On April 6,1978, after a lengthy jury trial in the Superior Court, the defendant was convicted on six indictments containing a total of nine counts charging him with burning dwelling houses in Boston at 413 and 461 Massachusetts Avenue and 3-5 Woodlawn Street (G. L. c. 266, § 1), burning the buildings at 413 Massachusetts Avenue and 3-5 Woodlawn Street with intent to defraud the insurer (G. L. c. 266, § 10), and bribery of a State employee (G. L. c. 268A, § 2). He received nine concurrent sentences: five sentences of fifteen to twenty years for arson, three sentences of two and one half to three years for arson to defraud an insurance company, and a sentence of two and one half to three years for bribery.
The defendant appeals, alleging several errors: (1) that the testimony of an immunized witness, Francis Fraine, was insufficiently corroborated by the testimony of one George Lincoln, (2) that the defendant’s admissions were insufficient to convict him of bribery, (3) that he was denied the right to cross-examine a witness on a critical issue, (4) that he was prejudiced by the observable presence of plainclothes police officers assigned to protect Lincoln, and (5) that he was denied the effective assistance of counsel. We affirm.
We briefly summarize the facts that the jury could have found and discuss below in more detail the evidence relevant to the errors alleged. The defendant was a licensed real estate and insurance broker. Fraine, an electrical inspector for the city of Boston, approached the defendant in early 1973 to seek his assistance in selling the building at 461 Massachusetts Avenue which Fraine owned. By November, 1973, the building had not been sold, and Fraine agreed with the defendant to have it burned. The defendant engaged the services of Lincoln to set fire to the building, and he set the first fire there on November 30, 1973. Fraine was not satisfied with the resulting damage, and Lincoln set a second fire on December 2, 1973.
*304After the first fire Fraine, according to his testimony, asked one James DeFuria, a lieutenant in the State police assigned to the Fire Marshal’s office, “Can you be of any aid to me in regards to . . . this particular fire?” DeFuria met with Fraine and promised to help him. Later he called Fraine to inform him that his insurance check for $18,000 had been processed. Fraine paid DeFuria $300. Three months after the fires Fraine conveyed the property to Lincoln.
In July of 1973 Paul Caruso purchased the property at 413 Massachusetts Avenue from the defendant and gave the defendant a mortgage. Caruso had a dispute with the defendant over repairs due on the property and made no payments on the mortgage. The defendant attempted to get Caruso to agree to have the property burned, but Caruso refused. In January 1974, the defendant began foreclosure proceedings on the mortgage and asked Lincoln to burn the building. Lincoln set a fire in the building on January 24, 1974. The defendant hired another person to set another fire there on January 28, 1974. Caruso told DeFuria, who investigated the fires, that the defendant had arranged to have them set.
Later that year Fraine advised the defendant to “loan” DeFuria some money because DeFuria was aware of some accusations against the defendant contained in a report pertaining to 413 Massachusetts Avenue. Both the defendant and DeFuria admitted to Fraine that the defendant had “loaned” DeFuria “a few dollars” to help the defendant in pending litigation between him and Caruso, and the defendant admitted to Lincoln that he had paid DeFuria to help the defendant collect the insurance proceeds for the fires at 413 Massachusetts Avenue and to retrieve from the Fire Marshal’s Office a report of Caruso’s statements to DeFuria implicating the defendant.
The defendant also engaged the services of Lincoln to burn the property at 3-5 Woodlawn in behalf of the owner. Lincoln set the fire there on February 14, 1975, and he was paid by both the defendant and the owner. The owner collected $13,400 in insurance.
*3051. The corroboration of Frame’s testimony. At trial two principal Commonwealth witnesses against the defendant were Frame and Lincoln. Fraine received a grant of immunity pursuant to G. L. c. 233, §§ 20E and 20F. The testimony of an immunized witness must be corroborated before it can serve as a ground for a conviction. G. L. c. 233, § 201.1
Although the defendant does not argue that Frame's testimony was not corroborated by the testimony of Lincoln, he does argue that the terms of Lincoln’s plea bargaining agreement with the Commonwealth amounted to a “virtual immunity” and that such “virtual immunity” also required Lincoln’s testimony to be corroborated. Because there was insufficient corroboration of Lincoln’s testimony, according to the defendant, the trial judge erred in failing to grant the defendant’s motions to strike and for required findings of not guilty on several of the indictments.2
We see no merit in the defendant’s “virtual immunity” argument. Lincoln’s agreement with the Commonwealth was that Lincoln would receive, in exchange for truthful testimony about his activities as an arsonist, protective custody, a government recommendation against incarceration on seventeen indictments pending against him, and relocation after the trials. Such an agreement does not provide him with the full protection of judicially granted immunity under G. L. c. 233, § 20G, and does not call into play the provisions of § 201. Since Lincoln had not been *306granted immunity under the provisions of the statute, his testimony did not need corroboration and therefore could provide sufficient corroboration for Frame's testimony. There is no other requirement in this Commonwealth that the testimony of an accomplice requires corroboration. Commonwealth v. Watkins, 377 Mass. 385, 389 (1979). We note that since all the terms of the plea bargain were disclosed to the defendant and explored in Lincoln’s testimony, the jury were adequately informed and could properly determine the credibility and weight of his testimony in light of the plea bargain. See Commonwealth v. Allen, 379 Mass. 564, 584-585 (1980).
2. Bribery. The defendant argues that the judge erred in denying his motion for a required finding of not guilty on the bribery indictment. The evidence consisted largely of the defendant’s admissions, contained in the testimony of Fraine and Lincoln, of making payments of money to DeFuria. DeFuria did not testify.
