Nos. 138, 142 and 395, Docket 90-1144 to 90-1147, 90-1221 and 90-1234.United States Court of Appeals, Second Circuit.Argued January 8, 1991.
Decided February 6, 1991.
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Bernard H. Udell, Brooklyn, N.Y., for appellant Barbara Alkins.
Alan G. Polak, New York City, for appellant Carol Small.
Paul Morgenstern, New York City, for appellant Linda Alkins.
Irving Anolik, New York City, for appellant Roberta Meyers.
David L. Lewis, New York City, for appellant Geraldine Watts.
Martin Geduldig, Hicksville, N.Y., for appellant Eloy Viejo.
Sean F. O’Shea, Asst. U.S. Atty., E.D. N.Y., Brooklyn, N.Y. (Andrew J. Maloney, U.S. Atty., E.D.N.Y., David C. James, Susan Corkery, Asst. U.S. Attys., E.D.N.Y., Brooklyn N.Y., on the brief), for appellee U.S.
Appeal from the Eastern District of New York.
Before FEINBERG, TIMBERS and NEWMAN, Circuit Judges.
TIMBERS, Circuit Judge:
 Appellants Barbara Alkins, Carol Small, Linda Alkins, Roberta Meyers, Geraldine Watts, and Eloy Viejo appeal from judgments entered February 2, 1990 and March 5, 1990, in the Eastern District of New York, Joseph M. McLaughlin, District Judge,
convicting them of conspiring to conduct and conducting the affairs of the Queens District Office of the New York Department of Motor Vehicles (DMV) through a pattern of racketeering activity and of violating other federal statutes.
 On August 17, 1989, appellants were arraigned on a superseding fifty-five count indictment. The indictment was the culmination of a large scale investigation into corruption at the DMV. It charged a scheme whereby clerks at the DMV would process applications for driver’s licenses, non-driver identification cards and registrations for vehicles — all absent the proper documentation and in return for cash payments. Many of the driver’s licenses and identification cards were provided to illegal aliens or to persons who desired to conceal their true identities. Many of the vehicle registrations were provided for stolen cars. These transactions were often arranged by “runners” who served as intermediaries between the “customers” and the clerks at the DMV.
 The indictment charged appellants with conducting the affairs of the DMV through a pattern of racketeering activity and of conspiring to do so. It set forth 31 acts of racketeering that appellants allegedly had committed in furtherance of their scheme. These acts included possession of stolen motor vehicles in violation of 18 U.S.C. § 2313 (1988) (2 acts); mail fraud in violation of 18 U.S.C. §§ 1341 and 1346 (1988) (27 acts); and soliciting and accepting bribes in violation of N.Y. Penal Law §§ 200.10 and 20.00 (McKinney 1988) (2 acts). Each of the racketeering acts, with the exception of the state law bribery acts, was charged as a substantive count in the indictment. In addition, the indictment included 10 counts charging possession of counterfeit securities of a state in violation of 18 U.S.C. § 513
 On appeal, appellants contend that (1) certain of their mail fraud convictions violated the ex post facto clause of the Constitution; (2) the district court’s instruction regarding the good faith defense to a mail fraud charge was inadequate; (3) the evidence did not establish that they engaged in a pattern of racketeering activity; (4) the district court improperly instructed the jury on a pattern of racketeering activity; (5) the district court erred in denying their request for a multiple conspiracies charge; and (6) the district court erred in limiting the cross-examination of a government witness. In addition, Linda Alkins contends that her conviction of possession of a stolen motor vehicle must be vacated since the government failed to prove that the motor vehicle in question crossed state boundaries. Meyers contends that her RICO convictions cannot stand since the evidence demonstrated only that she received gratuities and did not establish that she received bribes. Viejo contends that the evidence was insufficient to support his convictions on the RICO counts.
 For the reasons that follow, we affirm the judgments of conviction of all appellants on all counts on which they were convicted.
 We shall summarize only those facts and prior proceedings believed necessary to an understanding of the issues raised on appeal.
 The DMV is a state agency that is responsible for issuing vehicle registrations, driver’s licenses, learner’s permits, and non-driver identification cards. Applications for these documents are processed by DMV clerks, who are expected to ensure that the applicant submits the necessary supporting documents, to verify the applicant’s identity, and to collect any required fees. The DMV clerks process approximately 64 to 70 such transactions each day. When the clerk verifies that the application is complete, it is sent to Albany, where the registrations and licenses are printed and mailed to the applicants.
 To register a vehicle, an applicant must complete an MV-82 form. That form requires the applicant to provide his name, address, date of birth, vehicle description, vehicle identification number, and signature. The applicant must also submit to the clerk proof of identity and proof of ownership. The clerk is expected to verify the applicant’s signature and to record the type of documentation the applicant provided.
 To obtain a driver’s license, an applicant must fill out an MV-44 form. That form requires the applicant to provide his name,
address, date of birth, motorist identification number, as well as personal information, and driving history. The applicant is required to sign the form. The applicant also must submit to the clerk proof of identity. The clerk is expected to verify the applicant’s signature and to record the type of documentation the applicant provided.
