The defendant was tried before a jury in the Superior Court and convicted on charges of rape and commission of an unnatural and lascivious act. He appeals from these convictions pursuant to G. L. c. 278, §§ 33A - 33G. We transferred the appeal here on our own motion.

The defendant raises three issues: first, that the trial judge improperly excluded a line of questioning by defense counsel intended to show bias of the complaining witness; *223second, that since the prosecution’s use of peremptory challenges violated the principles enunciated in Commonwealth v. Soares, 377 Mass. 461, cert, denied, 444 U.S. 881 (1979), the judge improperly denied the defendant’s motion for a mistrial; and third, that the judge improperly denied the defendant’s motion to suppress certain items seized from the defendant’s car.

We agree that there was error in the exclusion of the questions intended to show bias and that there must be a new trial. As this conclusion is dispositive, we need not reach the defendant’s second and third grounds for reversal.1

We summarize the evidence presented by the prosecution. On December 2,1977, at approximately three o’clock in the morning the defendant picked up the complainant hitchhiking just outside of Malden Square. The complainant had been drinking heavily prior to the incident. The complainant testified that she asked to be let off at her boy friend’s house about one-half mile from Malden Square. Instead, the defendant drove to a nearby church parking lot where he forced the complainant to perform oral sex and to engage in intercourse twice. The complainant unsuccessfully attempted to escape from the car twice, resulting in the defendant’s punching her many times. At one point she screamed for about ten seconds. Seeing the headlights of an approaching car, the complainant, now naked and bleeding around the mouth, jumped from the defendant’s car and ran toward the other car screaming and waving her arms. The other car was a police cruiser. The police officers testified that they had entered the lot to investigate screams. On reaching the police car the complainant accused the defendant of raping her.

*224The defendant’s account differed in several material respects. His testimony raised the defense of consent. He testified that the complainant’s mouth was already bloodied when he picked her up; that she had told him it was the result of a fight with her boy friend. He testified that he entered the church parking lot at the complainant’s request to talk and so she could smoke some “angel dust.” They discussed sex. At the complainant’s suggestion they engaged in sexual acts. Shortly thereafter, the defendant saw a police cruiser approaching. He warned the complainant and told her to get dressed. He began to back up the car when the complainant jumped out, ran to the cruiser, and accused him of raping her. At no time prior to jumping out of the car did the complainant scream.

The defendant attempted to introduce evidence at trial that the complainant had been charged with prostitution, once each in May and September, 1977. The first complaint purportedly alleged that the complainant had approached an undercover police officer and solicited him to perform oral sex for twenty dollars. The second complaint purportedly alleged that the complainant was found undressed in a car engaged in sexual acts. Her male companion told the police officer that he had picked her up and she agreed to “perform all [sic] sex” for twenty dollars. The defendant intended to introduce this evidence either through cross-examination of the complainant or through the testimony of police officers involved in the complaints.

The defendant’s purpose to introduce this evidence was not to show that the complainant was or had been a prostitute, and that it was therefore more likely that she had solicited or consented to have sex with the defendant. Rather, it was to show that, having been found in a similar situation on two prior occasions, the complainant was herself arrested and charged with a crime. Thus, the allegation of rape against the defendant may have been motivated by her desire to avoid further prosecution.2

*225Over the defendant’s objection, the judge ruled that the defendant could neither offer testimony that the complainant had been charged with prostitution nor inquire about those charges in cross-examination of the complainant. The judge based this ruling on the prohibition in the Massachusetts rape-shield statute, G. L. c. 233, § 21B,3 against admitting in a rape trial evidence of reputation or of specific instances of a rape victim’s sexual conduct.

The defendant argues that the judge’s rulings under G. L. c. 233, § 21B, amounted to an unconstitutional abridgement of both his Sixth Amendment right of confrontation as elaborated in Davis v. Alaska, 415 U.S. 308 (1974), and its progeny, and the cognate rights guaranteed under art. 12 of the Declaration of Rights of the Massachusetts Constitution and by G. L. c. 263, § 5. Also, the defendant argues that his due process right to have a fair trial was abridged. He cites in this regard, In re Oliver, 333 U.S. 257, 273 (1948) (right to present relevant evidence in one’s defense), and Stovall v. Denno, 388 U.S. 293, 302 (1967). The Commonwealth challenges the defendant’s *226claims that G. L. c. 233, § 21B, as applied, deprived the defendant of any constitutional rights, and further claims that the defendant failed to demonstrate that the evidence proffered by the defendant adequately raised the issue of bias as to the complainant witness. In the view we take of this record, the issue of bias was squarely raised,4 and the judge misapplied the statute. Hence, we need not reach the constitutional contentions of the parties.5

