In this “Operation Court Broom” appeal, we affirm the appellants’ convictions and sentences.
FACTS
In the late 1980s, federal and state law enforcement officials conducted “Operation Court Broom,” an investigation into alleged corrupt activities occurring among judges and lawyers in the Dade County Florida Circuit Court. One of the targets of the investigation, Roy T. Gelber, took the office of circuit court judge for the Eleventh Judicial Circuit in Dade County in January 1989. Prior to becoming a circuit court judge in 1989, Gelber served as an elected county court judge for Dade County since 1987 and previously had practiced as a criminal defense attorney.
In Metropolitan Dade County, circuit court judges have the authority to appoint special assistant public defenders (SAPDs) and approve their compensation terms for which Metropolitan Dade County issues payment upon receipt of a court approved bill. Shortly after assuming the position of circuit court judge, Gelber had discussions with another circuit court judge, Alfonso C. Sepe, regarding making SAPD appointments for kickbacks. Sepe arranged to have Gelber appoint Arthur Massey, a lawyer, as an SAPD in return for kickbacks. Gelber appointed Massey to some eases and received kickbacks for those appointments. Likewise, Judge Harvey N. Shenberg arranged for Gelber to appoint Manny Casabielle and Miguel De-Grandy, lawyers, as SAPDs in return for kickback payments.
In August of 1989, state and federal law enforcement officials procured the services of Raymond Takiff, a lawyer, to act in an undercover capacity as a corrupt lawyer in the Operation Court Broom investigation. From August 1989 to June 1991, Takiff engaged in a number of corrupt activities with Gelber and other judges in the Eleventh Judicial Circuit. Most of Gelber’s conversations with Takiff regarding illegal conduct were tape-recorded. Takiff enlisted Gelber and other judges in activities ranging from paying kickbacks and fixing eases to releasing the name of a confidential informant believing that the informant would be killed. Sepe, Shenberg, and Judge Philip S. Davis participated in many of the schemes.
During the relevant period, Gelber recruited his secretary to assist him in the kickback scheme. Gelber asked the secretary if she knew any lawyers who would be willing to accept appointments as SAPDs in return for paying him kickbacks. Upon her agreement, Gelber used the secretary as a conduit to lawyers agreeing to join the kickback scheme. The secretary approached Arthur Luongo, Harry Boehme, and Nancy Lecht-ner, all lawyers, asking them to join in the kickback scheme. All of the lawyers agreed *1448to accept SAPD appointments in exchange for paying kickbacks.
Gelber approached William Castro, a lawyer, in the fall of 1989 about the possibility of Castro investing in Gelber’s corporation. Castro did not want to invest in the corporation, but he agreed to assist Gelber financially through paying kickbacks for receiving SAPD appointments. Gelber and Castro agreed that Castro would pay Gelber twenty percent of his anticipated fees within a few days of receiving appointments. Gelber began appointing Castro to cases, and Castro paid kickbacks for those appointments. Gel-ber received an average kickback payment of $1,000 from Castro. A few months after Castro began paying kickbacks to Gelber, Castro convinced Gelber to bring Kent Wheeler, a lawyer, into the kickback scheme. Castro served as an intermediary between Gelber and Wheeler because Gelber did not know Wheeler well.
From October 1989 to June 8,1991, Gelber appointed Castro to sixty-four cases and received $77,000 in kickbacks. From January 1990 to June 8, 1991, Gelber appointed Wheeler to thirty-seven cases and received $34,000 in kickbacks. Similarly, Gelber appointed Boehme to twelve cases for $13,000 in kickbacks; Lechtner to four cases for $7,000 in kickbacks; and Luongo to thirty-one cases for over $20,000 in kickbacks.
PROCEDURAL HISTORY
On May 27, 1992, a federal grand jury in the Southern District of Florida returned a superseding 106-count indictment against William Castro, Arthur Luongo, Harry Boehme, Nancy Lechtner, (appellants) and codefendants Harvey N. Shenberg, Alfonso Sepe, Phillip Davis, David Goodhart, and Arthur Massey. The indictment charged appellants with conspiracy to violate RICO in violation of 18 U.S.C. §§ 1962(d) and 1963(a), mail fraud in violation of 18 U.S.C. §§ 1341, 1346, and bribery in violation of 18 U.S.C. § 666(a)(2).1
Appellants moved to dismiss the RICO conspiracy count, mail fraud, and bribery counts for failure to state an offense. The district court denied these motions. In July 1992, appellants filed their first round of severance motions based on prejudicial mis-joinder seeking separate trials from each other, eodefendant Massey, and the indicted judges. The district court severed the trial of Judges Goodhart, Sepe, Shenberg, and Davis from appellants’ trial, and severed Massey’s trial from the appellants. The district court denied appellants’ subsequent motions to sever their trials from each other. The trial began on October 25,1993. At the close of the government’s case-in-chief, appellants moved for judgment of acquittal on all counts under Rule 29 of the Federal Rules of Criminal Procedure. The district court denied the motions. Appellants renewed the motions at the conclusion of their case, and the district court again denied the motions. The jury returned guilty verdicts as to all appellants on all counts.