 Documents that can be used as proof of identity include a driver’s license, a nondriver identification card, a birth certificate, a passport, or an alien registration card. Documents that can be used as proof of ownership of a vehicle include a certificate of title and a form issued by the state to used car dealers that transfers title from the dealer to a customer who has purchased the car. In New York, dealers use an MV-50 form to transfer title to a customer. The New Jersey reassignment form is an equivalent form. The clerks at the DMV are trained to recognize counterfeit documents.
 Barbara Alkins, Small, Linda Alkins, Meyers, and Watts (collectively the clerks) were all employed by the DMV. Viejo owned car dealerships in New York (E V Auto Sales) and New Jersey (Eloy Auto Sales).
 Several co-conspirators, who pleaded guilty to charges arising from the investigation, testified for the government. The government’s witnesses included the “runners” who acted as intermediaries between the “customers” and the clerks at the DMV. The runners provided a service whereby they would shepherd applications, together with the supporting documentation, through the process at the DMV. These runners often were granted special access. For example, they were allowed to proceed directly to the clerks’ windows and avoid the lines in which other applicants waited.
 Andy Williams, one of the runners, testified for the government. He was involved in obtaining registrations for stolen cars. The cars were stolen by a ring of car thieves led by Anthony Santos and operated out of New York. Williams submitted counterfeit New Jersey certificates of title, which were filled out in fictitious names as proof of ownership in connection with these transactions. These documents should not have been accepted since they were photocopies and were not properly authenticated. In addition, Williams did not submit proof of the purported owner’s identity since the cars were registered in phony names. Clerks at the DMV processed these applications in return for cash payments. The applications indicated that the clerks had received proof of identity. Williams testified that he paid Small approximately ten to fifteen times to register stolen vehicles. He paid Linda Alkins once or twice to do the same.
 On one occasion, Williams met Small in the DMV parking lot to inform her that he would be registering a stolen Porsche the following day. Small told Williams that it would cost $300 since a Porsche is an expensive car. The next day Small processed the fraudulent application in exchange for $300.
 Williams was associated with Woodrow Flemming, who also arranged to have stolen cars registered at the DMV. Flemming used counterfeit New Hampshire certificates of title. These were no longer in use in New Hampshire and therefore should not have been accepted by the clerks at the DMV. No proof of identity was submitted in connection with these car registrations, but the applications indicated that such proof had been submitted. These applications also were processed by clerks at the DMV in return for cash payments.
 Williams also, on occasion, gave his business card to individuals who wished to obtain driver’s licenses or non-driver identification cards without submitting proof of identity. These individuals were sent to Small who would process their applications for cash payments.
 Yizhaq Dvash testified for the government. He was an illegal alien and had pled guilty to an unrelated charge of passing counterfeit money. Dvash procured licenses for individuals who did not have the proper identification to obtain them legally. Most of Dvash’s clients were illegal aliens. Dvash testified that he paid the clerks to
process applications for driver’s licenses that were not accompanied by the proper identification. Dvash bought a DMV stamp from Linda Alkins and a stamp pad from Meyers to facilitate his “business”.
 Isabel Lozano operated the Roosevelt Insurance Agency. As part of her business, she registered vehicles at the DMV. Lozano also procured registrations at the DMV for stolen vehicles. She kept a record of these transactions that included the amount of money paid to the DMV clerk to ensure that the application would be processed. In connection with these transactions, Lozano used fifteen New Jersey reassignment forms that were signed by Viejo. The forms were otherwise blank when Lozano received them. She and her associate, Josefina Joniaux, completed the forms with false information so that they reflected sales of vehicles from Eloy Auto Sales to individuals living in New York. In reality, the vehicles had been stolen and the individuals did not exist. These forms were taken with corresponding MV-82 forms to the DMV by runners such as Joniaux and Marcos Amores. Of the fifteen applications that included the fraudulent New Jersey reassignment forms supplied by Viejo, two were processed by Small, one by Barbara Alkins, three by Meyers, and three by Watts. Six others were processed by clerks not charged in the instant indictment. Lozano’s records indicated that the clerks were paid $50 in exchange for processing the applications.
 In each instance, title to the car was transferred from E V Auto Sales to Eloy Auto Sales. Each vehicle was “sold” by one of two salespeople at Eloy Auto Sales: Diego Gomez or Jesus Bonilla. Viejo employed a total of eight salespeople.
 In an interview conducted by an Assistant United States Attorney, Viejo stated that he supplied the signed forms to “wash” documents through New York. In return, Viejo received four percent of the profit from the sale of the cars.
 Marcos Amores testified for the government. Amores was another runner who engaged in the practice of registering stolen vehicles at the DMV. He testified that he paid the clerks on many occasions to process applications for stolen vehicles without the proper documentation.
 The government also produced evidence that Linda Alkins in exchange for cash processed three driver’s licenses for a government informant who had no identification. Small also processed a driver’s license with no supporting identification for an undercover government agent.
