*165OPINION
By the Court,
Steffen, J.: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.
*166Under 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 convincing [the trier of fact’s] mind of the truth of the proposition asserted.” In re Winship, 397 U.S. 358, 367-68 (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
*167The 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 (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 (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. 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, 489 A.2d 386, 391 (Conn. App.Ct. 1985).
The trial judge correctly ruled that the evidence presented at *168the Miller hearing was irrelevant because its probity was unpersuasive under the three Miller conditions.2 The testimony of the witnesses did 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, 619 P.2d 968, 970 (Wash. 1980). A minimal threshold of relevancy is a prerequisite to invoking the constitutional standard. People v. Hackett, 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. 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.” Summit 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 (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, 592 P.2d 897, 901 (Kan. 1979) (emphasis in text); see also, People v. Cornes, 399 N.E.2d 1346, 1352 (Ill.App.Ct. 1980) *169(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.See, e.g., State v. Hutchinson, 688 P.2d 209, 213 (Ariz.Ct.App. 1984) (written offer of proof lacked sufficient facts to show that prior rape charge was unsubstantiated); State v. Anderson, 686 P.2d 193, 198-201 (Mont. *1671984) (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, 452 N.E.2d 591 (Ill.App.Ct. 1983) (victim’s prior rape complaints were inadmissible where the defendant was unable to show the complaints were false); Commonwealth v. Bohannon, 434 N.E.2d 163, 173 (Mass. 1982) (hospital records offered to prove prior false allegations of rape contained unsupported opinions by experts and unreliable hearsay); State v. Demos, 619 P.2d 968, 969-70 (Wash. 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, 371 N.E.2d 1248, 1251 (Ill.App.Ct. 1978) (evidence did not prove propensity to falsely cry rape without proof that the complaining witness had filed previous rape charges).
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, 585 P.2d 275, 279 (Colo. 1978) (there is no constitutional right to introduce irrelevant and highly inflammatory evidence).
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.)