The district court sentenced Castro to concurrent terms of thirty-seven months imprisonment, three years supervised release, and ordered him to pay a $1,400 special assessment. The district court sentenced Luongo to thirty-seven months imprisonment, three years supervised release, and ordered him to pay $850 in fines. The district court sentenced Lechtner to concurrent terms of thirty months imprisonment, three years supervised release, and ordered her to pay a $300 special assessment. The district court sentenced Boehme to concurrent terms of twenty-four months imprisonment, two years supervised release, and ordered him to pay a $500 special assessment. This appeal followed.
CONTENTIONS
First, appellants contend that the government failed to prove the existence of a single RICO conspiracy. Appellants assert that the government offered proof of multiple conspiracies, and that this constitutes an impermissible variance from the charge of a single *1449conspiracy. Appellants also claim that the district court’s failure to sever their trial amounted to a misjoinder. Second, appellants contend that the government failed to present evidence sufficient to establish that they agreed to affect the “operation or management” of the RICO enterprise as required under Reves v. Ernst & Young, 507 U.S. 170, 113 S.Ct. 1163, 122 L.Ed.2d 525 (1993).
Third, appellants contend that the district court’s jury instructions and the prosecutor’s summation constructively amended the RICO conspiracy count of the indictment by referring to the Eleventh Judicial Circuit as the RICO enterprise, rather than the Circuit Court of the Eleventh Judicial Circuit. Appellants insists that the district court’s instructions and the prosecutor’s summation resulted in an expansion of the indictment because the government failed to introduce evidence demonstrating that the Circuit Court of the Eleventh Judicial Circuit affected interstate commerce.
Fourth, appellants contend that their bribery convictions cannot stand because the evidence failed to prove that they intended to influence an agent of Metropolitan Dade County. Specifically, appellants argue that since the government charged Metropolitan Dade County as the agency receiving federal grant money, under 18 U.S.C. § 666 the government had to prove that appellants’ bribes were intended to influence or reward an agent of Metropolitan Dade County.
Fifth, appellants contend that the mail fraud counts fail to state an offense. Appellants assert that 18 U.S.C. § 1346 does not protect a sovereign state from the fraudulent deprivation of intangible rights. Also, appellants maintain that the term “honest services” in section 1346 is unconstitutionally vague. Sixth, appellants contend that the prosecutor impermissibly vouched for the credibility of a government witness and made improper and prejudicial remarks during closing arguments. Seventh, appellants contend that the district court erred in preventing them from offering evidence to prove a government witness’s self-interest, bias, and motive.
First, the government contends that a RICO conspiracy charge brings a defendant within the conspiracy regardless of the unre-latedness of the acts of the other members of the conspiracy as long as the government can show an agreement on an overall objective or that the defendant agreed to the commission of two or more predicate acts, individually or through others. The government contends that no material variance occurred because a reasonable trier of fact could have found beyond a reasonable doubt the existence of a single conspiracy. Also, for this reason, the government contends that the appellants were properly joined.
Second, the government contends that the appellants were convicted of a RICO conspiracy, and not a substantive RICO offense. Therefore, the government only had to allege and prove that the appellants “agreed” to affect the operation or management of the RICO enterprise, and not that the appellants actually exerted any control or direction over the RICO enterprise. Third, the government contends that when the prosecutor’s summation and the district court’s instructions are viewed in context, it is clear that no constructive amendment occurred. Fourth, the government contends that the evidence presented at trial was sufficient to establish that appellants intended to influence an agent of Metropolitan Dade County.
Fifth, the government contends that the plain language of 18 U.S.C. §§ 1341 and 1346 does not exclude governmental entities such as a state from coverage under the mail fraud statute. The government also asserts that this circuit has already rejected a void-for-vagueness challenge to section 1346. Sixth, the government contends that it properly argued the credibility of the witness based on the evidence in the record and did not make prejudicial remarks during closing arguments. Seventh, the government contends that the district court did not abuse its discretion in preventing appellants’ proffer of extrinsic evidence to show specific prior conduct to impeach a government witness.
ISSUES
The issues we address in this appeal are: (1) whether a material variance or misjoinder occurred; (2) whether sufficient evidence ex*1450isted to establish that appellants conspired to participate in the RICO enterprise; (3) whether the district court’s instructions and the prosecutor’s summations constructively amended the RICO conspiracy count of the indictment; (4) whether appellants were properly convicted for bribery under 18 U.S.C. § 666(a)(2); (5) whether appellants were properly convicted for mail fraud under 18 U.S.C. §§ 1341, 1346; (6) whether prose-cutorial misconduct occurred through impermissible vouching for witness’s credibility and through improper remarks; and (7) whether the district court abused its discretion in excluding appellants’ proffered evidence.