 Meyers, Watts, and Viejo testified on their own behalf. Meyers denied accepting cash for processing fraudulent applications. She testified that at most she received tips or coffee money for performing multiple transactions; and these were turned in with her cash receipts. there was no record of any tips on the days when she was charged with processing fraudulent applications.
 Watts denied accepting cash for processing fraudulent applications. She testified that she was approached on two occasions by Dvash, who offered to pay her for processing fraudulent applications; but she rejected these advances. Watts further testified that she tried to avoid doing work for Joniaux since she knew that her documents often were forgeries. She said that she did accept applications from Marcos Amores, whose work was neat. Watts stated that she had made mistakes in the past when she accepted forged documents. Finally, she explained the statement she made upon learning of her arrest on mail fraud charges to the effect that everyone in the office could be arrested for mail fraud; she said that she meant that due to pressure the DMV clerks could forget to indicate that a specific identification had been provided.
 Viejo also denied any wrongdoing. As part of his defense, he presented the testimony of some of his salespeople. They testified that it was part of the ordinary course of business for Viejo to supply them with blank, signed New Jersey reassignment forms. They were responsible for completing the information regarding the purchaser of the vehicle. Viejo’s son testified that English was Viejo’s second language.
 Appellants’ motions for judgments of acquittal at the close of the evidence were denied. The jury returned guilty verdicts against all appellants on the RICO substantive and conspiracy counts. In addition, Barbara Alkins was convicted on one count of possession of a stolen motor vehicle in violation of 18 U.S.C. § 2313
(1988); on three counts of possession of counterfeit securities of a state in violation of 18 U.S.C. § 513 (1988); and on nine counts of mail fraud in violation of 18 U.S.C. §§ 1341 and 1346 (1988). She was acquitted on one count of possession of counterfeit securities of a state. Small was convicted on two counts of possession of counterfeit securities of a state and on three counts of mail fraud. One of her mail fraud convictions subsequently was dismissed by the district court. Linda Alkins was convicted on one count of possession of a stolen motor vehicle; on four counts of possession of counterfeit securities of a state, and on one count of mail fraud. Meyers and Watts were both convicted on three counts of mail fraud. Viejo was convicted on fifteen counts of mail fraud; he was acquitted on three counts of mail fraud.
 Barbara Alkins was sentenced to a 21 month term of incarceration, followed by 2 years of supervised release. Small was sentenced to an 18 month term of incarceration, followed by 2 years of supervised release. Linda Alkins was sentenced to a 21 month term of incarceration, followed by 2 years of supervised release. Meyers was sentenced to a 12 month term of incarceration, followed by 2 years of supervised release. Watts was sentenced to a 9 month term of incarceration, followed by 4 years of supervised release. Viejo was sentenced to a 26 month term of incarceration, followed by 3 years of supervised release. Judgment was entered against Barbara Alkins, Small, Linda Alkins, Meyers, and Watts on February 2, 1990, and against Viejo on March 5, 1990.
 These appeals followed.
 We turn first to appellants’ contentions concerning their mail fraud convictions. Small, Meyers, Watts, and Viejo contend that certain of their mail fraud convictions violated the ex post facto clause of the Constitution. They also contend that the district court’s instruction on the good faith defense to mail fraud was inadequate. We reject both contentions.
 We consider first the challenge of appellants Small, Meyers, Watts, and Viejo to certain of their mail fraud convictions. They contend that their convictions on six of the mail fraud counts violated the ex post facto clause of the Constitution. We disagree.
 The mail fraud convictions involved on the instant appeal are based on the definition of a scheme to defraud in 18 U.S.C. § 1346
(1988). that statute was passed in response to the Supreme Court’s holding in McNally v. United States, 483 U.S. 350
(1987). In McNally, the Court held that the mail fraud statute applied only to schemes to defraud individuals of property rights, but not to schemes to defraud them of the intangible right to honest government. Id. at 360. Section 1346 brings schemes “to deprive another of the intangible right of honest services” within the purview of the federal mail fraud statute. It was enacted after the McNally decision and became effective on November 18, 1988. Anti-Drug Abuse Act of 1988, Pub.L. No. 100-690, § 7603(a), 102 Stat. 4181, 4508 (1988).
 In nineteen of the mail fraud counts charged in the instant indictment, appellants’ conduct took place entirely after the effective date of § 1346. With regard to six counts (counts 40, 42-44, 49, and 52), however, appellants processed fraudulent applications for vehicle registrations prior to the effective date of the statute, but the resulting registrations were mailed after the effective date of the statute. Appellants contend that their convictions on those six counts cannot stand since their fraudulent conduct occurred prior to November 18, 1988.
 “[T]wo critical elements must be present for a criminal or penal law to be ex post facto: it must be retrospective, that is, it must apply to events occurring before its enactment, and it must disadvantage the offender affected by it.” Weaver v. Graham, 450 U.S. 24, 29 (1981) (footnote omitted). “The critical question is whether the law changes the legal consequences of acts completed before its effective date.” Weaver, supra, 450 U.S. at 31.