In reviewing the denial of a motion for a required finding of not guilty, we consider the evidence in the light most favorable to the Commonwealth and draw such inferences from that evidence as would be permitted a rational jury. Commonwealth v. Sherry, 386 Mass. 682, 687 (1982). See Commonwealth v. Scanlon, 373 Mass. 11, 19 (1977); Commonwealth v. Medina, 380 Mass. 565, 573 (1980). We hold that there was sufficient evidence to convict the defendant of at least one of several incidents of alleged bribery,3 an incident involving the defendant’s paying De-Furia to retrieve from the State Fire Marshal’s Office in Boston records allegedly containing some accusations made by Caruso against the defendant. Lincoln testified that the defendant had told him that he was paying DeFuria to retrieve these records. This admission was supplemented by other direct and circumstantial evidence: that DeFuria was *307a lieutenant at the State Fire Marshal’s Office, that Caruso had been interviewed by personnel at that office, that there were no records of that interview at the office, that DeFuria and the defendant had dealt with each other in another transaction, and that Fraine had advised the defendant to pay DeFuria to obtain DeFuria’s assistance.
“An admission in a criminal case is a statement by the accused, direct or implied, of facts pertinent to the issue, which although insufficient in itself to warrant a conviction tends in connection with proof of other facts to establish his guilt.” Commonwealth v. Bonomi, 335 Mass. 327, 347 (1957). The defendant’s admission, combined with the direct and circumstantial evidence summarized above, provided sufficient proof of bribery. We see no reason to depart from the settled law of the Commonwealth, as the defendant urges us to do, that a defendant’s admissions do not require corroboration in order to serve as a basis for a conviction (Commonwealth v. Machado, 339 Mass. 713 [1959]), and that the corpus delicti need not be proven separately without considering these admissions (Commonwealth v. Zelenski, 287 Mass. 125, 130 [1934]; Commonwealth v. Kimball, 321 Mass. 290, 292-293 [1947]).4 There was no error in denying the defendant’s motion.5
*3083. Cross-examination. On direct examination by the Commonwealth, Caruso was asked about a foreclosure proceeding in which the defendant and Caruso were opposing parties. In response to the question, “Who testified for Shaheen [in that proceeding]?” Caruso answered, over objection, “Lieutenant James DeFuria.” On cross-examination the judge excluded the first two questions, “And what did he say?” and “What did Lieutenant DeFuria say in the courtroom, Mr. Caruso?” The judge continued to exclude questions to the same effect subsequently asked during the extensive cross-examination, although he made it clear that the defendant could cross-examine to disclose bias, prejudice, or lack of credibility. See Commonwealth v. Hesketh, 386 Mass. 153, 160-161 (1982). The defendant argues that he was denied his right to cross-examine Caruso on a critical issue.
It was properly within the judge’s discretion to allow the admission of Caruso’s testimony for the limited purpose of disclosing the nature of the relationship between the defendant and DeFuria. See Commonwealth v. Florentino, 381 Mass. 193, 195 (1980). The defendant’s questions on cross-examination were overly broad and would have permitted the introduction of collateral matters. The trial judge is not required to permit questions on cross-examination which are not properly formed to elicit relevant testimony, Commonwealth v. Kennedy, 3 Mass. App. Ct. 218, 222-223 (1975), and has discretion to exclude testimony pertaining to collateral matters, Commonwealth v. Chase, 372 Mass. 736, 747 (1977), Commonwealth v. Kronis, 1 Mass. App. Ct. 303, 307 (1973). In view of the extensive cross-examination which was allowed, there was no error in excluding the questions which would have introduced in evidence testimony given in another proceeding.
*3094. Officers in the courtroom. The defendant argues that the plainclothes police officers assigned to protect Lincoln should have been seated, as he requested, unobtrusively among the spectators instead of on the side of the courtroom facing the jury. The presence of these officers, he argues, combined with Lincoln’s testimony that the Commonwealth had promised that he would be “personally protected from bodily harm by possible assailants” prejudiced the defendant by making it appear that he presented a threat to Lincoln. When defense counsel questioned the seating arrangements for these officers, the trial judge commented, in the jury’s absence, that the “gentlemen sitting in the leather chairs on the side of the courtroom in civilian clothes . . . look like lawyers or spectators, as far as I’m concerned.” The defendant has not pointed to anything which would call the trial judge’s observation into question. Moreover, we find nothing which would indicate that the purpose of the officers’ presence was known to the jury or that their presence prejudiced the defendant’s right to a fair trial. Contrast Commonwealth v. Hogan, 12 Mass. App. Ct. 646, 655-656 (1981) (plainclothes police officers escorted witnesses to the stand). There was no abuse of discretion in the denial of the defendant’s request (which was never made the subject of a formal motion) to seat the officers elsewhere.
5. Ineffective assistance of counsel. In a separate brief filed pro se,6 the defendant lists forty-five particulars to support his claim that he was denied the effective assistance of trial counsel. Several of the claims are frivolous on their face. Many others deal with the preparation of the case or with collateral matters. These claims would require a factual foundation before their merits could be properly evaluated. The defendant, however, had made no effort to obtain the requisite foundation by filing a motion for new *310trial, with suitable supporting materials, in the trial court. See Mass.R.Crim.P. 30(b) and (c), 378 Mass. 900-901 (1979). We decline to pass upon the contentions on this inadequate record. We would venture the general observation, however, that the trial transcript appears to show zealous work for the defendant by his counsel, who, among other things, engaged in extensive and probative cross-examination of witnesses, made timely and persistent objections, made and argued motions to strike and for directed verdicts, put on witnesses in defense, forcefully argued the defendant’s position to the jury and requested jury instructions. The record does not suggest that counsel’s performance fell below “that which might be expected from an ordinary fallible lawyer.” Commonwealth v. Saferian, 366 Mass. 89, 96 (1974).
Judgments affirmed.