STANDARDS OF REVIEW
This appeal involves multiple issues requiring differing standards of review. We review the claim of a material variance through viewing the evidence in the light most favorable to the government to determine whether a reasonable trier of fact could have found that a single conspiracy existed beyond a reasonable doubt. United States v. Reed, 980 F.2d 1568, 1581 (11th Cir.), cert. denied, 509 U.S. 932, 113 S.Ct. 3063, 125 L.Ed.2d 745 (1993). We will uphold the conviction unless the variance (1) was material and (2) substantially prejudiced the defendant. Reed, 980 F.2d at 1581. Our review of the claim of a misjoinder is plenary. United States v. Morales, 868 F.2d 1562, 1567 (11th Cir.1989).
We review the sufficiency of the evidence de novo, viewing the evidence in the light most favorable to the government and drawing all reasonable inferences in favor of the jury’s verdict. United States v. Church, 955 F.2d 688, 693 (11th Cir.), cert. denied, 506 U.S. 881, 113 S.Ct. 233, 121 L.Ed.2d 169 (1992). In evaluating whether the indictment was constructively amended, we review the district court’s jury instructions and the prosecutor’s summation “in context” to determine whether an expansion of the indictment occurred either literally or in effect. United States v. Behety, 32 F.3d 503, 509 (11th Cir. 1994), cert. denied, — U.S.-, 115 S.Ct. 2568, 132 L.Ed.2d 820 (1995).
In reviewing the claim of prosecutorial misconduct, we assess (1) whether the challenged comments were improper and (2) if so, whether they prejudicially affected the substantial rights of the defendant. United States v. Obregon, 893 F.2d 1307, 1310 (11th Cir.), cert. denied, 494 U.S. 1090, 110 S.Ct. 1833, 108 L.Ed.2d 961 (1990). We review a district court’s evidentiary rulings for abuse of discretion. United States v. Calle, 822 F.2d 1016, 1020 (11th Cir.1987). Finally, our review of a district court’s legal conclusion is de novo. United States v. Waymer, 55 F.3d 564, 568 (11th Cir.1995).
DISCUSSION
I. Material Variance and Joinder
Appellants contend that at best the government’s proof at trial revealed the existence of multiple conspiracies even though the indictment only charged a single conspiracy. For this reason, appellants claim that a material variance occurred that constitutes reversible error under United States v. Sutherland, 656 F.2d 1181, 1189 (5th Cir. Unit A 1981), cert. denied, 455 U.S. 949, 102 S.Ct. 1451, 71 L.Ed.2d 663 (1982).2 Appellants also contend that they were improperly joined because the government failed to prove that any of them knew about other lawyers participating in the kickback scheme or whether any of them knew of the existence of a single conspiracy.
A material variance between an indictment and the government’s proof at trial occurs if the government proves multiple conspiracies under an indictment alleging only a single conspiracy. Kotteakos v. United States, 328 U.S. 750, 66 S.Ct. 1239, 90 L.Ed. 1557 (1946). In order to prove a RICO conspiracy, the government must show an agreement to violate a substantive RICO provision. United States v. Gonzalez, 921 F.2d 1530, 1539 (11th Cir.), cert. denied, 502 U.S. 860, 112 S.Ct. 178, 116 L.Ed.2d 140 *1451(1991). Specifically, the government must prove that the conspirators agreed to participate directly or indirectly in the affairs of an enterprise through a pattern of racketeering activity. 18 U.S.C.A. § 1962(d) (West 1984); United States v. Sutherland, 656 F.2d 1181, 1191-1192 (5th Cir. Unit A 1981), cert. denied, 455 U.S. 949, 102 S.Ct. 1451, 71 L.Ed.2d 663 (1982).
The government may prove the existence of an “agreement” to participate in a RICO conspiracy through showing (1) the existence of an agreement on an overall objective, or (2) in the absence of an agreement, on an overall objective that the defendant agreed personally to commit two or more predicate acts. United States v. Church, 955 F.2d 688, 694 (11th Cir.1992), cert. denied, 506 U.S. 881, 113 S.Ct. 233, 121 L.Ed.2d 169 (1992). In meeting its burden of proof on showing an agreement on an overall objective, the government must offer direct evidence of an explicit agreement on an overall objective or, in the absence of direct evidence, the government must offer circumstantial evidence demonstrating “that each defendant must necessarily have known that others were also conspiring to participate in the same enterprise through a pattern of racketeering activity.” Sutherland, 656 F.2d at 1193-94; see also, United States v. Valera, 845 F.2d 923, 929-30 (11th Cir.1988), cert. denied, 490 U.S. 1046, 109 S.Ct. 1953, 104 L.Ed.2d 422 (1989).