 The government urges us to reject appellants’ ex post facto
claim since the crime of mail fraud is not complete until there is a mailing. Schmuck v. United States, 489 U.S. 705, 711 (1989). The “`application of a statute to [a crime] that began prior to, but continued after, the effective date of [the statute],'” does not violate the ex post facto clause. United States v. Torres, 901 F.2d 205, 226 (2 Cir. 1990) (citation omitted). The government reasons that the crime continued until the mailings occurred and since they did not occur until after the effective date of the statute, the ex post facto clause was not violated. If appellants themselves had placed the fraudulent registrations in the mail after the effective date of the statute, we would be inclined to accept that reasoning. In the instant case, however, appellants did not do so. Since we must focus on appellants’ conduct subsequent to the effective date of § 1346, we cannot adopt the government’s reasoning.
 The ex post facto clause serves two principal aims. It ensures that individuals have been provided fair notice of conduct that will subject them to criminal sanctions and it is a check against vindictive legislation. Weaver, supra, 450 U.S. at 28-29; Dufresne v. Baer, 744 F.2d 1543, 1546 (11 Cir. 1984) cert. denied, 474 U.S. 817 (1985). These goals would be jeopardized if Congress were able to criminalize conduct after it has occurred simply by making criminality turn on a jurisdictional fact that is bound to occur after enactment and is the unpreventable consequence of conduct by the defendant before enactment. The application of such a statute to impose criminal penalties on an individual whose conduct was not criminal when performed would violate the ex post facto clause.
 The facts in the instant case, however, do not pose that problem. First of all, there is no question that the basic conduct in question was criminal under state law. Having committed it, appellants were not powerless to prevent the consequences of their actions. They were convicted of mail fraud because they caused the mails to be used in connection with their fraudulent scheme. 18 U.S.C. § 1341 (1988). “Where one does an act with knowledge that the use of the mails will follow in the ordinary course of business, or where such use can reasonably be foreseen, even though not actually intended, then he `causes’ the mails to be used.” Pereira v. United States, 347 U.S. 1, 8-9 (1954). Appellants’ conduct, from which the mailings followed in the ordinary course of business, occurred prior to the effective date of the statute. That conduct, however, would not have resulted in criminal penalties against appellants if they had taken steps to prevent the final element of the crime from occurring, such as alerting DMV officials to the existence of the fraudulent applications. Instead, appellants, by virtue of their acquiescence, permitted the mailing to occur after the enactment of § 1346. Since appellants permitted the final element of the crime to occur after the effective date of the statute, their mail fraud convictions did not violate the ex post facto
 We hold that appellants’ mail fraud convictions based on fraudulent conduct that occurred prior to the effective date of § 1346 did not violate the ex post facto clause since appellants could have taken steps after the effective date of that statute to halt the mailings.
 We consider next appellants’ contention that the district court’s instruction on the good faith defense to mail fraud was inadequate. We find no merit in this contention.
 Good faith is a complete defense to a mail fraud charge United States v. Bronston, 658 F.2d 920, 931 (2 Cir. 1981),
cert. denied, 456 U.S. 915 (1982). If an individual believes that the information set forth in a mailing is true, it follows that he cannot have the requisite intent to defraud. The government must prove lack of good faith beyond a reasonable doubt. Id.
 In the instant case, the district court instructed the jury as follows:
“Since an essential element of the crime charged is intent to defraud, it follows that good faith on the part of a defendant is a complete defense to a charge of fraud. A defendant has no burden to establish a defense of good faith. The burden is on the government to prove fraudulent intent and consequent lack of good faith beyond a reasonable doubt.
Under the anti-fraud statutes, even false representations or statements or omissions of material facts do not amount to a fraud unless done with fraudulent intent. However misleading or deceptive a plan may be, still it is not fraudulent if it was devised or carried out in good faith. An honest belief in the truth of the representations made by a defendant is a good defense, however inaccurate the statement may turn out to be.”
 Watts requested that the district court define “good faith”. The court declined to change its instruction, stating that the term was self-explanatory. A court has discretion to determine what language to use in instructing the jury as long as it adequately states the law. United States v. Hsieh Hui Mei Chen, 754 F.2d 817, 825 (9 Cir.), cert. denied, 471 U.S. 1139 (1985); United States v. Taylor, 562 F.2d 1345, 1364 (2 Cir.), cert. denied, 432 U.S. 909 (1977). The instruction given by the district court here adequately stated the good faith defense. The court did state the meaning of “good faith” when it instructed the jury that “[a]n honest belief in the truth of the representations made by a defendant is a good defense, however inaccurate the statement may turn out to be.” No further elaboration was necessary.
 We hold that the district court adequately instructed the jury on the good faith defense to mail fraud.
 This brings us to Linda Alkins’ claim that there was insufficient evidence to support her conviction of possession of a stolen motor vehicle. Specifically, Alkins contends that there was insufficient evidence from which the jury could infer that the vehicle in question crossed a state boundary. Although evidence of the vehicle’s movement from New Jersey to New York was not overwhelming, we hold that it was sufficient to warrant the jury’s verdict. In making this determination, we view the evidence in the light most favorable to the government to determine whether a rational jury could have found Alkins guilty beyond a reasonable doubt. United States v. Chang An-Lo, 851 F.2d 547, 554 (2 Cir.), cert. denied, 488 U.S. 966 (1988).
