A Superior Court jury found the defendant, Joseph E. LaVelle, guilty on two indictments charging distribution of a counterfeit controlled substance. G. L. c. 94C, § 32G (1990 ed.). Prior to trial the judge denied the defendant’s motion to dismiss the indictments on the ground that the integrity of the grand jury proceeding had been impaired. At trial the judge granted the Commonwealth’s motion in limine to exclude evidence pertaining to the Commonwealth’s sole eyewitness. Claiming prejudicial error, the defendant made a timely appeal to the Appeals Court, which affirmed his convictions. Commonwealth v. LaVelle, 33 Mass. App. Ct. 36 (1992). We granted further appellate review. After reviewing the record, we conclude that any errors made at trial did not prejudice the defendant’s case, and, therefore, we affirm the convictions, though we would not have ruled as the trial judge ruled.

LaVelle was but one of many targets in a Framingham police “sting” operation codenamed “Last Call.” The operation was designed to stop rampant drug sales among patrons of certain bars and other establishments in Framingham. The police enlisted the aid of confidential informants who would enter these bars, approach individuals whom the police suspected of drug dealing, and attempt to purchase cocaine. In this case, two Framingham police detectives and an informant, John Robinson, planned to buy cocaine from LaVelle at a nightclub along Route 9. Because LaVelle denies ever meeting Robinson at the nightclub, Robinson’s report is the only account of the drug transaction.

Robinson testified that he approached LaVelle at the nightclub in mid-October, 1986, and asked if he could buy drugs from him. LaVelle responded affirmatively, and Robinson reported this information to the two Framingham detectives. Then on October 21, 1986, the detectives asked Robinson to attempt to buy cocaine from LaVelle at the nightclub. The detectives strip searched Robinson, gave him $100 for the drug purchase, and then followed him to the nightclub. When Robinson entered the nightclub, the detectives remained in their automobile. They neither confirmed La[*148] Velle’s presence in the nightclub nor checked to see if his car was in the parking lot. After several minutes, Robinson came from the nightclub and handed to the detectives what they presumed to be cocaine. There is conflicting evidence as to whether a field test was performed at that time. However, a subsequent laboratory test revealed that the substance was not cocaine.

Robinson testified that while he was in the nightclub he asked LaVelle if “he had anything for me.” LaVelle wanted to see the money first, so Robinson showed him the one hundred dollar bill and then asked for a gram of cocaine. LaVelle proceeded to usher Robinson over to a hallway where he then took a small packet out of a cigarette box. LaVelle admitted that the amount was only three-fourths of a gram, so he reduced the price. Robinson took the packet.

Three days later, after the laboratory report showed that the substance obtained from LaVelle was not cocaine, the detectives sent Robinson back to the nightclub, following the same procedures, to see if he could replace the counterfeit cocaine with the real thing. According to Robinson, LaVelle gave him a gram of cocaine to replace the “garbage” he had given him the first time. Laboratory tests confirmed that this second gram also did not contain cocaine. LaVelle was subsequently arrested and charged with two counts of distributing a counterfeit controlled substance. Robinson testified that prior to LaVelle’s arrest LaVelle drove into Robinson’s driveway and allegedly said, “You shouldn’t be doing what you’re doing — it’s wrong. You’ve got to be careful of your family.” Robinson interpreted this as a "threat.

In June, 1987, before the trial began, Robinson made false allegations of assault to the police. From the affidavits of the police officers, Robinson, who was then living in Holliston, claimed that he had been assaulted by three men in his backyard but later admitted to a Framingham detective with whom he had been working on operation Last Call that he had fabricated the entire story. Robinson claimed the incident was a reaction to the pressures of his work as a police informant. He feared for his family’s safety and felt he[*149] needed greater police protection. This incident was disclosed neither to the grand jury nor to the trial jury.

1. Grand jury proceedings. The defendant makes three objections to the grand jury proceedings: (1) the case presented to the grand jury was based almost exclusively on hearsay; (2) the Commonwealth failed to provide the grand jury with information regarding the informant’s criminal record; and (3) the Commonwealth failed to inform the grand jury of their right to know the identity and background of the informant. The trial judge denied the defendant’s motion to dismiss the indictments; we affirm that decision.