In this ease, the indictment charged a single RICO conspiracy, and the government presented evidence that adequately proved the existence of a single conspiracy. At trial, Gelber testified that he informed the appellants that they would not only receive appointments from him but also from another judge in the circuit court. In light of this testimony, each appellant knew that at least two circuit judges agreed to use the Circuit Court of the Eleventh Judicial Circuit to engage in a kickback scheme. In addition to Gelber’s testimony, other evidence adduced at trial indicates appellants’ agreement to participate in and awareness that others also participated in a single conspiracy. For example, when Gelber’s secretary asked appellant Boehme to enroll in the kickback scheme, she asked him whether he wished to join the “preferred list” for court appointments. Similarly, appellant Lechtner was informed that a kickback scheme was “something that’s being done” in the Circuit Court of the Eleventh Judicial Circuit. Appellant Castro actually recruited another lawyer to join the kickback scheme. In light of this evidence, we find that each appellant agreed on an overall objective and agreed personally to commit two or more predicate acts by paying kickbacks for SAPD appointments.
Additionally we note that, contrary to appellants’ assertions, in proving the existence of a single RICO conspiracy, the government does not need to prove that each conspirator agreed with every other conspirator, knew of his fellow conspirators, was aware of all of the details of the conspiracy, or contemplated participating in the same related crime. United States v. Pepe, 747 F.2d 632, 659-60 (11th Cir.1984).3 In viewing the evidence in the light most favorable to the government, a jury could have reasonably concluded that one common agreement on a single overall objective existed. Consequently, we find that no material variance occurred.
In considering appellants’ misjoinder claim, we recognize that the Federal Rules of Criminal Procedure prohibit joinder of defendants unless the indictment covered the same act or transaction or the same series of acts or transactions. Fed.R.Crim.P. 8(b). In this circuit we have observed that “[w]hether or not separate offenses are part of a ‘series of acts or transactions’ under 8(b) depends ... on the relatedness of the facts underlying each offense.... [W]hen the facts underlying each offense are so closely connected that proof of such facts is necessary to establish each offense, joinder of defendants and offenses is proper.” United States v. Welch, 656 F.2d 1039, 1049 (5th Cir. *1452Unit A 1981) (quoting United States v. Gentile, 495 F.2d 626, 630 (5th Cir.1974)), cert. denied, 456 U.S. 915, 102 S.Ct. 1767, 1768, 72 L.Ed.d 173 (1982).
Since more than sufficient evidence existed in this trial to support the indictment and conviction of a single conspiracy, we conclude that no misjoinder occurred. United States v. Weinstein, 762 F.2d 1522, 1541, modified on other grounds, 778 F.2d 673 (11th Cir.1985), cert. denied, 475 U.S. 1110, 106 S.Ct. 1519, 89 L.Ed.2d 917 (1986).4
II. Sufficiency of the Evidence
Appellants contend that the government’s evidence was insufficient to establish that they conspired to participate in the “operation or management” of the RICO enterprise. Appellants argue that under Reves v. Ernst & Young, 507 U.S. 170, 113 S.Ct. 1163, 122 L.Ed.2d 525 (1993), the government was required to produce evidence showing that appellants agreed to exercise control or direction in the management of the Circuit Court of the Eleventh Judicial Circuit. Appellants suggest that as outsiders they could not have exerted the requisite degree of control over the “operation or management” of the Circuit Court of the Eleventh Judicial Circuit to meet the requirements of Reves.
As a preliminary matter, we reject appellants’ limited reading of Reves. Under Reves, section 1962(c) liability is not limited to insiders or upper management as appellants suggests. Reves, 507 U.S. at 184-86, 113 S.Ct. at 1173. In Reves, the Supreme Court emphasized that because the statute includes the phrase “to participate directly or indirectly,” RICO liability is not confined to those with a formal position in the enterprise. Reves, 507 U.S. at 178-80, 113 S.Ct. at 1170.5 The language in Reves indicates that persons in appellants’ position fall within the scope of section 1962(c)’s coverage because “an enterprise might be operated or managed by others associated with the enterprise who exert control over it as, for example, by bribery.” Reves, 507 U.S. at 184, 113 S.Ct. at 1173 (emphasis added).
We reject the appellants’ narrow reading of Reves and their attempt to infuse the Reves analysis into this case. In this case, the indictment charged the appellants with RICO conspiracy under section 1962(d), and not a substantive RICO offense under section 1962(c). This court recently decided that the Reves “operation or management” test does not apply to section 1962(d) convictions. United States v. Starrett, 55 F.3d 1525, 1547 (11th Cir.1995); see also Napoli v. United States, 45 F.3d 680, 683, 684 (2d Cir.), cert. denied, — U.S. -, 115 S.Ct. 1796, 131 L.Ed.2d 724 (1995). Our view of the evidence in the light most favorable to the government indicates that more than sufficient evidence existed to demonstrate that appellants “agreed” to affect the operation or management of the Circuit Court of the Eleventh Judicial Circuit through paying kickbacks.