 Linda Alkins was convicted, pursuant to 18 U.S.C. § 2313
(1988), of one count of possession of a stolen motor vehicle that had crossed state boundaries. That statute provides that:
“Whoever receives, possesses, conceals, stores, barters, sells, or disposes of any motor vehicle or aircraft, which has crossed a State or United States boundary after being stolen, knowing the same to have been stolen, shall be fined not more than $5,000 or imprisoned not more than five years, or both.”
 To prove a violation of that statute, the government must demonstrate that “(1) the motor vehicle [was] stolen; (2) the defendant knew the vehicle [was] stolen; (3) the defendant possessed, stored, received or concealed the vehicle; and (4) the vehicle crossed state lines after being stolen.” United States v. Mitchell, 876 F.2d 1178, 1180 (5 Cir. 1989).
 In the instant case, the parties stipulated that a certain Jeep Cherokee was stolen in New Jersey. When she registered the vehicle, Linda Alkins knew it was stolen since that message would have been displayed on her computer terminal when she typed in the vehicle identification number. Accordingly,
the only element Linda Alkins challenges is whether the government proved that the vehicle crossed the border from New Jersey to New York.
 The government may establish the location and movement of a vehicle by circumstantial evidence. United States v. Minor, 815 F.2d 472, 474 (8 Cir. 1986). In the instant case, the evidence established that the Jeep Cherokee was stolen in New Jersey by Anthony Santos and his associates, a car theft ring that operated out of New York. Santos lived in New York. One of the runners, Andy Williams, testified that he had seen other cars that were stolen by Santos’ gang in New York. The car here involved was registered to a New York address. Newly registered cars are required to be inspected in New York within ten days of registration. A rational jury could have inferred from those facts that the Jeep Cherokee crossed the border from New Jersey to New York after it was stolen.
 We hold that there was sufficient evidence to convict Linda Alkins of possession of a stolen motor vehicle that had been transported from New Jersey to New York.
 We turn now to appellants’ contentions concerning their RICO convictions. They contend that their conduct was isolated and sporadic, and therefore did not constitute a pattern of racketeering activity. They further contend that the court’s erroneous instruction on the pattern element requires reversal. They also contend that the court erred in denying their request for a multiple conspiracies charge. Meyers contends that her conviction must be vacated since she was guilty only of accepting gratuities and not of accepting bribes. Viejo challenges the sufficiency of the evidence on his RICO convictions. We shall consider these contentions seriatim. We reject each of them.
 We turn first to appellants’ challenge to the sufficiency of the evidence on the pattern element. We find no merit in appellants’ characterization of their actions as isolated and sporadic. We hold that the evidence demonstrated that the racketeering acts charged against each appellant were sufficiently related and posed the threat of continuity essential to establishing a pattern under RICO. Prior to considering appellants’ convictions individually, we set forth the general principles that govern our analysis.
 To convict appellants on the RICO counts, the government was required to prove beyond a reasonable doubt that appellants conducted the affairs of an enterprise engaged in interstate commerce through a pattern of racketeering activity. 18 U.S.C. § 1962(c) (1988). Appellants challenge the government’s proof only as to the pattern element.
 Proof of at least two acts of racketeering activity is necessary, but is not sufficient to convict under RICO. H.J. Inc. v. Northwestern Bell Tel. Co., 109 S.Ct. 2893, 2899 (1989) United States v. Indelicato, 865 F.2d 1370, 1382 (2 Cir.) (en banc), cert. denied, 109 S.Ct. 3192 (1989); 18 U.S.C. § 1961(5) (1988). “[T]o prove a pattern of racketeering activity a . . . prosecutor must show that the racketeering predicates are related, and that they amount to or pose a threat of continued criminal activity.” H.J. Inc., supra, 109 S.Ct. at 2900 (emphasis in original).
 “An interrelationship between acts, suggesting the existence of a pattern, may be established . . . [by] proof of their temporal proximity, or common goals, or similarity of methods, or repetitions.” Indelicato, supra, 865 F.2d at 1382. In United States v. Tillem, 906 F.2d 814 (2 Cir. 1990), we considered a case in which employees of the New York City Department of Health solicited bribes in exchange for passing grades on health inspections. We held that the predicate acts (violations of the Hobbs Act) were related since “they all sought a `common goal,’ — the receipt of free money or services in exchange for the Department defendants giving restaurants a passing test score after inspecting them.” Id. at
825 (citation omitted); see also United States v. Gelb, 881 F.2d 1155, 1163 (2 Cir.) (schemes involving meter tampering and bribery designed to cheat the Postal Service out of postage were sufficiently related to establish a pattern), cert. denied, 110 S.Ct. 544 (1989); United States v. Bortnovsky, 879 F.2d 30, 41 n. 16 (2 Cir. 1989) (“predicate act[s] involv[ing] efforts by the defendants to recover on false insurance claims, whether it be for fire or theft” were sufficiently related to establish a pattern).