“Our review of the propriety of any indictment is limited to determining whether the grand jury received sufficient evidence to find probable cause for arrest . . . and whether the integrity of the grand jury proceedings was impaired” (citation omitted). Commonwealth v. McGahee, 393 Mass. 743, 746-747 (1985). In regard to the defendant’s first objection, we have held that “it is not enough to justify dismissal of an indictment that the jurors received hearsay or hearsay exclusively, and this is so even when better testimony was available for presentation to the grand jury.” Commonwealth v. St. Pierre, 377 Mass. 650, 655 (1979) (police officer with no personal involvement in the case allowed to present hearsay evidence to a grand jury). See also Mass. R. Crim. P. 4(c), 378 Mass. 849 (1979). ^[1] On the other hand, we have said repeatedly that “sound policy dictates a preference for the use of direct testimony before grand juries.” St. Pierre, supra at 656, citing Commonwealth v. Lincoln, 368 Mass. 281, 285 n.2 (1975). Therefore, we have indicated that in certain “extraordinary circumstances” a grand jury’s dependence upon hearsay might impair the integrity of the proceeding. St. Pierre, supra at 655, 656. Commonwealth v. O’Dell, 392 Mass. 445, 450-451 (1984). If, for example, the prosecutor[*150] intentionally or knowingly deceived the grand jury, then the defendant could rightly claim that the integrity of the grand jury was impaired. St. Pierre, supra at 655. Commonwealth v. Mayfield, 398 Mass. 615, 621 (1986). In addition, if the hearsay testimony fails to reach the level of probable cause needed to support the arrest, then the indictment might be vulnerable. St. Pierre, supra at 656. In any case, the defendant bears a heavy burden to show impairment of the grand jury proceeding. Commonwealth v. Shea, 401 Mass. 731, 734 (1988).

After reviewing the record, we conclude that there is no evidence that the prosecution knowingly deceived or misled the grand jury, nor did the evidence presented fail to reach the appropriate level of probable cause. In addition to the hearsay regarding Robinson’s statements to the police, the grand jury also heard the nonhearsay testimony of a detective who assisted Robinson in the sting operation. Moreover, the prosecutor was justified in not disclosing Robinson’s identity to the grand jury because of his precarious role as a police informant. Lastly, the defendant’s claim that reliance on hearsay rather than direct testimony deprived the defendant of “valuable discovery and possible impeaching evidence” is without merit. The informant’s identity was revealed to the defendant nearly one year before the trial, providing more than enough time for discovery and preparation of an adequate defense.

Regarding the second objection, we note that “ [prosecutors are not required in every instance to reveal all exculpatory evidence to a grand jury,” Commonwealth v. Mc-Gahee, 393 Mass. 743, 746 (1985), citing O’Dell, supra at 447, but they must disclose evidence that would “greatly undermine the credibility of evidence likely to affect the grand jury’s decision to indict.” McGahee, citing Commonwealth v. Connor, 392 Mass. 838, 854 (1984). We believe that informing the grand jury of Robinson’s convictions for larceny and breaking and entering, occurring over six years before the investigation began, would not have greatly undermined the[*151] credibility of the evidence against LaVelle and would not have significantly affected the decision to indict. ^[2]

The defendant’s third objection is likewise without merit. There is no right to discover an informant’s identity or background through grand jury proceedings distinct from the principles outlined above.

2. Evidence of prior bad acts and the Bohannon exception. The well-established rule in Massachusetts is that “[sjpecific acts of prior misconduct of the witness . . . not material to the case in which he testifies cannot be shown by the testimony of impeaching witnesses or other extrinsic evidence to affect [the witness’s] credibility.” P.J. Liacos, Massachusetts Evidence 149 (5th ed. 1981). Commonwealth v. Schaffner, 146 Mass. 512, 515 (1888). ^[3] Into this weathered edifice we have chiseled a narrow exception, recognizing that in special circumstances the interest of justice forbids strict application of the rule. Commonwealth v. Bohannon, 376 Mass. 90, 94 (1978), S.C., 385 Mass. 733 (1982), citing Miller v. Curtis, 158 Mass. 127, 131 (1893) (rule against introducing witness’s prior bad acts is not inflexible). We have applied this exception in only one case, Commonwealth v. Bohannon, where we allowed evidence of prior false accusations of rape to impeach a witness’s credibility. Specifically, the special circumstances included: “the witness was the victim in the case on trial, her consent was the central issue, she was the only Commonwealth witness on that issue, her testimony was inconsistent and confused, and there was a basis in independent third-party records for concluding that the prior accusations of the same type of crime had been made and were false.” Commonwealth v. Sperrazza, 379 Mass. 166, 169[*152] (1979), citing Bohannon, supra at 95. ^[4] LaVelle now asks us to expand the Bohannon exception to cover the facts of his case. His arguments, however, are not persuasive.

Generally, “[t]he admissibility of . . . evidence of prior bad acts lies in large measure in the discretion of the trial judge.” Commonwealth v. McGeoghean, 412 Mass. 839, 841 (1992). In Sperrazza, we held that ,a trial judge did not abuse his discretion to limit cross-examination on a collateral matter when he excluded evidence that the Commonwealth’s sole eyewitness to the defendant’s presence at a murder scene had falsely reported that she had been kidnapped. Sperrazza, supra at 169. As in Sperrazza, we find no abuse of discretion in the present case. Like Bohannon, there was only one eyewitness and the defendant had independent third-party evidence that the eyewitness had made prior false allegations to the police. However, unlike Bohannon, the witness Robinson was not the victim in the trial, the witness’s testimony was not inconsistent and confused, the false report did not concern a crime similar to the one at trial, nor was there a pattern of false allegations of the same crime. Given this factual predicate, we hold that the trial judge did not abuse his discretion in determining that Robinson’s prior false claims were collateral or cumulative and that the Bohannon exception does not apply. ^[5]

[*153] 3. Evidence of bias. The defendant also asserts that the evidence concerning Robinson’s false assault report should have been admissible to show bias. Certainly, in contrast to prior bad acts, evidence of bias is almost never a collateral matter. Liacos, supra at 145. Indeed, cross-examination to show bias or prejudice is a matter of right that may assume constitutional dimensions if the witness has testified to material facts. Commonwealth v. Michel, 367 Mass. 454, 459 (1975).