III. Constructive Amendment of Indictment
A constructive “amendment occurs when the essential elements of the offense contained in the indictment are altered to broaden the possible bases for conviction *1453beyond what is contained in the indictment.” United States v. Behety, 32 F.3d 503, 508 (11th Cir.1994) (quoting United States v. Keller, 916 F.2d 628, 634 (11th Cir.1990), cert. denied, 499 U.S. 978, 111 S.Ct. 1628, 113 L.Ed.2d 724 (1991)), cert. denied — U.S. -, 115 S.Ct. 2568, 132 L.Ed.2d 820 (1995). The indictment may be amended as a result of erroneous jury instructions or a prosecutor’s statements. Behety, 32 F.3d at 508. When a constructive amendment occurs it violates “a fundamental principle” stemming from the Fifth Amendment: specifically, “that a defendant can only be convicted for a crime charged in the indictment.” United States v. Keller, 916 F.2d 628, 633 (11th Cir.1990), cert. denied, 499 U.S. 978, 111 S.Ct. 1628, 113 L.Ed.2d 724 (1991).
In this case, appellants contend that a constructive amendment of the indictment occurred on the RICO conspiracy count because both the prosecutor’s summation and the district court’s jury instructions substituted the “Eleventh Judicial Circuit” for the “Circuit Court of the Eleventh Judicial Circuit” as the RICO enterprise affecting interstate commerce. Appellants argue that the jury relied on proof of the Eleventh Judicial Circuit’s effect on interstate commerce. Appellants claim that the government failed to prove that the Circuit Court of the Eleventh Judicial Circuit affected interstate commerce.
In determining whether an indictment was constructively amended, we must assess the prosecutor’s comments and the court’s instructions “in context” to see whether the indictment was expanded either literally or in effect. United States v. Andrews, 850 F.2d 1557, 1559 (11th Cir.1988) (en banc), cert. denied, 488 U.S. 1032, 109 S.Ct. 842, 102 L.Ed.2d 974 (1989). Admittedly, at trial, the prosecutor referred to the Eleventh Judicial Circuit, rather than the Circuit Court of the Eleventh Judicial Circuit, as the RICO enterprise in his closing argument. The prosecutor immediately informed the jury, however, to rely on Judge Smith’s testimony which only defined the Circuit Court of the Eleventh Judicial Circuit. Similarly, the district court instructed the jury that the Eleventh Judicial Circuit was the RICO enterprise that must have affected interstate commerce to satisfy the requirements of section 1962(d).
Even though the jury heard the term Eleventh Judicial Circuit during the trial, the government’s evidence focused on the circuit court’s effect on interstate commerce. For example, the government presented testimony from the court administrator for the Eleventh Judicial Circuit of Dade County who testified that the circuit court judges traveled out of state on business. Moreover, he testified that the circuit court purchased and used computers, books, and supplies from vendors outside of Florida. Neither the court administrator nor Judge Smith explained to the jury that the Circuit Court of the Eleventh Judicial Circuit was a division of the Eleventh Judicial Circuit.
When we view the prosecutor’s single remark, the district court’s instructions, and the evidence proffered at trial in context, we do not believe the jury could have convicted appellants based upon a charge not contained in the indictment.
IV. Bribery Convictions
Appellants contend that their bribery convictions must be reversed. Appellants assert that since the government charged them under 18 U.S.C. § 666(a)(2), the government was required to show that they intended to enter into a direct exchange with an agent of the organization receiving federal funds.6 Appellants argue that the government produced no evidence showing that they intended to influence or reward anyone in the Dade County Finance Department. Moreover, appellants challenge the sufficiency of the evidence presented at trial to establish that *1454Metropolitan Dade County received federal grants in excess of $10,000.
At trial, the appropriate inquiry was: did the government prove beyond a reasonable doubt that the appellants (1) gave or offered to give a thing of value to any person (2) with the corrupt intent to influence or reward an agent of an organization that in a one-year period received benefits in excess of $10,000 under a federal program (3) in connection with any business transaction or series of transactions of such organization, government, or agency involving anything of the value of $5,000 or more. 18 U.S.C.A. § 666(a)(2) (West 1976 & Supp.1995). The government presented evidence at trial establishing that the appellants (1) paid kickbacks to Judge Gelber (2) with the intent to have Judge Gelber appoint them as SAPDs and authorize an agent of the Dade County Finance Department to issue them compensation checks (3) in connection with their rendering of legal services of a value exceeding $5,000.