 Similarly, in the instant case, the predicate acts charged against the clerks all involved a common goal — the receipt of cash bribes in exchange for processing fraudulent licenses and registrations for stolen vehicles. The predicate acts charged against Viejo also were related to one another. Each involved Viejo supplying a signed, blank New Jersey reassignment form so that a registration could be obtained for a stolen vehicle. Viejo also benefitted financially from these transactions.
 We consider now the racketeering acts upon which appellants’ convictions were based. The government proved one act of possession of a motor vehicle and nine acts of mail fraud to support Barbara Alkins’ RICO convictions. All but one of these acts involved processing a fraudulent application for a vehicle registration in exchange for a cash payment. These acts all had a common goal and the methods used to perpetrate them were similar. They thus were sufficiently related to one another to establish a pattern of racketeering activity.
 Small’s convictions were supported by proof of two acts of bribery and two acts of mail fraud. Three of these acts involved the processing of fraudulent registrations and one involved the processing of a fraudulent driver’s license in exchange for cash payments. All the acts had a common goal and were characterized by similar methods. Indeed, the two acts of mail fraud both involved New Jersey reassignment forms supplied by Viejo to Lozano. These acts were sufficiently related to establish a pattern of racketeering activity.
 Linda Alkins’ convictions were supported by proof of one act of possession of a stolen vehicle and one act of mail fraud. Both acts involved the processing of fraudulent registrations in exchange for cash. Both acts involved New Jersey reassignment forms that were supplied by Viejo to Lozano. These acts had a common goal and were sufficiently related to establish a pattern of racketeering activity.
 Both Meyers’ and Watts’ RICO convictions were supported by three acts of mail fraud. In each case, appellants processed fraudulent applications for vehicle registrations that were supplied by Lozano and included New Jersey reassignment forms furnished by Viejo. These acts had a common purpose and were characterized by identical methods. They satisfied the relatedness requirement of the pattern element of RICO.
 Fifteen acts of mail fraud supported Viejo’s RICO convictions. Each act involved his supplying a signed, blank New Jersey reassignment form for the purpose of registering a stolen vehicle at the DMV. Viejo received four percent of the profit from the sale of these vehicles. These acts had a common purpose and were characterized by identical methods. The relatedness element of the pattern requirement of RICO was satisfied as to Viejo.
 The evidence also demonstrated that appellants’ conduct posed the threat of continuing criminal activity. In determining this element, we have held that external facts can be considered Indelicato, supra, 865 F.2d at 1383; United States v. Kaplan, 886 F.2d 536, 542 (2 Cir. 1989), cert. denied, 110 S.Ct. 1127 (1990). External facts may include evidence of crimes not charged in the indictment if the defendants are aware that they may face such proof. Kaplan, supra, 886 F.2d at 543-44.
 In the instant case, the testimony of the runners and of Isabel Lozano indicated that appellants’ conduct was not isolated and sporadic; rather, it was repeated and widespread. That testimony indicated that appellants’ conduct was not limited to the acts charged as predicates in the indictment.
The fact that the clerks processed many applications that did not result in fraudulent licenses and registrations speaks only to the fact that most visitors to the DMV do not require such a service. It does not negate the inference that the clerks made themselves available to process applications for those people who could not legally obtain licenses and vehicle registrations. The evidence indicates that this activity would have continued but for its discovery. Gelb, supra, 881 F.2d at 1164.
 We hold that there was sufficient evidence to establish that each appellant engaged in a pattern of racketeering activity under RICO. The proof adduced at trial showed that the racketeering acts with which appellants were charged were related and posed the threat of continuity.
 Appellants contend and the government concedes that the district court’s instruction on the pattern element of RICO misstated the law of this circuit. We agree that the court erred, but we hold that it did not rise to the level of plain error and therefore does not require reversal.
 The district court instructed the jury that
“A pattern consists of at least two acts of racketeering activity. There are a total of 31 acts charged in the indictment. Not all the defendants are charged with all 31 acts. The unlawful acts making up the pattern of racketeering activity need not be shown to be related to each other. The government need only prove that two or more predicate acts were carried out by each particular defendant in the conduct of the affairs of the enterprise.”
 That instruction follows the approach of United States v. Ianniello, 808 F.2d 184, 190-92 (2 Cir. 1986), cert. denied, 483 U.S. 1006 (1987). We overruled Ianniello in Indelicato.
As explained above, the law of this circuit is that the acts that constitute the pattern of racketeering activity must be related and continuous or pose the threat of continuity. The court’s contrary instruction was erroneous.
 The charge was circulated in advance. There is no indication in the record that appellants objected to it as required by Fed.R.Crim.P. 30. Since appellants failed to object to the improper pattern charge, we may reverse only for plain error United States v. Scarpa, 913 F.2d 993, 1020-21 (2 Cir.), cert. denied, 111 S.Ct. 57 (1990); Tillem, supra, 906 F.2d at 824-25; Fed.R.Crim.P. 52(b).
