SUHRHEINRICH, Circuit Judge, delivered the opinion of the court, in which ENGEL, Senior Circuit Judge, joined. JONES, Circuit Judge (pp. 1374-76), delivered a separate concurring opinion.
SUHRHEINRICH, Circuit Judge.
Defendant Mullins was convicted on one count of conspiracy to obstruct justice in violation of 18 U.S.C. §§ 371, 1503, and 1512, two counts of tampering with witnesses in violation of 18 U.S.C. § 1512(b)(2)(B), and three counts of obstruction of justice in violation of 18 U.S.C. § 1503, arising out of his interference with a federal grand jury investigation involving the aviation section of the Detroit Police Department. Mullins filed a timely notice of appeal and challenges these convictions on numerous procedural and substantive grounds. For the reason stated below, we AFFIRM.
I.
In 1990, a grand jury in the Eastern District of Michigan conducted an investigation into the use of the Detroit Police Department (DPD) “secret service fund.” As part of its investigation, the grand jury issued subpoenas for the production of the flight logs of certain DPD officers assigned to the department’s aviation section. Among the logbooks subpoenaed were those kept by defendant Mullins.
After the subpoenas were served, Mullins instructed various aviation section officers to alter their logs before producing them in order to delete any references to questionable destinations such as Las Vegas and Atlantic City. Mullins also altered his own logs and those of at least one other aviation section officer. After the logs were turned over, an aviation section officer informed the government of these alterations and deletions. A second grand jury issued a second set of subpoenas to compel the testimony of the aviation section officers whose logs had been altered.
On October 23,1991, the grand jury indicted Officer Mullins and Commander Dabrow-ski, head of the aviation section, for conspiring to obstruct justice, obstructing justice, and tampering with witnesses and documents. Dabrowski pleaded guilty to the conspiracy charge and agreed to testify for the government in return for the government’s recommendation that he not be sentenced to imprisonment. The prosecution against Mullins proceeded to trial and the jury found him guilty on six of the ten counts against him. The district court sentenced Mullins to a term of twenty-seven months in prison for each of the six convictions, but ordered .these sentences to run concurrently.
II.
A. Sufficiency of the Evidence
Mullins first asserts that, as to the charges of conspiring to obstruct justice (Count I) and obstructing justice by inducing Officer Belk to alter his flight log (Count V), the [1368]*1368evidence was insufficient as a matter of law. We disagree.
1. Conspiracy
To convict Mullins of a conspiracy under 18 U.S.C. § 371, the government was required to prove (1) that there was an agreement whose object was to obstruct justice, (2) that Mullins knowingly and voluntarily joined in this agreement, and (3) that at least one overt act was committed in furtherance of the object of the agreement. United States v. Meyers, 646 F.2d 1142, 1143-44 (6th Cir.1981). Twenty-six overt acts were alleged, including four instances in which Mullins altered his own logbook, four instances in which Mullins altered the logbooks of others, and thirteen instances in which Mullins directed others to alter their logbooks.
The government’s evidence showed that when the grand jury subpoenas arrived, Dabrowski bought a new logbook and transcribed entries from Mullins’ log into it. Both Mullins and Dabrowski inspected the logbooks of other officers and, on several occasions, Mullins directed the officers to make changes to their records. One officer testified that he went over his logbook with Mullins “five or six times” as the two of them decided “what to do.” Another testified that Mullins told him to “correct” his log and then take it to Dabrowski for review. From these facts, it may reasonably be inferred that Mullins, Dabrowski and others were acting pursuant to an agreed objective of preventing certain information from reaching the grand jury.
Mullins argues that, because Dabrowski testified that Mullins did not instruct him to alter his logbook and that he made the alterations without Mullins’ knowledge, this conclusively established that the two had no “agreement”, to obstruct justice. Mullins’ argument is unpersuasive. Even though a juror might have concluded, based on that portion of Dabrowski’s testimony, that there was no conspiracy between Mullins and Da-browski, that is not the issue. The issue is limited to whether, in light of this testimony, no reasonable juror could find, beyond a reasonable doubt, the existence of the conspiracy charged in this case. Jackson v. Virginia, 443 U.S. 307, 319, 99 S.Ct. 2781, 2789, 61 L.Ed.2d 560 (1979). We hold that this testimony, while it might support an acquittal, does not require one. This point is denied.