In this case, the defendant argues that the incident reveals (1) a close relationship between Robinson and the detectives, (2) Robinson’s need to seek police protection from physical harm, and (3) Robinson’s need to avoid prosecution for making false statements to police officers. ^[6] The defendant correctly states that a criminal defendant has the right to cross-examine a government witness to reveal a motive which might prompt the witness to testify falsely on behalf of the government. See Commonwealth v. Dougan, 377 Mass. 303 (1979). Cf. G. L. c. 233, § 201 (conviction cannot be based solely on testimony of immunized witness). Determining whether the evidence demonstrates bias, however, falls within the discretion of the trial judge. See, e.g., Commonwealth v. D’Agostino, 344 Mass. 276, 280, cert, denied, 371 U.S. 852 (1962). We have upheld a trial judge’s determination that proffered evidence does not show bias when the witness’s statements to the police made before “he became susceptible to official pressure” do not differ significantly from his testimony at trial. Compare Commonwealth v. Haywood, 377 Mass. 755, 762-763 (1979) (arrest record showing charges pending against witness was properly excluded as collateral when statements made before the witness’s arrest did not dif[*154] fer from witness’s testimony at trial), with Commonwealth v. Connor, 392 Mass. 838, 841 (1984) (defendant has right to question witness about pending criminal charges when witness’s prior statements were inconsistent with testimony at trial), and Commonwealth v. Martinez, 384 Mass. 377, 380-381 (1981) (trial judge erred by refusing to allow cross-examination on witness’s pending appeals of criminal convictions when witness first testified as to observing defendant two or three times and then testified on rebuttal as to seeing him fifteen or sixteen times). In Haywood, we upheld a trial judge’s determination that an arrest record was collateral to the issue of bias because if the record were admitted, then the Commonwealth would be entitled to introduce the witness’s prior consistent statements and hence there would be no evidence that pending charges affected the witness’s testimony. Haywood, supra at 762-763. Similarly, in LaVelle’s case there is no evidence that Robinson ever changed his account of the drug deal with LaVelle, and therefore, there is no evidence of bias to justify overturning the trial judge’s decision to exclude the incident as collateral. ^[7]

This case is analogous to Commonwealth v. Donahue, 369 Mass. 943, 951, cert. denied, 429 U.S. 833 (1976), in which we held that because there was extensive inquiry into the witness’s bias and credibility in general, it was within the judge’s discretion to exclude a specific inquiry. We have stated that “[t]he right [to cross-examine to show bias or prejudice] is not necessarily infringed by curbing inquiry if the matter sought to be elicited has been sufficiently aired.” Commonwealth v. Hicks, 377 Mass. 1, 8 (1979). In this[*155] case, the defense counsel was allowed to explore on cross-examination several issues bearing on the witness’s bias and credibility including payment for undercover work, use of aliases, a false report of the death of his son, prior undercover work for operation Last Call, and three prior felony convictions. Based on the breadth and depth of this cross-examinatian over areas which impugned the witness’s credibility and raised the possibility of bias, we conclude that if any errors as to the admissibility of evidence were made at trial, the defendant suffered no prejudice. ^[8]

4. Hearsay evidence. Lastly, the defendant claims that the trial judge committed reversible error by admitting hearsay evidence of Robinson’s past relationship with the police for the purpose of bolstering his credibility and reliability. He points to a detective’s testimony concerning Robinson’s initial contacts with police, his knowledge of drug trafficking activity, his motives for aiding the police, his participation in operation Last Call, and his statements concerning LaVelle. While the testimony of the detective as to statements made by Robinson is clearly hearsay, “[t]he hearsay rule forbids only the testimonial use of reported statements. It does not preclude the use of such statements for other valid purposes such as . . . the state of police knowledge which impelled the approach to the defendant.” Commonwealth v. Miller, 361 Mass. 644, 659 (1972). See Commonwealth v. Bradshaw, 385 Mass. 244, 269-270 (1982) (prosecutor entitled to present full picture of events surrounding the incident). After[*156] reviewing the detective’s testimony, we affirm the trial judge’s determination that, to the extent the testimony included hearsay statements, the information was relevant to the state of police knowledge which led them to use Robinson as an informant and to seek out LaVelle as a possible drug trafficker.

For these reasons, we conclude that there were no prejudicial errors, and, therefore, we affirm the convictions.

Judgments affirmed.