OPINION

The defendants, Gus Kalevas and Thomas Davenport, are named in a seven-count indictment charging them with obstructing and impeding a grand jury investigation, subornation of perjury, intimidation of witnesses, the making of false statements before a grand jury, and conspiracy to commit the aforementioned acts. The indictment alleges that Kalevas and Davenport conspired to obstruct a grand jury investigation of Kalevas’ activities in connection with an interstate prostitution business. Specifically, the indictment charges that Kalevas and Davenport, a lawyer specializing in criminal defense practice, procured and induced Albert Schlanger, Charles Leris and Russel Joseph, all of whom were associated with the affairs of the Roxy Burlesque Theatre, to testify falsely before the grand jury.1 In addition, the indictment alleges that Davenport violated 18 U.S.C. § 1512 by using intimidation and by threats, and engaging in misleading conduct to cause potential grand jury witnesses to evade subpoenas by the grand jury. The indictment further charges, in a separate count in which only Kalevas is named, that he violated 18 U.S.C. § 1623 by giving false testimony to the grand jury by submitting a document that misstated the income of the Roxy Burlesque Theatre for the week of June 4, 1984.

Defendant Davenport moves to dismiss the indictment and requests additional discovery, a bill of particulars, and severance from the trial of Kalevas. Kalevas moves to sever his trial from that of Davenport.2

DISMISSAL OF THE INDICTMENT

Davenport moves to dismiss the indictment, or alternatively for an in camera inspection of the grand jury proceedings, on the grounds that the grand jury may not have been informed of the criminal *1525activities of the grand jury witnesses; that the grand jury may have been improperly instructed on the applicable laws; and that if Schlanger, Leris and Joseph did not testify before the grand jury, the limitations on the use of hearsay evidence in grand jury proceedings were exceeded. Davenport has not presented the slightest evidential support for these conjectural claims. Given the absence of any factual support for the allegations of misconduct, there is no reason to disregard the presumption of regularity of grand jury proceedings by either dismissing the indictment or inspecting the minutes in camera.3 “Speculation and surmise as to what occurred before the grand jury is not a substitute for fact.”4 While counsel for Davenport stated during oral argument that his investigator “had been told” by counsel for Joseph that Joseph did not testify before the grand jury and that “there was a strong question” whether Schlanger had testified, Davenport has submitted no affidavit from Joseph or Schlanger to support the claim that they did not appear before the grand jury or any explanation for failure to submit one.5 If an inspection of grand jury minutes were to be granted on the paucity of “information and belief allegations” here submitted, in effect it would mandate the granting of such applications in almost every case — a result contrary to the long established policy in this circuit6 and upheld by the Supreme Court.7

The Supreme Court, in Costello v. United States,8 made clear that an indictment, valid on its face, returned by a legally constituted and unbiased grand jury is all that is required by the Fifth Amendment.9 While courts have carved narrow exceptions to the Supreme Court’s holding in Costello,10 dismissal of the indictment is not warranted, whether or not Joseph appeared before the grand jury. “Presentation to a grand jury of hearsay or other evidence inadmissible at trial is not per se prohibited ... at least so long as the reliance upon it is not so extensive as to mislead the grand jury as to the strength of the evidence.”11 Similarly, the prosecution is under no obligation to present evidence of the backgrounds of witnesses appearing before the grand jury since impeachment evidence would not constitute substantial evidence negating other proof offered to establish probable cause that the defendant committed the crimes charged.12 Davenport’s motion to dismiss the indictment is denied.

Davenport also moves to dismiss count six of the indictment on two grounds. First, he alleges that count six, which charges him with violations of 18 U.S,C. *1526§ 1512, is “improperly pleaded” because it does not provide enough information to allow preparation of defenses and to protect against double jeopardy. Count six states, in its entirety:

The Grand Jury further charges:

In or about May, June, and July 1984, in the Southern District of New York and elsewhere, defendant THOMAS DAVENPORT, and others known to the Grand Jury, unlawfully, wilfully and knowingly did use intimidation and threaten other persons and attempt to do so, and engaged in misleading conduct towards other persons, with intent to cause and induce said persons to evade legal process summoning those persons to appear as witnesses in an official proceeding, to wit, a Grand Jury investigation in the United States District Court for the Southern District of New York. (Title 18, United States Code, Sections 1512 and 2.)

The foregoing sufficiently, although not in great detail, informs the defendant of the crime charged; it both parallels the language of section 1512 and sets forth an approximate time and place for the acts allegedly committed. Our Court of Appeals has stated on several occasions that “an indictment need do little more than to track the language of the statute charged and state the time and place (in approximate terms) of the alleged crime.”13 Here, in addition to the constitutionally sufficient indictment allegation,14 the government, by letter dated October 10, 1985, has provided the defendants with the names of the alleged victims of the intimidation and with more specific dates.