2. Obstruction
Mullins insists that he cannot be convicted under Count V of the indictment because that count requires proof that he “did aid and abet .another” in obstructing justice “by aiding, inducing or procuring the creation by [another officer] of false and fraudulent entries in [that officer’s] pilot logbook.” Mullins contends there was no proof, direct or circumstantial, of his having “aided or abetted” Dabrowski in committing an obstruction of justice.
Mullins’ argument is misdirected. The crime charged, as the second portion quoted makes clear, is obstruction of justice through inducing a particular officer to change records in that officer’s flight log. The officer whose logbook is the focus of Count V testified that Mullins told him to alter his logbook and to take it to Dabrowski for Dabrowski to see. Thus, the evidence was sufficient to permit a finding of guilty on Count V.
The government pleaded the count in terms of accessorial principles, perhaps because it was difficult to tell — as between Mullins and Dabrowski — who was the principal and who the accessory. It is axiomatic, however, that the government may always prove the defendant is guilty as a principal, even where the indictment charges only that he acted as an accessory. United States v. Garcia-Nunez, 709 F.2d 559, 562 (9th Cir.1983) (citing United States v. Bryan, 483 F.2d 88, 95-97 (3rd Cir.1973)). Thus, the government’s use of accessorial liability phrasing in Count V did not preclude it from showing, as it did, that Mullins was guilty as a principal. Mullins alleges no prejudice from this immaterial variance, nor could there have been any. This point is denied.
B. Instructions
Mullins also contends that his convictions must be reversed because the trial [1369]*1369court erred in refusing to instruct the jury regarding “specific intent.” Mullins proffered an instruction requiring the jury to return a verdict of acquittal if it found that the government failed to prove that Mullins had a “specific intent to obstruct justice.” Mullins farther defined this “specific intent” as proof that he “knowingly did an act which the law forbids ..., purposely intending to violate the law.”
The trial court refused Mullins’ request and instructed the jury, with respect to the charges of obstructing justice, that the government must prove:
The defendant Gene R. Mullins then corruptly endeavored to influence, obstruct or impede the due administration of justice ... with the intent of purpose to obstruct.
As to the charges of tampering, the district court instructed the jury that the government must prove:
[T]he defendant ... knowingly attempted to use intimidation or to corruptly persuade the person identified in the indictment; and
The defendant did so with intent to cause or induce the person to alter, destroy, mutilate, or conceal an object or impair the object’s integrity or availability for use in a federal grand jury proceeding.
These instructions accurately and succinctly convey the mental states necessary for conviction under 18 U.S.C. §§ 1503, 1512. See United States v. Jeter, 775 F.2d 670, 679 (6th Cir.1985) (mens rea for § 1503 is the “general intent of knowledge as well as the specific intent of purpose to obstruct”) (emphasis omitted), cert. denied, 475 U.S. 1142, 106 S.Ct. 1796, 90 L.Ed.2d 341 (1986); United States v. Scaife, 749 F.2d 338, 348 (6th Cir.1984) (mens rea for § 1512 is a “knowing” use of corrupt persuasion with an intent to interfere with official proceedings). The district court’s instructions had the added advantage of accurately conveying the law without subjecting the jury to a confusing discourse on the difference between “general” and “specific” intent. See Liparota v. United States, 471 U.S. 419, 433 n. 16, 105 S.Ct. 2084, 2092 n. 16, 85 L.Ed.2d 434 (1985) (courts encouraged to “eschew use of difficult legal concepts like ‘specific intent’ ”); United States v. S & Vee Cartage Co., 704 F.2d 914, 919 (6th Cir.) (instruction on mens rea adequate “without resorting to the words ‘specific intent’”), cert. denied, 464 U.S. 935, 104 S.Ct. 343, 78 L.Ed.2d 310 (1983). Taken as a whole, we hold the jury instructions “fairly and adequately submitted] the issues and applicable law to the jury.” United States v. Buckley, 934 F.2d 84, 87 (6th Cir.1991) (quoting United States v. Martin, 740 F.2d 1352, 1361 (6th Cir.1984)).
