Can a witness be granted immunity from prosecution for perjury?

See also United States v. Thevis, supra, 665 F.2d 616, 640, footnote 27, where the court stated: "The incentive for abuse is strong given that the witness, because of immunity, is in no worse a legal position for having testified, and because of the heavy burden on the government to prove lack of taint, the witness in practice may improve his legal position. [p] Nor are we convinced that perjury prosecutions are an adequate deterrent. Successful perjury prosecutions are not common, and in many cases the penalty for the substantive crime will far surpass perjury penalties."

Finally,

"An immunity decision ... would require a trial judge, in order to properly assess the possible harm to public interests of an immunity grant, to examine pre-trial all the facts and circumstances surrounding the government's investigation of the case. Such collateral inquiries would necessitate a significant expenditure of judicial energy, possibly to the detriment of the judicial process overall, and would risk jeopardizing the impartiality and objectivity of the judge at trial." (United States v. Thevis, supra, 665 F.2d at p. 640.)