Second, in arguing for dismissal of count six Davenport raises several constitutional challenges to 18 U.S.C. § 1512, which is part of the Victim and Witness Protection Act of 1982.15 Davenport argues that count six is constitutionally defective because 18 U.S.C. § 1512(c) shifts the burden of proof from the government to the defendant. Section 1512(c) provides an affirmative defense to a defendant “that the conduct consisted solely of lawful conduct and that the defendant’s sole intention was to encourage, induce, or cause the other person to testify truthfully,” as to which the defendant has the burden of proof by a fair preponderance of the evidence. Davenport asserts that section 1512(c) violates the Supreme Court’s decision in Mullaney v. Wilbur16 striking down a Maine statute that did not require the prosecution to prove every element of the offense charged beyond a reasonable doubt.

In Patterson v. New York,17 decided two years after Mullaney, the Supreme Court upheld New York’s murder statute, which provides an affirmative defense of “extreme emotional disturbance” which the defendant must prove by a preponderance of the evidence. The Court made clear that neither Mullaney nor the Constitution prohibits a legislature from requiring a defendant to prove an affirmative defense by a preponderance of the evidence. The Court reaffirmed that the Due Process Clause requires that the prosecution prove each and every element of the crime charged beyond a reasonable doubt, but held that it need not negate by such a standard the non-existence of affirmative mitigating defenses that may be raised.18

*1527The indictment, based upon the statute, sets forth the elements of the offense — the knowing use of intimidation or physical force, threats, or misleading conduct, with intent to cause or induce any person to evade legal process19 — which the prosecution must prove beyond a reasonable doubt. The elements of the affirmative defense, the lawful nature of the conduct and the intent to encourage, induce, or cause truthful testimony, are independent facts, proof of which would be sufficient to avoid criminal liability.20 Section 1512(c) does not impermissibly shift the burden of proof to a defendant. The government, to prevail, and despite evidence to sustain the prof-erred defense, must upon the entire case prove the essential ingredients of the crime charged before it may obtain a conviction; thus section 1512(c) meets the demands of the Due Process Clause.

Davenport also alleges that section 1512 is constitutionally deficient because there is no mens rea requirement. The argument was rejected by this Court in United States v. Wilson21 after examining cases challenging similar criminal statutes. There the Court held that a conviction under section 1512 requires a showing that a person intimidated, threatened, or misled another “ ‘with intent to’ (1) withhold testimony or other matter from an official proceeding, or (2) cause them to evade legal process or absent themselves from an official proceeding.” 22 None of the arguments raised by Davenport persuade the Court that its pri- or holding was erroneous.

Davenport’s final constitutional challenge to section 1512 is that the statute is void for vagueness because it fails to give sufficient notice as to what constitutes “intimidation” or “misleading conduct” and because subsection (d) provides that official proceedings need not be pending at the time the offense occurs. In United States v. Wilson, this Court held that the statute is not unconstitutional, stating, “[wjhether the statements made and the acts engaged in amount to ‘true threats’ is a question of fact for the jury.”23

Prior to its amendment in 1982, section 1503 made it unlawful, among other things, to “intimidate” witnesses. Not only were convictions upheld under section 1503 on the basis of intimidation,24 but the statute withstood numerous constitutional challenges.25 The use of “intimidation” in section 1512 does not render the statute unconstitutionally vague. Similarly, Davenport’s allegation that section 1512’s use of “misleading conduct” is insufficient to place a defendant on notice as to what conduct is prohibited, ignores the detailed definition of “misleading conduct” set forth in 18 U.S.C. § 1515(3).26 In fact, the statute defines misleading conduct as knowing or intentional conduct, and does so in a manner which adequately apprises a person of the prohibited conduct.

*1528Finally, Davenport argues that section 1512(d), which provides that “an official proceeding need not be pending or about to be instituted at the time of the offense,” eliminates the requirement that the victim of the tampering be under subpoena, thereby rendering the statute unconstitutionally vague. Courts have long held that the subject of tampering need not be under subpoena for a defendant to be liable for obstructing justice.27 Section 1512(d) makes explicit this judicial determination and does not render the statute void for vagueness.28 On the contrary, it is more precise on this subject than the prior statute.29

For these reasons, Davenport’s motion to dismiss count six of the indictment is denied.

SEVERANCE

Davenport and Kalevas both move to be tried separately on the ground that their defenses are antagonistic. In particular, Davenport wishes to call Kalevas as an exculpatory witness, while at the same time presenting evidence tending to inculpate Kalevas. Counsel for Kalevas states that it is his intention to prove that it was Davenport, and not Kalevas, who engaged in the activities in the indictment. In addition, both defendants allege that Kalevas will be prejudiced if Davenport introduces Kalevas’ indictment in United States v. Castellano,30 in an attempt to explain why he met with Kalevas and the others. Davenport also asserts he will be prejudiced if the government elicits evidence relating to Kalevas’ alleged criminal activities.