*227We do not believe that the prohibition in the rape-shield statute sweeps so broadly as to render inadmissible evidence of specific instances of a complainant’s sexual conduct in situations when that evidence is relevant to show the complainant’s bias. The statutory bar to the admission of evidence of specific instances of sexual conduct is essentially a reflection of a pre-existing common law rule. In rape cases, evidence of specific instances of prior sexual intercourse with persons other than the defendant long has been inadmissible. See Commonwealth v. Gouveia, 371 Mass. 566, 569 (1976); Commonwealth v. McKay, 363 Mass. 220, 226 (1973); Commonwealth v. Regan, 105 Mass. 593 (1870). The justification for this rule is twofold. First, collateral questions relating to the specific acts would prolong the trial and divert the attention of the trier of fact from the alleged criminal acts of the defendant. See Commonwealth v. McKay, supra at 227. Second, such evidence has little probative value on the issue of consent. “[T]he victim’s consent to intercourse with one man does not imply her consent in the case of another.” Id. Nor is the fact that a woman engages in sex for hire relevant to the issue of her credibility. “The rule is well established that the fact that a female witness is a prostitute or keeps a house of ill fame is not admissible to impeach her.” Commonwealth v. Vandenhecke, 248 Mass. 403, 404 (1924).

The major innovative thrust of the rape-shield statute is found in the first sentence, which reverses the common law rule under which evidence of the complainant’s general *228reputation for unchastity was admissible. See Commonwealth v. McKay, supra at 226 (stating rule). Such reputation evidence was considered probative on the issue of consent (see Commonwealth v. Kendall, 113 Mass. 210 [1873]) and was therefore admissible when consent was in issue. Cf. Commonwealth v. McKay, supra at 225. This rule was “part of a legal tradition, established by men, that the complaining woman in a rape case is fair game for character assassination in open court.” Commonwealth v. Manning, 367 Mass. 605, 613-614 (1975) (Braucher, J., dissenting). Reformers have argued that inquiries into the sexual history of the rape complainant chills her willingness to testify. Moreover, reputation evidence is only marginally, if at all, probative of consent. See Commonwealth v. Manning, supra at 613-617 (Braucher, J., dissenting). Rape-shield statutes are “aimed at eliminating a common defense strategy of trying the complaining witness rather than the defendant. The result of this strategy was harassment and further humiliation of the victim as well as discouraging victims of rape from reporting the crimes to law enforcement authorities.” State v. Williams, 224 Kan. 468, 470 (1978). See Tanford & Bocchino, Rape Victim Shield Laws and the Sixth Amendment, 128 U. Pa. L. Rev. 544 (1980) (collecting literature and authorities, together with appendix of various statutes enacted); cf. Fed. R. Evid. 412. The legislative history of § 21B is “limited.” Burnim, Massachusetts Rape-Shield Law — An Over-Step in the Right Direction, 64 Mass. L. Rev. 61, 63 (1979). There is nothing in the history of the enactment of § 21B which indicates any legislative consideration of constitutional issues, and, more particularly, the question of impeachment by proof of bias.6

In certain circumstances, however, evidence of prior acts, statements or circumstances may be relevant to show a *229complainant’s motive to accuse falsely the defendant. Reasonable cross-examination to show motive or bias has long been a matter of right.7 Commonwealth v. Cheek, 374 Mass. 613, 615 (1978). See Commonwealth v. Haywood, 377 Mass. 755, 760 (1979), and cases cited therein; Commonwealth v. Byron, 14 Gray 31 (1859); W.B. Leach & P.J. Liacos, Massachusetts Evidence 120-121 (4th ed. 1967). We do not read the rape-shield statute as abridging this right. The right to cross-examine a complainant in a rape case to show a false accusation may be the last refuge of an innocent defendant. “A defendant has the right to bring to the jury’s attention any ‘circumstance which may materially affect’ the testimony of an adverse witness which might lead the jury to find that the witness is under an ‘influence to prevaricate’” (emphasis in original). Commonwealth v. Haywood, supra at 760, quoting from Commonwealth v. Marcellino, 271 Mass. 325, 327 (1930), quoting from Day v. Stickney, 14 Allen 255, 258 (1867). We have in the past recognized that this right may assume constitutional dimensions. Commonwealth v. Ferrara, 368 Mass. 182, 189 (1975). Commonwealth v. Graziano, 368 Mass. 325, 330 (1975). See Davis v. Alaska, supra. Bias may be shown by “any competent means.” Commonwealth v. Redmond, 357 Mass. 333, 338 (1970). Evidence of bias is not rendered inadmissible simply because it may indicate that the witness committed or was charged with a crime. See id.; Commonwealth v. West, 312 Mass. 438, 441 (1942).

The Commonwealth argues that evidence of the prostitution charges is not relevant to show that the complainant was biased because nothing in the record suggests that there was ever an actual threat of prosecution against the com*230plainant, and because, even under the defendant’s theory of the encounter, there was never any mention of money in exchange for sex. The Commonwealth’s argument is apparently based in part on the tendency of its version of the facts, if believed, to refute the defendant’s bias theory — e.g., the police officers testified they heard screams before entering the parking lot, and the complainant testified that she didn’t know the approaching car was a police car.