Moreover, we are unable to discern any possible prejudice to Mullins under the instructions given. Mullins defended on the theory that the changes he made and ordered were merely to avoid embarrassment for the department and not with an intent to obstruct justice. This defense could be made, and was in fact made, just as effectively under the instructions given as they could have been under the instructions proffered. The fact that the jury was not convinced regarding Mullins’ explanations cannot be attributed to the district court’s instructions. Therefore, even assuming error, there is no basis for reversal.
Mullins second argument with respect to the jury instructions concerns the district court’s refusal to give the following instruction:
In order to complete the offense of destroying evidence, it is necessary to show that the defendant knew that the documents to be altered or destroyed bore a reasonable relationship to the inquiry of the pending grand jury which he was charged with obstructing.
Mullins contends that the grand jury was investigating possible misuse of the department’s “secret service fund” and, therefore, any changes with regard to improprieties in the aviation section did not bear a “reasonable relationship” to the grand jury’s investigation. In support, Mullins cites United States v. Bashaw, 982 F.2d 168, 170 (6th Cir.1992); United States v. Sun Myung Moon, 718 F.2d 1210, 1236 (2d Cir.1983), cert. denied, 466 U.S. 971, 104 S.Ct. 2344, 80 L.Ed.2d 818 (1984); and United States v. Ryan, 455 F.2d 728, 734 (9th Cir.1971).
[1370]*1370Bashaw does not require an instruction such as that offered by Mullins. Rather, Bashaw merely illustrates the obvious point that where the conduct complained of occurred after the judicial proceeding was completed, no intent to obstruct that proceeding can be shown. In Bashaw, the only evidence of misconduct was that the defendant “stared” at the jurors during his brother’s trial and then made threatening comments to them after the trial was over. This court reversed a conviction under 18 U.S.C. § 1503, because there was “no evidence that the conduct which is the basis for the indictment could have interfered with the due administration of justice.” Bashaw, 982 F.2d at 171.
Moon presented the opposite scenario. There, as in this case, the defendant produced fraudulently prepared documents in response to a grand jury subpoena. The court reversed the conviction, however, because — unlike the present case — the fraudulent creation of the documents was done before the jury subpoenaed the information and before such a subpoena could have been reasonably expected. Moon, 718 F.2d at 1222-23. Thus, an intent to obstruct the grand jury could not be shown.
The Ninth Circuit’s decision in Ryan more closely supports Mullins’ claims. There, the alteration of documents occurred both before and after the grand jury’s subpoena. The court reversed defendant’s conviction because “[t]here was not an iota of evidence in the record showing any relevancy of [the altered documents] to the grand jury investigation.” Ryan, 455 F.2d at 734.
In order to convict someone of violating § 1503, the government must prove that there was a judicial proceeding underway that the defendant’s actions were intended to obstruct. Cf. Pettibone v. United States, 148 U.S. 197, 207, 13 S.Ct. 542, 546, 37 L.Ed. 419 (1893) (construing predecessor statute to § 1503). A grand jury investigation is such a proceeding. United States v. Simmons, 591 F.2d 206, 208 (3d Cir.1979). The issue in Ryan, we believe, was whether the investigation was being conducted by the IRS, in which case § 1503 did not apply, or by the grand jury. Inasmuch as the grand jury in Ryan was never informed of the subpoenas and never reviewed the documents or any other evidence regarding the defendants,1 the court’s reversal seems clearly based on the ground that no “judicial proceeding” had been obstructed. Mullins’ attempt to convert “relevancy,” discussed by the Ryan court as a means of proving an ongoing judicial proceeding, into a separate element is unsupported by the language of § 1503 and, therefore, must fail. Therefore, we hold that the government need not prove, as an element of the crime, that the alterations made in response to a grand jury subpoena were relevant to the grand jury’s investigation.
In the present case, the evidence conclusively showed that what Mullins did, he did in response to the grand jury’s subpoena. The alterations Mullins made and ordered were intended to deprive the grand jury of evidence that it had decided was relevant to its investigation. There is no authority requiring this court to second-guess the scope of the grand jury’s investigation or to reverse Mullins’ convictions simply because the abuses Mullins now contends he sought to hide may not have been precisely the abuses that he asserts the grand jury sought to expose. The district court did not err in refusing Mullins’ instruction.