 “Plain error is defined as an error so egregious and obvious as to make the trial judge and prosecutor derelict in permitting it, despite the defendant’s failure to object.” Tillem, supra, 906 F.2d at 825. The plain error doctrine results in reversal only “when necessary to redress a miscarriage of justice.” Id.
 The erroneous instruction here did not affect the fundamental fairness of the trial since, as demonstrated above, there was substantial evidence that the acts of racketeering were related and posed the threat of continuity. Id. The court’s erroneous instruction did not result in a miscarriage of justice.
 We hold that the erroneous instruction on the pattern element of RICO given by the district court did not constitute plain error and does not require reversal.
 This brings us to appellants’ contention that the district court erred in denying their request for a multiple conspiracies charge. We hold that the failure to give the requested charge did not prejudice appellants and therefore does not require reversal.
 A conviction cannot stand if the government has alleged a single conspiracy, but its proof demonstrates multiple conspiracies. Kotteakos v. United States, 328 U.S. 750 (1946). Accordingly, “where the proof is susceptible to the inference that there was more than one conspiracy, the question of whether one or more than one conspiracy has been established is a question of fact for a properly instructed
jury.” United States v. Maldonado-Rivera, 922 F.2d 934, 962 (2 Cir. 1990); accord United States v. Uccio, 917 F.2d 80, 87 (2 Cir. 1990); United States v. Friedman, 854 F.2d 535, 561 (2 Cir. 1988), cert. denied, 490 U.S. 1004 (1989). If the evidence admits of no possibility that there was more than one conspiracy, a multiple conspiracies charge is not necessary United States v. Martino, 664 F.2d 860, 875 (2 Cir. 1981) cert. denied, 458 U.S. 1110 (1982).
 Even if a multiple conspiracies charge should have been given, the failure to do so does not automatically require reversal. “To justify reversal . . . appellants must . . . demonstrate both the likelihood of multiple conspiracies having existed, and substantial prejudice resulting from the failure to give the requested charge.” United States v. Barlin, 686 F.2d 81, 89 (2 Cir. 1982). Appellants have not sustained that burden.
 “Multiple conspiracies exist where the evidence shows separate networks operating independently of each other.” Id. To prove a single conspiracy, the government must demonstrate that the conspirators agreed on a common purpose. Maldonado-Rivera, supra, 922 F.2d at 963; United States v. Beech-Nut Nutrition Corp., 871 F.2d 1181, 1191 (2 Cir.), cert. denied, 110 S.Ct. 324 (1989); Friedman, supra, 854 F.2d at 562. “So long as the alleged RICO co-conspirators have agreed to participate in the affairs of the same enterprise, the mere fact that they do not conspire directly with each other `does not convert the single agreement to conduct the affairs of an enterprise through a pattern of racketeering activity into multiple conspiracies.'”Friedman, supra, 854 F.2d at 562-63 (citation omitted).
 In the instant case, the evidence demonstrated that appellants agreed on a common purpose, i.e., “to operate the [DMV] for private gain through a pattern of racketeering activity.” Id.
at 563. The evidence demonstrated that the clerks at the DMV cooperated with one another by communicating how to process the fraudulent documents. Moreover, each was aware of the “nature and extent” of the enterprise and that their role was only part of a larger scheme. Beech-Nut, supra, 871 F.2d at 1191. The clerks were aware of the various runners who sought to obtain false documentation for car thieves, illegal aliens and others who wished to conceal their true identities. Similarly, Viejo was aware that the signed forms he was supplying ultimately would find their way to the DMV as part of a scheme to register stolen vehicles. The evidence indicated that there was only one conspiracy to operate the DMV through a pattern of racketeering activity. Appellants were not prejudiced by the failure to give a multiple conspiracies charge.
 We hold that the district court’s denial of appellants’ requested charge on multiple conspiracies does not require reversal since there was ample evidence of a single conspiracy and appellants were not prejudiced by the failure to give the requested charge.
 We turn next to Meyers’ contention that her RICO conviction must be vacated since the evidence showed, at worst, that she accepted gratuities. She contends that the government was required to prove that she was guilty of accepting bribes under New York State law. We find no merit in this contention.
 The racketeering acts supporting a RICO conviction may include “any act . . . involving . . . bribery . . . which is chargeable under State law and punishable by imprisonment for more than one year.” 18 U.S.C. § 1961(1)(A) (1988). Meyers argues that under New York law she was guilty only of receiving gratuities, a misdemeanor not punishable by more than one year. N.Y. Penal Law § 200.35 (McKinney 1988). She contends therefore that her RICO conviction cannot stand.
 Meyers’ contention simply misunderstands the charges against her. Crimes involving state law bribery are sufficient, but not necessary, to support a RICO charge. In the instant case, the government alleged and proved that three
acts of mail fraud supported Meyers’ RICO conviction. Two or more acts of mail fraud that are related and continuous or pose the threat of continuity can support a RICO conviction. 18 U.S.C. § 1961(1)(B) (1988); see also United States v. Porcelli, 865 F.2d 1352, 1355 (2 Cir.) (mail fraud as racketeering acts supporting RICO conviction), cert. denied,
110 S.Ct. 53 (1989); United States v. Teitler, 802 F.2d 606, 611 (2 Cir. 1986) (same). Since the government did not allege bribery under New York law as one of the racketeering acts in which Meyers engaged, the fact that her conduct may have been chargeable under New York law only as a misdemeanor, is immaterial to her conviction.
