charges, Sperlak testified that he met Rains' former boyfriend the following day and was told by him that no such rape had occurred. Sperlak confronted Rains with this fact and she "just looked at the ground like she like she was caught in a lie." Sperlak also described confronting Rains about the allegations made against her father when he observed her writing a letter to him. Again, Rains said nothing and again reacted as if she had been caught in a lie.
Brown also called a Ms. Sprinkle. She testified that she lived in Fallon for approximately seven years and had attended school with Rains. Sprinkle stated that Rains told her that she had been raped by both Brown and by Darren Summerville. Sprinkle testified that Rains did not seem at all upset about the alleged rape by Mr. Summerville and that she did not believe her because Rains had repeatedly lied to her about other matters. Sprinkle also testified that Rains lied when she said she had had sexual relations with a Johnny Pereira and had had a baby resulting from that activity. However, Sprinkle asked Pereira about this and he responded that he had never even had sex with her.
Another witness called by Brown was Frankie Sue Aja Jones. Ms. Jones testified that Rains accused her fiance, Roger Gobel, of raping her. However, Jones said that Rains did not seem to be at all upset about this supposed rape, and that when she came home the evening of the alleged event, she was happy and made no mention of the alleged sexual assault. The prosecution moved to strike Ms. Jones' testimony relative to Roger Gobel because Rains made these accusations after Brown's trial. The district court granted his motion.
At the conclusion of the Miller hearing, the district court confirmed Brown's convictions, finding that it was not established that Rains had made false accusations. With regard to the testimony of Mr. Sperlak and Ms. Sprinkle, the court found that neither established that the accusations were false. However, I believe the only reasonable inference that can be drawn from the witnesses' testimony and the reaction of Rains is that the allegations were shown to be false by a preponderance of the evidence. It is also reasonable to assume that Rains' father, Summerville, Pereira, and Gobel would not admit to sexually assaulting Rains if called to the stand. Since Brown would receive no benefit of the doubt from the district court, Brown's counsel should have attempted to call these additional witnesses, to make certain that falsity was proved. However, even without their testimony, every reasonable inference is that all of Rains' accusations of sexual assault or illicit sex were false.
This was a close case that hinged upon the credibility of the complaining witness and Brown. The facts of the alleged assault are not compelling. At trial, a number of witnesses testified that Rains had a poor reputation for truth and veracity. If the jury had also heard that she had falsely accused many other men of sexual assault, the result may have been in Brown's favor.
It was also error for the district court, at the Miller hearing, to preclude additional witnesses from testifying about allegations of sexual assault which Rains fabricated after the trial here in question. While our order of remand did direct the district court to hear evidence concerning the prior false allegations, we were not aware of any others. The evidence of false accusations is not admitted to establish anything about the complaining witness's sexual conduct, *1385 but rather to attack her truth and veracity by showing her propensity to make false accusations of sexual assault. Evidence of a poor reputation for truth and veracity does not become more or less prejudicial because the events which imparted this knowledge to the testifying witness happened after the alleged criminal conduct. See 81 Am.Jur.2d Witnesses to Worker's Compensation, § 565 (1976); Fisher v. Conway, 21 Kan. 18 (1878). Therefore, the district court should have permitted witnesses to describe false accusations of sexual assault which Rains made after the trial. This evidence should have been received at the Miller hearing whether it came from newly discovered witnesses, or from a trial witness like Ms. Jones who had new probative information.
Brown established that Rains had made false accusations of sexual assault and illicit sex against a number of men and this should have mandated a new trial so that this evidence could be presented to a jury. The district court consistently and assertively ruled against Brown, first at the trial by prohibiting the testimony of false accusations, then refusing to find that the false accusations were established by a preponderance of the evidence at the Miller hearing, and finally, in sentencing Brown to a very lengthy penalty. In reviewing this case in its totality, I consider the jury verdicts unreliable because the jury did not hear all of the relevant evidence. Therefore, I would reverse and remand for a new trial.
SPRINGER, J., concurs.
NOTES
[1]  See, e.g., State v. Hutchinson, 141 Ariz. 583, 688 P.2d 209, 213 (App.1984) (written offer of proof lacked sufficient facts to show that prior rape charge was unsubstantiated); State v. Anderson, 211 Mont. 272, 686 P.2d 193, 198-201 (1984) (dismissal of charges does not prove falsity especially where victim's mother vehemently insisted her daughter not experience the rigors of trial); People v. Alexander, 116 Ill.App.3d 855, 72 Ill.Dec. 338, 452 N.E.2d 591 (1983) (victim's prior rape complaints were inadmissible where the defendant was unable to show the complaints were false); Commonwealth v. Bohannon, 385 Mass. 733, 434 N.E.2d 163, 173 (1982) (hospital records offered to prove prior false allegations of rape contained unsupported opinions by experts and unreliable hearsay); State v. Demos, 94 Wash.2d 733, 619 P.2d 968, 969-70 (1980) (inactive status of rape file because police could not locate the victim proves nothing about the truth or falsity of the original charges); People v. Vaughn, 56 Ill.App.3d 700, 14 Ill.Dec. 195, 198, 371 N.E.2d 1248, 1251 (1978) (evidence did not prove propensity to falsely cry rape without proof that the complaining witness had filed previous rape charges).
[2]  See also, Hughes v. Raines, 641 F.2d 790, 793 (9th Cir.1981) (the Sixth Amendment does not prevent the trial court from excluding questions into extraneous issues that have little, if any, probative value); People v. McKenna, 196 Colo. 367, 585 P.2d 275, 279 (1978) (there is no constitutional right to introduce irrelevant and highly inflammatory evidence).
[3]  In Covington v. State, 703 P.2d 436, 442 (Alaska Ct.App.1985), the court stated that

A majority of the courts which have considered the issue permit such evidence only if the defendant makes a showing out of the presence of the jury that the witness' prior allegations of sexual assault were false, as, for example, where the charges somehow had been disproved or where the witness had conceded their falsity.
(Citations omitted.)