We reject appellants’ suggestion that the government had to show a direct quid pro quo relationship between them and an agent of the agency receiving federal funds. We believe that the appellants’ narrow reading of the bribery statute would belie the statute’s purpose “to protect the integrity of the vast sums of money distributed through federal programs from theft, fraud, and undue influence by bribery.” S.Rep. No. 225, 98th Cong., 2d Sess. 369-370 (1984), reprinted in 1984 U.S.C.C.A.N. 3182, 3510-11. It is clear from the record that the appellants knew that payments for SAPD services came from Metropolitan Dade County and not the circuit court. Moreover, appellants also knew that they could not receive payments from Metropolitan Dade County unless a circuit court judge authorized Metropolitan Dade County to pay the bill or influenced an agent in the Dade County Finance Department to issue the checks. We believe that the government proved that appellants not only intended to influence Gel-ber, but they also intended to influence an agent in the Dade County Finance department by having Gelber authorize the agent to issue payments for their SAPD services. Accordingly, we hold that appellants were properly convicted of bribery under 18 U.S.C. § 666(a)(2).
Appellants also contend that the district court erred in admitting the testimony, over objections, establishing that Metropolitan Dade County received federal grants in excess of $10,000. Appellants argue that the district court should have excluded the testimony of Willis Patterson, an assistant controller in the Dade County Finance Department, as a violation of Federal Rules of Evidence 602 and 1002.
We cannot agree with appellants’ suggestion that the district court abused its discretion in admitting Patterson’s testimony. According to Rule 602 of the Federal Rules of Evidence, a witness may not testify to a matter unless evidence is introduced to establish that the witness possesses personal knowledge of the matter.7 In this case, the record shows that Patterson had personal knowledge about the federal grants that Metropolitan Dade County received. Patterson testified that he was the assistant controller of the Dade County Finance Department for the past seven years, and his department was responsible for receiving federal grant monies on behalf of the county.8 The defense had an opportunity to cross-examine Patterson about his personal knowledge but did not examine him. Accordingly, we find that the district court did not abuse its discretion in admitting this testimony.
*1455Similarly, we reject appellants’ contention that under Rule 1002 of the Federal Rules of Evidence or “the best evidence rule” the district court should have precluded Patterson’s testimony because the government should have entered composite exhibit 406 that detailed federal funds Metropolitan Dade County received. We do not believe that Rule 1002 of the Federal Rules of Evidence was implicated in this ease because the questions posed to Patterson did not seek to elicit the “contents” of composite exhibit 406. See, e.g., Allstate Ins. Co. v. Swann, 27 F.3d 1539, 1542-43 (11th Cir.1994) (recognizing that Fed.R.Evid. 1002 does not always require the introduction of a writing merely because the writing contains facts similar to the testimony). Rather, the questions were aimed at showing that Dade County received substantially more than $10,000 in federal grants, and not necessarily the exact amount or details surrounding the county’s receipt of millions of dollars in federal grants. See Swann, 27 F.3d at 1542-43 (finding that the best evidence rule was not implicated where an insurance underwriting manager’s answers to questions based on his familiarity with underwriting guidelines and did not necessarily require him to state the contents of the underwriting guidelines).
V. Mail Fraud
Appellants seek to invalidate their mail fraud conviction because they claim (1) that the term “honest services” in the mail fraud statute is unconstitutionally vague, and (2) that the mail fraud statute does not extend to cover schemes whose ultimate intent is to deprive a sovereign state of intangible rights.
Since the appellants’ void-for-vagueness challenge to section 1346 does not raise a First Amendment issue, we will consider section 1346 as applied to the facts of this case. United States v. Waymer, 55 F.3d 564, 568 (11th Cir.1995); United States v. Awan, 966 F.2d 1415, 1424 (11th Cir.1992). In assessing a statute under a void-for-vagueness challenge, we may find a statute unconstitutionally vague when it fails to “define the criminal offense with sufficient definiteness that ordinary people can understand what conduct is prohibited and in a manner that does not encourage arbitrary and discriminatory enforcement.” Kolender v. Lawson, 461 U.S. 352, 357, 103 S.Ct. 1855, 1858, 75 L.Ed.2d 903 (1983).
Moreover, this court has observed that “[t]he constitutionality of a vague statutory standard is closely related to whether the standard incorporates a requirement of mens rea.” Waymer, 55 F.3d at 568 (citing Colautti v. Franklin, 439 U.S. 379, 99 S.Ct. 675, 58 L.Ed.2d 596 (1979)). In United States v. Conner, this court also mentioned that “the statutory requirement that an act must be willful or purposeful may not render certain, for all purposes, a statutory definition of the crime which is in some respects uncertain. But it does reheve the statute of the objection that it punishes without warning an offense which the accused was unaware.” United States v. Conner, 752 F.2d 566, 574 (11th Cir.) (quoting Screws v. United States, 325 U.S. 91, 102, 65 S.Ct. 1031, 1036, 89 L.Ed. 1495 (1945) (Douglas, J., concurring)), cert. denied sub nom., Taylor v. United States, 474 U.S. 821, 106 S.Ct. 72, 88 L.Ed.2d 59 (1985). When the Second Circuit addressed a challenge to section 1341 of the mail fraud statute in United States v. Margi-otta, that circuit found that section 1341 was not unconstitutionally vague because it “contains the requirement that the defendant must have acted willfully and with the specific intent to defraud.” United States v. Margiotta, 688 F.2d 108, 129 (2d Cir.1982), cert. denied, 461 U.S. 913, 103 S.Ct. 1891, 77 L.Ed.2d 282 (1983).