C. Brady Violations
Muhins argues that his convictions must be set aside'because the government failed to produce, after specific request, certain exculpatory and impeachment evidence. See Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, [1371]*137110 L.Ed.2d 215 (1963). Mullins’ assertion encompasses three categories of information: (1) Brady material that the government never produced, (2) Brady material that was provided at trial, but not in time for Mullins to put it to effective use, and (3) the “true nature” of Dabrowski’s plea agreement. Individually, and cumulatively, these arguments lack merit and do not justify reversal.
1. Material Never Disclosed
Mullins first claims that the government should have turned over matérials arising from its interviews with Inspector Parker, Mullins’ superior officer. This evidence, Mullins claims, would have negated the government’s proof of motive by showing that the questionable flights were, in fact, authorized. Additionally, Mullins contends the government’s proof of motive would have been negated by the testimony of Ronald Garlick which would rebut Dabrowski’s testimony that Garlick paid “kickbacks” to Mullins for certain purchases by the aviation section.
As a general proposition, “[tjhere is no general constitutional right to discovery in a criminal case, and Brady did not create one-” Weatherford v. Bursey, 429 U.S. 545, 559, 97 S.Ct. 837, 846, 51 L.Ed.2d 30 (1977). Rather, Brady is concerned only with cases in which the government possesses information which the defendant does not, and the government’s failure to disclose the information deprives the defendant of a fair trial. Reversal is only required, therefore, where “there is a ‘reasonable probability’ that, had the evidence been disclosed to the defense, the result of the proceeding would have been different. A reasonable probability is a probability sufficient to undermine the confidence in the outcome.” United States v. Bagley, 473 U.S. 667, 682, 105 S.Ct. 3375, 3383, 87 L.Ed.2d 481 (1985). Furthermore, the Brady rule only applies to “the discovery, after trial, of information which had been known to the prosecution but unknown to the defense.” United States v. Agurs, 427 U.S. 97, 103, 96 S.Ct. 2392, 2397, 49 L.Ed.2d 342 (1976) (emphasis added).
In United States v. Clark, 928 F.2d 733 (6th Cir.), cert. denied, — U.S. -, 112 S.Ct. 144, 116 L.Ed.2d 110 (1991), this court stated that the government’s failure to disclose potentially exculpatory information does not violate Brady “where a defendant ‘knew or should have known the essential facts permitting him to take advantage of any exculpatory information,’ or where the evidence is available to defendant from another source.” Id. at 738 (quoting United States v. Grossman, 843 F.2d 78, 85 (2d Cir.1988), cert. denied, 488 U.S. 1040, 109 S.Ct. 864, 102 L.Ed.2d 988 (1989)). Clark disposes of Mullins’ argument with regard to Parker because, as the government claims and Mullins does not refute, the government conducted only one proffer interview of Parker and sent a copy of Parker’s proffer letter to Mullins’ attorney three months before trial.
The issue with respect to Garlick’s information is more complex. .The government admits that it was in possession of a summary of. an interview with Garlick conducted by the FBI in which Garlick denied paying any kickbacks. The government argues, however, that it had no obligation to disclose that information to Mullins because Garliek’s denial was “well-known.” In support, the government cites to a newspaper article, published during the trial, that quoted Garlick as saying that “there was never any payoffs there made to anybody.”
Besides having constructive notice, it also appears that Mullins had actual notice of Garliek’s claims. By way of affidavit, Gar-lick’s attorney recounts the fact that, during Mullins’ trial, he was approached by Mullins’ attorney who asked if Garlick would be willing to testify on Mullins’ behalf. The affidavit specifically notes that Mullins’ attorney believed that “Garliek’s testimony would be exculpatory of Mr. Mullins with regard to certain testimony by another witness concerning alleged payoffs or kickbacks....”2 Therefore, because Garlick’s denial was [1372]*1372known by Mullins in time for him to attempt to make use of it in his defense, we hold that the government’s failure to disclose that information did not violate due process under Brady. See Clark, 928 F.2d at 738.
