OPINION

This appeal arises from the refusal of a witness, on grounds of self-incrimination, to answer questions upon an oral deposition taken in a civil antitrust action. Pursuant to Fed.R.Civ.P. 37, plaintiffs filed a motion to compel the testimony of the witness, Edward H. McCulloch. Pursuant to Fed.R.Civ.P. 26(c) and 30(d), McCulloch moved for a protective order terminating the deposition entirely. The district court denied both motions and both parties appealed. We affirm the denial of both motions.

Brought against four manufacturers of contract hardware, the antitrust suit alleges that the defendants illegally conspired to fix prices at inflated levels by allocating jobs, territories, and customers, and by jointly enforcing such restrictions through their distributors. During the years 1954-1965, McCulloch was national sales manager and later vice-president of sales for Russwin, a division of Emhart Corp., one of the defendants.

Plaintiffs first contend that McCul-loch has no right to assert his privilege against self-incrimination because there is not the remotest chance that he could be criminally prosecuted for his part in the antitrust violations committed by his employer Emhart. They cite the oft-stated rule that “if the testimony sought cannot possibly be used as a basis for, or in aid of, a criminal prosecution against the witness,” the Fifth Amendment rule ceases to apply, its object being to protect the witness from participating in the establishment of his own guilt. Brown v. Walker, 161 U.S. 591, 597 , 16 S.Ct. 644 , 40 L.Ed. 819 (1896). Thus, if by reason of a grant of immunity or the statute of limitations, the only danger of prosecution is an imaginary one, the witness is not justified in refusing to answer. See e. g., United States v. Goodman, 289 F.2d 256, 259 (4th Cir. 1961), vacated on other grounds, 368 U.S. 14 , 82 S.Ct. 127 , 7 L. Ed.2d 75 .

In the present ease, however, McCul-loch did not receive a grant of immunity or even informal assurances that he would not be prosecuted by federal or state governments. Furthermore, it appears that the statute of limitations for criminal conspiracy had not run at the time of the deposition, particularly since McCulloch had been working for one or more of the corporate defendants up until the time of the deposition and arguably could have remained a part of the conspiracy at that time.

Although the federal government and the states do not appear particularly interested in bringing criminal actions against the defendant corporations or their employees, the right to assert one’s privilege against self-incrimination does not depend upon the likelihood, but upon the possibility of prosecution. See Hoffman v. United States, 341 U.S. 479, 486-487 , 71 S.Ct. 814 , 95 L.Ed. 1118 (1951); Isaacs v. United States, 256 F.2d 654, 658 (8 Cir. 1958).

Plaintiffs also contend that, in voluntarily testifying to and admitting certain incriminating facts, McCulloch waived any privilege against testifying further concerning his involvement in the alleged conspiracy. Whatever may be the rule with respect to such a “waiver” by a criminal defendant who elects to take the stand in his own behalf, see Brown v. United States, 356 U.S. 148, 155-166 , 78 S.Ct. 622 , 2 L.Ed.2d 589 (1958), an ordinary witness may “pick the point beyond which he will not go,” and refuse to answer any questions about a matter already discussed, even if the facts already revealed are incriminating, as long as the answers sought may tend to further incriminate him. Shendal v. United States, 312 F.2d 564, 566 (9 Cir. 1963). See Hashagen v. United States, 283 F.2d 345, 349 (9 Cir. 1960).

Rogers v. United States, 340 U. S. 367 , 71 S.Ct. 438 , 95 L.Ed. 344 (1951), relied upon by plaintiffs, does not hold to the contrary. That case merely invoked the well-accepted rule that where incriminating facts have been revealed without claiming the privilege, the privilege cannot then be invoked to avoid disclosure of the details. The Court then held, however, that “[a]s to each question to which a claim of privilege is directed, the court must determine whether the answer to that particular question would subject the witness to a ‘real danger’ of further crimination.” Id. at 374 , 71 S.Ct. at 442 (footnote omitted).

The proper inquiry in this case then, is not whether McCulloch waived his privilege simply by giving incriminating testimony as to certain company practices, but whether, in light of his prior disclosures, the testimony sought could possibly incriminate him further.

Criminal conspiracies in restraint of trade are difficult to prove. Consequently, the testimony sought by plaintiffs, dealing with McCulloch’s knowledge and intent and with specific instances of attempted restraint on competition, could very well provide a link in the chain of evidence needed in a subsequent prosecution. If the answers could possibly provide such a link, the witness may refuse to answer. See Bursey v. United States, 466 F.2d 1059, 1072 (9 Cir. 1972); Shendal v. United States, supra, 312 F.2d at 565 . The testimony sought in this case is much more incriminating and extensive than that sought in Shendal, supra, where this court upheld a witness’ refusal to say how much money he (illegally) collected from a gambling debtor, even though the witness had earlier testified as to the nature of the collection, the person who sent him, and the manner in which the money was delivered.

McCulloch’s claim that the district court abused its discretion in denying his motion to terminate the deposition entirely is without merit. Under Fed.R.Civ.P. 26(c) and 30(d), a district court has broad discretion with respect to the termination of a deposition. The cases relied on by McCulloch are totally inapposite to the present case.

The district court’s orders are affirmed.