An analysis of requests for severance must begin from the position that, absent a showing of substantial prejudice, defendants who are indicted jointly should be tried jointly.31 Here, this concept is strengthened by the fact that the indictment charges a conspiracy, in which the defendants seeking to be severed are alleged to have acted in concert.32 Even if each defendant intends to save himself at the expense of the other, that does not give rise, without more, to a showing adequate to overcome the presumption in favor of a joint trial.33 Severance for reasons of mutual antagonism may be granted only where “the jury, in order to believe the core of testimony offered on behalf of that defendant, must necessarily disbelieve the testimony offered on behalf of his codefendant.” 34

*1529Judged by this standard, the defendants fail to sustain their claims of mutually antagonistic defenses that would foreclose a fair trial. Each makes vague allegations that he may prove the other is guilty. Davenport’s defense strategy, according to his counsel, will be that Kalevas “may well have conspired” with Schlanger, Joseph and Leris to obstruct justice.35 Upon its face this is sheer conjecture. Counsel for Kalevas asserts he intends to prove through the testimony of Russel Joseph that it was Davenport who conspired with the others.

The defendants have failed to demonstrate the requisite level of antagonism between their defenses. Neither defendant has shown how he will be prejudiced by his attempt to place the blame upon his co-defendant and thereby exonerate himself. Moreover, even if they succeed in presenting evidence to support their allegations, the jury need not disbelieve the core of Kalevas’ testimony in order to believe Davenport or vice versa; their defenses are not mutually exclusive.36 The jury, for example, could accept the government’s proof, finding that each defendant was a participant in the crimes charged against them, or it could believe that neither defendant committed the alleged acts. Stating it slightly differently, the jury could believe both defendants to the extent that it believes Kalevas that Davenport conspired to obstruct justice and suborn perjury and believes Davenport that Kalevas participated in the same activities, but believe neither defendant’s contention that he did not commit the alleged acts. Further, the jury could believe Davenport that he attended the meeting with Kalevas, Schlanger, Joseph and Leris for the purpose of becoming Kalevas’ counsel in United States v. Castellano, while believing that Davenport also conspired to obstruct justice and intimidated witnesses who were likely to appear before the grand jury.

As to Davenport’s claim that severance is justified because he has “a compelling need” to call Kalevas as an exculpatory witness, it suffices to point to the affidavit of Kalevas’ counsel wherein he states his intent “to urge the jury to believe that it was Davenport not Kalevas who engaged in the conspiracy charged in the indictment.” 37 Davenport has failed to make any showing that Kalevas would offer exculpatory testimony on his behalf at a severed trial or that Kalevas would waive his Fifth Amendment privilege.38

Both defendants fear prejudice if the jury learns of Kalevas’ other alleged criminal activities, particularly his indictment in United States v. Castellano. Counsel for Davenport has stated he plans to prove that the purpose for Davenport’s meeting with Kalevas was to persuade Kalevas to retain him as counsel in the Castellano matter, not to conspire to suborn perjury or obstruct justice. Davenport and Kalevas both contend that testimony concerning the Castellano indictment will prejudice Kalevas’ ability to obtain a fair trial.

The relevance of the other criminal charges pending against Kalevas to Davenport’s defense here is not immediately apparent. While Davenport may offer as a defense that he attended meetings solely for the purpose of speaking to Kalevas *1530about representing him in a matter wherein Kalevas was named as a defendant, the specific details concerning’ the proposed retention do not add anything to his proposed defense. It would be sufficient to support his defense that the purpose of the meeting was to discuss his retention to represent Kalevas in a pending prosecution. If the jury should find that Davenport committed the acts alleged, his original purpose in associating himself with Kalevas would not shield him from liability.

Moreover, the specific details of the crimes charged may not be admissible under Fed.R.Evid. 403. Even if the other charges of criminal conduct alleged under the prior Kalevas indictment were shown to be somehow relevant to the charges in this case, the probative value of the precise nature of those unrelated charges in assisting Davenport’s defense would be subject to exclusion upon a claim of its prejudicial effect on Kalevas.39 Defendants’ claims, based on evidence which may be both irrelevant and inadmissible under Rule 403, are too speculative to support a motion for severance.40

Kalevas' argument that severance should be granted because the government may impeach Davenport with statements Davenport made to the FBI regarding Kalevas is also too speculative to support a pre-trial motion for severance. Before the government can use Davenport’s statements to impeach his credibility, Davenport must testify at trial. In that event, the government would not necessarily be in a position to use the relatively few statements Davenport made regarding Kalevas as impeachment material. Any alleged admissions or statements of an inculpatory nature by Davenport could be confined to him. Finally, the evidence must meet the requirements of Rule 403, as well as the requirements for admitting hearsay evidence. As noted above, mere surmise and conjecture are insufficient grounds for severing the trial of two defendants charged with engaging in a conspiracy.