Finally, Mullins argues that the government should have disclosed that its initial interview of Garlick was conducted under a grant of immunity. Had he known of the immunity, Mullins asserts, he could have subpoenaed Garlick and compelled his testimony.
This argument, although intermingled by Mullins with the previous argument, proceeds from an entirely distinct premise. Mullins asserts that Brady requires the government to disclose a grant of immunity. In this, he is correct. See Giglio v. United States, 405 U.S. 150, 154-55, 92 S.Ct. 763, 766, 31 L.Ed.2d 104 (1972) (failure to disclose government’s promise not to prosecute its key witness required a new trial). The basis for this requirement, however, is that the information is relevant to impeach the witness, not that it is directly exculpatory of the defendant. Clearly, Brady recognizes no distinction between evidence which serves to impeach a government witness’ credibility and evidence which is directly exculpatory of the defendant. Both are “evidence favorable to the accused” and must be disclosed.
Here, however, the fact of Garlick’s immunity does not fall within either category. It cannot be said that the mere fact Garlick was given immunity makes it any less likely that Mullins was guilty of the crimes charged. Nor can it be argued that this grant of immunity was “favorable to the accused” as impeachment evidence because the government did not call Garlick and, thus, there was no one to impeach.
In essence, Mullins argues that there is a third category of information encompassed by Brady; information relevant to neither guilt nor credibility but which might be of use to the defendant in acquiring exculpatory or impeachment evidence that the defendant had thought was unavailable. We find no authority for this third classification and, specifically, no authority that the government must disclose promises of immunity made to individuals the government does not have testify at trial. Accordingly, we hold that the government had no duty to disclose Garlick’s immunity to Mullins.
We further hold that, even assuming a Brady violation and further assuming Mullins would have called Garlick and elicited favorable testimony regarding kickbacks, such evidence falls short of creating a “reasonable probability” of a different result. As discussed, there is more than ample evidence in the record to support the jury’s verdict. The mere fact that Mullins might have contradicted Dabrowski’s testimony on the somewhat-collateral issue of kickbacks would not cast any doubt on the testimony of the other officers and the altered logbooks themselves. With no showing of prejudice, Mullins’ assertions of a Brady violation provide no cause for reversal.
2. Material Disclosed at Trial
Mullins’ second category of Brady violations is equally unavailing. There, Mullins alleges that the Jencks Act documents turned over following the testimony of each of the government’s witnesses, contained Brady information that should have been turned over before trial. This issue is controlled by United States v. Presser, 844 F.2d 1275 (6th Cir.1988), in which this court held that evidence properly disclosed after testimony at trial pursuant to the Jencks Act cannot be subject to earlier disclosure on the basis of Brady. Id. at 1283-84. To this extent, the Jencks Act overrides Brady and is the sole requirement for the disclosure of such evidence. The government complied and, therefore, there was no error.
3. Dabrowski Plea Agreement
Mullins’ third category of alleged prosecu-torial misconduct concerns the nature of the government’s agreement with Dabrowski in exchange for his testimony. The government timely disclosed, and Mullins made full use of, the fact that the government had promised to seek only probation for Dabrow-ski’s plea of guilty to conspiracy. After Mullins’ trial, however, the district court rejected the government’s recommendation and informed Dabrowski that he would be sen[1373]*1373tenced to some incarceration. At this point, Dabrowski withdrew his plea agreement and the government dismissed the charges against him. Mullins argues that this was the “true nature” of the agreement all along and that its non-disclosure warrants reversal.
This claim lacks merit because it is sheer speculation. Mullins offers no proof for his assertion that the government had previously promised Dabrowski that his charges would be dropped. Instead, it appears that the government determined it would dismiss the charges against Dabrowski only after the district court refused the plea bargain, and that the government did so as a matter of grace rather than obligation. Even if the government had always intended, though not promised, to drop Dabrowski’s charges, it need not have disclosed that fact to Mullins. The government’s lenience, neither bargained for nor relied upon, would not have been relevant to impeach Dabrowski because it would not establish a quid pro quo for Dabrowski’s testimony. This claim, like the previous two, provides no basis for reversal.