However, the defendant is entitled to present his own theory of the encounter to the jury. The bias theory is not inconsistent with the defendant’s version of the facts. The relevancy of testimony depends on whether it has a “rational tendency to prove an issue in the case.” Commonwealth v. LaCorte, 373 Mass. 700, 702 (1977). See Commonwealth v. Durkin, 257 Mass. 426, 427 (1926). Under the defendant’s theory he and the complainant, previously strangers to each other, were in a car late at night parked in a vacant parking lot. Having just engaged in sexual acts, they were both naked. A police car was approaching. The defendant intended to show that the complainant, having been found in a similar situation on two prior occasions, had been arrested on each occasion and charged with prostitution. We cannot say that this evidence has no rational tendency to prove that the complainant was motivated falsely to accuse the defendant of rape by a desire to avoid further prosecution.

The Commonwealth’s reliance on Commonwealth v. Haywood, supra, and Commonwealth v. Santos, 376 Mass. 920 (1978), is misplaced. In Haywood, the trial judge concluded that the witness’s arrest record was not probative of bias because the witness’s arrest took place after the witness made his initial statements to the police, and because his trial testimony, which was given subsequent to the arrest, was in every material respect consistent with his original statements. In contrast, the basis for any bias on the part of the complainant here already existed at the time of the complainant’s initial accusation. In Santos, unlike here, the ex-*231eluded evidence was offered to impeach credibility generally, and had no tendency to show bias or motive directly.

We emphasize that we do not depart from the long held view that prostitution is not relevant to credibility.8 Commonwealth v. Vandenhecke, 248 Mass. 403 (1924). Nor do we depart from the policy of the statute in viewing prostitution or the lack of chastity as inadmissible on the issue of consent. Where, however, such facts are relevant to a showing of bias or motive to lie, the general evidentiary rule of exclusion must give way to the constitutionally based right of effective cross-examination. See Davis v. Alaska, supra; Chambers v. Mississippi, 410 U.S. 284 (1973); State v. DeLawder, 28 Md. App. 212 (1975); State v. Jalo, 27 Or. App. 845 (1976). Furthermore, we do not reach consideration of the admissibility of evidence of the specific factual circumstances underlying the prostitution complaints.9 Without intimating the proper result, we observe that under the common law the trial judge retains broad discretion to control the scope of cross-examination, and to limit that scope once the jury have been “adequately exposed” to the issue of bias. Commonwealth v. Dougan, 377 Mass. 303, 309-310 (1979). Commonwealth v. Hicks, 377 Mass. 1, 8 (1979). In the exercise of this discretion a trial judge should consider the important policies underlying the rape-shield statute. He should exclude evidence of specific instances of a complainant’s sexual conduct in so far as that is possible without unduly infringing upon the defendant’s right to show bias.10 We emphasize, however, as we did in *232Commonwealth v. Ahearn, 370 Mass. 283, 287 (1976), “[t]his is not a case where the judge merely limited the scope of such examination, within his discretion; he excluded the total inquiry by his . . . rulings.” This ruling related to a critical issue of the case and hence the convictions cannot stand. Commonwealth v. Ferrara, supra. Cf. Commonwealth v. Bohannon, 376 Mass. 90 (1978). The convictions are reversed and the cases are remanded for a new trial.

So ordered.

(concurring in the result). I concur with the comments of Justice Braucher in his separate opinion. I add that as I read the opinion of the court, it is narrowly and carefully confined to cases where the disputed evidence is clearly relevant to a showing of bias or motive to lie by the complaining witness. If the court’s opinion is not read in this cautious fashion, there is a danger that there will be unwarranted inroads upon the rape-shield law, G. L. c. 233, § 21B, and the legislative purposes which inspired that statute.

(concurring in the result). I agree with the court that the rape-shield law, G. L. c. 233, § 21B, does not abridge the right of a criminal defendant to show that a rape victim had a motive to accuse the defendant falsely. A contrary conclusion would raise a serious constitutional question. Davis v. Alaska, 415 U.S. 308, 316-318 (1974). See Commonwealth v. Bohannon, 376 Mass. 90, 93 n.3 (1978), and cases cited; Burnim, Massachusetts Rape-Shield Law — An Over-Step in the Right Direction, 64 Mass. L. Rev. 61, 65-72 (1979). But I think the judge should adhere to the policy of the rape-shield law and conduct a preliminary hearing to determine whether the weight and relevance of the evidence offered outweigh its prejudicial effect on the *233victim. In the present case the fact of prior criminal complaints against the victim for prostitution provided a very slender basis for inferring a motive for false accusation, particularly in view of the conceded fact that she ran, naked and bleeding, from the defendant’s car to a police cruiser. But the judge did not hold a preliminary hearing and did not permit the defendant to make an appropriate offer of proof. I therefore agree that the conviction must be reversed.