Davenport contends, as a further basis for severance, that he will be prejudiced if the government elicits evidence of Kalevas’ alleged criminal activities. This claim is no better founded than Davenport’s claim that Kalevas may be prejudiced if Davenport discusses Kalevas’ other criminal conduct. Davenport has failed to demonstrate either that Kalevas will testify, thereby subjecting himself to potentially harmful impeachment evidence, or, more importantly, that the jury will be unable to keep the evidence relevant to each defendant separate. “The Court has no doubt that a properly instructed jury will be able to compartmentalize the evidence against each defendant and render a fair verdict as to each.”41

The final ground for severance is Davenport’s argument that count seven of the indictment is misjoined under Rule 8 or should be severed because it charges only Kalevas with making false statements before a grand jury. While only Kalevas is alleged to have violated 18 U.S.G. § 1623, all of the conduct alleged in the indictment pertains to an alleged scheme by Kalevas and Davenport to obstruct a single grand jury investigation. The indictment charges Davenport with conspiring with Kalevas to commit obstruction of justice, subornation of perjury and the making of false declarations before a grand jury. Both Davenport *1531and Kalevas are charged in count two with obstruction of justice by creating a false document for presentation to the grand jury. Further, Davenport is named in six of the indictment’s seven counts. It is axiomatic that a defendant need not be charged in each count of the indictment where he participated in a series of acts constituting the offenses.42 Count seven is not improperly joined. Nor is Davenport entitled to severance “simply because certain evidence may be admissible only against [Kalevas].”43 Davenport has failed to demonstrate substantial prejudice as a result of the joinder of count seven.

Defendants’ motions for severance are denied. As our Court of Appeals has repeatedly said, the belief of each defendant that he would stand a better chance of acquittal if tried separately from his co-defendant is not a sufficient ground for severance.44

DISCOVERY

By letter dated August 1, 1985, counsel for Davenport requested exculpatory material pursuant to Brady v. Maryland,45 including but not limited to the prior criminal history of Charles Leris, Albert Schlanger, Russel Joseph, Carol Joseph, Ann Markinson and any other witness the government reasonably expects to testify, as well as immunity orders and non-prosecution or limited prosecution agreements between the government and the aforementioned persons.46 Defendant Davenport now moves for discovery of Brady material having the “tendency to exculpate a defendant.” On this basis, Davenport seeks information from the government detailing the alleged illegal activities, or income derived from illegal activities, of Leris, Schlanger, Russel and Carol Joseph and Ann Markinson.

The purpose of the rule of Brady is to assure that a defendant gains access to material exculpatory evidence known to the government, not to provide a defendant with a general right of pre-trial discovery of all the evidence in the prosecution’s files.47 Our Court of Appeals has held, however, that Brady also imposes a duty on the prosecution to produce evidence which tends to impeach critical prosecution witnesses, upon whose testimony the government will rely on the central factual issues in controversy, by demonstrating their motive to testify favorably to the government.48 In that regard, the Court directs the government to produce to the defendants any evidence in its possession relating to the prior criminal history of Charles Leris, Albert Schlanger, Russel Joseph, Carol Joseph or Ann Markinson.

Davenport also seeks discovery of the grand jury subpoenas of the persons he allegedly intimidated in violation of 18 *1532U.S.C. § 1512. Not only has Davenport failed to demonstrate that grand jury subpoenas constitute exculpatory evidence, but section 1512 makes clear that the victims of the alleged intimidation need not have been served with subpoenas for criminal liability to attach. Davenport is not entitled to his requested discovery. Moreover, to the extent Davenport seeks the subpoenas in an effort to discover who the government contends was intimidated or threatened by Davenport, this information has been supplied in the government’s October 10, 1985 letter to defense counsel.

BILL OF PARTICULARS

Defendant Davenport moves for the production of a bill of particulars setting forth the dates, times and places at which Davenport is alleged to have suborned perjury and the specific statements or conduct the government contends constitute threats or intimidation of prospective witnesses. Counts three, four and five of the indictment, relating to the alleged subornation of penury, state the names of those who committed perjury, when they testified before the grand jury and the nature of their testimony. The government, in the letter to defense counsel dated October 10, 1985, supplied the defendants with the names of the persons allegedly intimidated by Davenport and approximate dates for those acts. The indictment, as supplemented by the government, provides defendants with sufficient information to enable them to prepare their defenses and otherwise satisfies the demands of Wong Tai v. United States.49 The granting of the requested particulars would do little more than restrict the government’s proof at trial, which is not the purpose of a bill of particulars.50 Davenport’s motion for a bill of particulars is denied.

SO ORDERED.