D.Prior Bad Acts
Mullins argues that the district court committed reversible error by allowing the government to introduce evidence of illegal kickbacks and unauthorized use of departmental planes. This evidence, Mullins claims, was irrelevant, highly prejudicial, and barred by Rule 404(b) of the Federal Rules of Evidence. This point lacks merit.
Rule 404(b) expressly lists proof of “motive” as an issue upon which the defendant’s prior bad acts may rightfully be considered. Here, the government sought to show that the logbooks subpoenaed by the grand jury contained information tending to prove wrongdoing involving the aviation section. In so doing, the government sought to prove Mullins’ motive for altering, and ordering others to alter, these logbooks. Where the charges involve obstruction of justice, such proof of the “underlying” offense is often highly relevant to a defendant’s motive. See United States v. Maggitt, 784 F.2d 590, 597 (5th Cir.1986) (evidence of bank robbery admissible to show motive for defendants’ threats to grand jury witness); United States v. Arnold, 773 F.2d 823, 833 (7th Cir.1985) (evidence of defendants’ loansharking activities admissible to show motive to obstruct grand jury investigation of same). Therefore, admitting this evidence was not error.
There is no showing here that the jury was confused or mislead by this evidence, or that the evidence resulted in. undue delay in the presentation of the government’s case, which might require exclusion of this evidence under Rule 403.. Rather, it appears that this evidence — clearly prejudicial in that it painted Mullins as a man with something to hide — was not unfairly prejudicial inasmuch as Mullins was charged, in essence, with a coverup. This point is denied.
E.Selective Prosecution
Mullins claims that he was selectively prosecuted because of his association with former mayor Coleman Young. Asserting that his political associations are a “fundamental right,” Mullins contends that he may not be prosecuted where others similarly situated have not, simply as punishment for the exercise of that fundamental right. The government claims that others similarly situated were prosecuted in that Dabrowski, the commander of the aviation section, was also indicted. Mullins replies that the fact the government indicted Dabrowski, and then dropped those charges, strengthens his claim.
The government has broad discretion in determining who will be charged and with what crime. Wayte v. United States, 470 U.S. 598, 607, 105 S.Ct. 1524, 1530, 84 L.Ed.2d 547 (1985). To make a prima facie case of selective prosecution, the defendant must show that “ ‘the government’s discriminatory selection of him has been invidious or in bad faith, i.e., based upon such impermissible considerations as race, religion, or the desire to prevent the exercise of his constitutional rights.’ ” United States v. Hazel, 696 F.2d 473, 474 (6th Cir.1983) (quoting United States v. Berrios, 501 F.2d 1207, 1211 (2nd Cir.1974)). Moreover, a defendant must “ ‘allege sufficient facts to take the question past the frivolous state and raise a reasonable doubt as to the prosecutor’s purpose.’ ” [1374]*1374United States v. Bustamante, 805 F.2d 201, 202 (6th Cir.1986) (quoting United States v. Larson, 612 F.2d 1301, 1304-05 (8th Cir.), cert. denied, 446 U.S. 936, 100 S.Ct. 2154, 64 L.Ed.2d 789 (1980)) (emphasis in Bustamante).
We hold that Mullins has failed to make a prima facie case of selective prosecution. Commander Dabrowski, who Mullins admits does not share Mullins’ political attachment to former Mayor Young, was also prosecuted in this case. The fact that, when the district court rejected Dabrowski’s plea bargain, the government dropped its charges, does not indicate an invidious motive on the part of the government in pressing its case against Mullins. As discussed above, the apparent rationale for dropping the charges against Dabrowski was in recognition of his assistance in convicting Mullins.
Rather than a case of selective prosecution, this is a fairly ordinary example of a case in which the government forgoes charges against a number of persons involved in a crime in order to strengthen its case against one of the principal actors. Mullins, by his own admissions, carried influence in the aviation section beyond that attributable to his rank. The evidence shows that he was the principal actor in this scheme to obstruct the grand jury. The government’s decision to pursue him, even at the cost of its case against others, is not cause for reversal.
III.
For the reasons discussed above, Mullins’ convictions are AFFIRMED.