 We hold that Meyers’ RICO conviction should stand regardless of the status of her conduct under New York criminal law, since the government alleged and proved that she violated the federal mail fraud statute.
 This brings us to Viejo’s contention that the evidence was insufficient to support his RICO convictions. He contends that the evidence does not establish his agreement to participate in the conspiracy. We disagree.
 Viejo faces a “very heavy burden” in challenging the sufficiency of the evidence. Scarpa, supra, 913 F.2d at 1003 United States v. Garcia, 907 F.2d 380, 382 (2 Cir. 1990). We will uphold a jury’s verdict if “after viewing the evidence in the light most favorable to the prosecution, any rational trier of fact could have found the essential elements of the crime beyond a reasonable doubt.” Jackson v. Virginia, 443 U.S. 307, 319 (1979) (emphasis in original). “[T]he government [is not] required to preclude every reasonable hypothesis which is consistent with innocence.” Chang An-Lo, supra, 851 F.2d at 554.
 To sustain the RICO charges against Viejo, the government was required to prove that he agreed to participate in the affairs of the DMV through at least two predicate crimes. United States v. Rastelli, 870 F.2d 822, 828 (2 Cir.), cert. denied, 110 S.Ct. 515 (1989); Friedman, supra, 854 F.2d at 561. In addition, the government was required to prove “that he [knew] the general nature of the conspiracy and that the conspiracy extend[ed] beyond his individual role.” Rastelli, supra, 870 F.2d at 828. The government was not required to prove that Viejo conspired directly with the clerks at the DMV. Rastelli, supra, 870 F.2d at 828; Friedman, supra, 854 F.2d at 562. There was sufficient evidence from which the jury reasonably could conclude that the government had sustained its burden with respect to Viejo.
 Viejo contends that the evidence demonstrated that he supplied blank, signed New Jersey reassignment forms to all his salespeople. He contends that this evidence demonstrates that he was an unwitting dupe of Gomez and Bonilla who passed the forms to Isabel Lozano. Evidence presented to the jury justifies its rejection of the inference that Viejo asked it to draw. The most compelling evidence of Viejo’s participation in the conspiracy consists of his own statements to an Assistant United States Attorney. During that interview, Viejo admitted that the purpose of the blank forms was to “wash” documents through New York. He also admitted that he knew that these documents would be filled out falsely and that he supplied the forms because he received a four percent commission on the sales of the stolen vehicles. These statements indicate that he knew that his was only one role in a larger conspiracy and that he knew that the ultimate goal of the conspiracy was to register stolen vehicles in New York. The fact that the interview was conducted in English, Viejo’s second language, goes only to the weight to be accorded to the evidence. That matter was properly left to the jury’s judgment. United States v. Villegas, 899 F.2d 1324, 1339 (2 Cir.), cert. denied, 111 S.Ct. 535 (1990).
 We hold that there was sufficient evidence to convict Viejo of conducting the affairs of the DMV through a pattern of racketeering activity and of conspiring to do so.
 Finally, we address appellants’ contention that the court erred in limiting their cross-examination of a government witness. Specifically, they contend that they should have been allowed to question Yizhaq Dvash about a complaint that was filed against him in the Southern District of New York for counterfeiting. That complaint included an allegation that Dvash was in possession of a nine millimeter pistol. The prosecution claimed that in truth Dvash was in possession of a beeper, not a gun. Appellants contend that they should have been allowed to pursue this line of questioning to determine whether the government had dropped gun possession charges against Dvash in exchange for his testimony.
 We will reverse a district court’s decision to limit cross-examination only if it amounted to an abuse of discretion Tillem, supra, 906 F.2d at 827. The court here refused to allow appellants to cross-examine Dvash on this subject since the evidence did not bear on credibility and, in any event, was of limited relevance and was likely to cause confusion and delay. We find no error in this ruling.
 This evidence, even if relevant, was cumulative at best. The jury already knew that Dvash was an illegal alien and a counterfeiter, and they knew of his role in the corrupt activities at the DMV. It therefore was already in a position to judge his motive for testifying for the government. Id. at 828.
 We hold that the district court did not abuse its discretion in limiting the cross-examination of Yizhaq Dvash.
 To summarize:
 We hold that appellants’ mail fraud convictions did not violate the ex post facto clause since appellants, after the effective date of § 1346, could have halted the mailings that they had caused, but they failed to do so. We also hold that the court’s instruction on the good faith defense to mail fraud was adequate. We likewise hold that there was sufficient evidence to establish the pattern of racketeering activity element of RICO as to each appellant; the court’s erroneous instruction on that element did not amount to plain error. We further hold that the failure to give a requested multiple conspiracies charge did not prejudice appellants. Finally, we hold that the court did not abuse its discretion in limiting the cross-examination of a government witness. We find no merit in the remainder of appellants’ claims of error.