We believe that the reasoning from the foregoing cases is instructive here. In this ease, the government had to prove that the appellants had the “specific intent” to defraud. 18 U.S.C.A. §§ 1341, 1346 (West 1984 & Supp.1995). The jury found that appellants had the specific intent to defraud the state of Florida of its honest services. In light of the foregoing reasoning, we hold that the term “honest services” in section 1346 was not unconstitutionally vague as applied to the appellants.9
*1456In considering appellants’ argument regarding the scope of the mail fraud statute’s protection, we decline to adopt appellants’ construction of 18 U.S.C. §§ 1341 and 1346. Under appellants’ interpretation of sections 1341 and 1346, the mail fraud statute would not protect states. First, appellants contend that it is inconsistent with federalism principles to apply this statute to a sovereign state. The Supreme Court has made it clear, however, that Congress may forbid putting letters into the post office when “such acts are done in furtherance of a scheme that it regards contrary to public policy, whether it can forbid the scheme or not.” Badders v. United States, 240 U.S. 391, 393, 36 S.Ct. 367, 368, 60 L.Ed. 706 (1916). Therefore, appellants’ federalism argument is without merit.
Appellants also suggest that Congress’s enactment of section 1346 restricts section 1341’s protection to nongovernmental victims. In 1988, Congress enacted section 1346 of the mail fraud statute to state an offense for the deprivation of intangible rights such as “honest services,” thus overruling the Supreme Court’s decision in McNally v. United States, 483 U.S. 350, 107 S.Ct. 2875, 97 L.Ed.2d 292 (1987). Pub.L. No. 100-690, § 7603, 102 Stat. 4508 (codified as amended at 18 U.S.C. § 1346 (1988)); see also 134 Cong.Rec. Hll,251 (daily ed. Oct. 21, 1988). Appellants assert that sections 1341 and 1346 read together seek to punish “whoever having devised or intended to devise any scheme or artifice to deprive ‘another’ of the intangible right of honest services ... places in any post office or authorized depository for mail matter....” Appellants argue that the term “another” cannot encompass a state. We disagree.
Neither the plain language of section 1346 nor its legislative history supports the limitation appellants urge. We find it instructive to note that prior to section 1346’s enactment, similar questions arose regarding the reach of section 1341’s protection. In United States v. Martinez, the Third Circuit found that the mail fraud statute protected the Commonwealth of Pennsylvania from deprivation of its property interests. United States v. Martinez, 905 F.2d 709, 715 (3d Cir.), cert. denied, 498 U.S. 1017, 111 S.Ct. 591, 112 L.Ed.2d 595 (1990).
Indeed, other cases decided based upon section 1341 violations, prior to the clarifying amendment of section 1346, support our finding that the mail fraud statute does protect governmental entities such as a state. See, e.g., United States v. Coyne, 4 F.3d 100, 110-11 (2d Cir.1993) (upholding mail fraud convictions where a county was victim of mail fraud); United States v. Paccione, 949 F.2d 1183 (2d Cir.1991) (affirming mail fraud conviction where city of New York defrauded), cert. denied, 505 U.S. 1220, 112 S.Ct. 3029, 120 L.Ed.2d 900 (1992); United States v. Wilson, 904 F.2d 656, 660-61 (11th Cir.1990) (upholding mail fraud conviction where indictment alleged defendants intended to defraud the Internal Revenue Service), cert. denied, 502 U.S. 889, 112 S.Ct. 250, 116 L.Ed.2d 205 (1991). We can discern no reason to read sections 1341 and 1346 as appellants suggest to exclude states, and presumably, all governmental entities from the mail fraud statute’s protection. We believe that such a result would belie a clear congressional intent to construe the mail fraud statute broadly. See generally United States v. Martinez, 905 F.2d 709 (3d Cir.1990).
VI. Prosecutorial Misconduct
Appellants contend that prosecutorial misconduct occurred in two respects. First, appellants allege that the prosecutor impermis-sibly vouched for the credibility of Gelber, the government’s main witness. Primarily, appellants’ challenge the prosecutor’s attempts to elicit testimony from Gelber regarding the truth telling provisions in his plea agreement. Second, appellants contend that the prosecutor made disparaging remarks about the defense attorneys and other improper remarks. Appellants state that the prosecutor suggested that prosecutors are sworn to pursue justice while criminal defense attorneys are beholden to the manipulation of the justice system.
When faced with a question of whether improper vouching occurred we ask: *1457“whether the jury could reasonably believe that the prosecutor was indicating a personal belief in the witness’s credibility.” United States v. Sims, 719 F.2d 375, 377 (11th Cir. 1983), cert. denied, 465 U.S. 1034, 104 S.Ct. 1304, 79 L.Ed.2d 703 (1984). In applying this test, we look for whether (1) the prosecutor placed the prestige of the government behind the witness by making explicit assurances of the witness’s credibility, or (2). the prosecutor implicitly vouched for the witness’s credibility by implying that evidence not formally presented to the jury supports the witness’s testimony. Sims, 719 F.2d at 377.
Since appellants’ initial concern is about Gelber’s testimony surrounding his plea agreement, we note that prosecutors are not generally prohibited from entering a plea agreement into evidence for the jury’s consideration. United States v. Dennis, 786 F.2d 1029, 1047 n. 18 (11th Cir.1986), cert. denied, 481 U.S. 1037, 107 S.Ct. 1973, 95 L.Ed.2d 814 (1987). Moreover, our careful review of the circumstances under which this testimony was elicited compels us to find that a jury could not have reasonably believed that the prosecutor was personally vouching for Gelber’s credibility, or that the prosecutor was indicating that evidence beyond what was presented to the jury supported Gelber’s testimony. In this case, the prosecutor merely questioned Gelber about the requirements of the plea agreement to testify fully and truthfully. Furthermore, in his questioning of Gelber, the prosecutor merely pointed out that Gelber risked prosecution if he perjured himself. We have found similar questioning proper. See United States v. Sims, 719 F.2d 375, 377 (11th Cir.1983), cert. denied, 465 U.S. 1034, 104 S.Ct. 1304, 79 L.Ed.2d 703 (1984). Consequently, we find that no prosecutorial misconduct occurred with respect to impermissible vouching.
A similar result obtains in our consideration of the prosecutor’s alleged disparaging remarks and other improper statements. We may find prosecutorial misconduct where (1) a prosecutor makes improper remarks (2) that prejudicially affect the substantial rights of the defendant. United States v. Eyster, 948 F.2d 1196, 1206 (11th Cir.1991).
Both the prosecution and defense came close to making improper comments as they exchanged vitriol during closing arguments. Appellants challenge the prosecutors following remark: “And these fellows here, these guys are prosecutors, they’re sworn to be prosecutors, to pursue justice. These defense counsel, they represent their clients, they come in here and say what they want to help their clients.” While we do not condone the prosecutor’s remarks, we cannot find that they constitute grounds for reversal. The prosecutor made the statement on rebuttal in response to the defense counsel’s comments that the prosecutors were liars and suborn-ers of perjury. The defense counsel invited the prosecutor’s concomitant attack. In light of the circumstances surrounding the exchange and the substantial evidence against the appellants, we cannot agree that appellants suffered any prejudice. See United States v. Cotton, 631 F.2d 63, 66 (5th Cir.1980) (where defense counsel referred to government agents as liars, and persons engaged in coverups, government entitled to respond to assertions), cert. denied, 450 U.S. 1032, 101 S.Ct. 1743, 68 L.Ed.2d 227 (1981).
Appellants also contend that the prosecutor made improper statements by trying to prove guilt by association. We find this contention meritless as the prosecutor properly commented on the evidence presented to the jury when he described the close association that appellants shared with others involved in the kickback scheme prior to and during their criminal activities. United States v. Tisdale, 817 F.2d 1552, 1555 (11th Cir.) (stating that when the evidence supports a prosecutor’s comments, no error occurs), cert. denied, 484 U.S. 868, 108 S.Ct. 194, 98 L.Ed.2d 145 (1987).
VII. Exclusion of Witness Testimony
Appellants contend that reversible error occurred when the district court precluded them from introducing a witness to expose Gelber’s self-interest, bias, or motive to testify falsely. It is clear from the record, however, that appellants sought to impeach Gelber’s credibility through introducing testi*1458mony of a convicted drug dealer regarding Gelber’s alleged prior bad act of soliciting help to smuggle marijuana.
The district court did not abuse its discretion in excluding this proposed testimony. Specific instances of prior bad acts may not be admitted through extrinsic evidence to attack a witness’s credibility. Fed.R.Evid. 608(b); see also United States v. Darwin, 757 F.2d 1193, 1204 (11th Cir.1985), cert. denied, 474 U.S. 1110, 106 S.Ct. 896, 88 L.Ed.2d 930 (1986). Consequently, we find that the district court did not abuse its discretion in excluding this testimony.
CONCLUSION
For the foregoing reasons, we affirm appellants’ convictions and sentences.
AFFIRMED.