SWYGERT, Senior Circuit Judge:

George Lada, Tommy Orr, Mark Auk, and Tony Auk appeal their jury convictions for conspiracy to violate the Dyer Act and for substantive violations of the Dyer Act, 18 U.S.C. § 2312, 2313. The appellants raise a number of issues on appeal: (1) whether the district court abused its discretion in refusing to allow defense counsel to cross-examine a government witness on certain matters; (2) whether the district court abused its discretion in refusing to order the government to disclose a prior statement of a non-testifying witness; (3) whether the district court erred in instructing the jury on "deliberate ignorance"; (4) whether the district court correctly refused defendants' requested instruction on defense theories of the case; (5) whether the evidence is sufficient to support the convictions; (6) whether the district court correctly admitted evidence on the search of one of the appellant's premises; (7) whether the court erred in its aiding and abetting instruction; and (8) whether the possible inadvertent admission of a search warrant into evidence was reversible error. We reject all of the appellants' arguments and affirm the convictions.

I

Codefendants John Wesley Ervin and George Blanton Ali ran a car theft operation based in Detroit, Michigan. The two would purchase salvage automobiles to obtain the salvage titles and the vehicle identification number (VIN) tags, metal plates bearing the manufacturer's serial numbers identifying the cars. Next, they would arrange for an associate to steal a car that generally matched the description of the salvage car. Finally, they would attach the salvage car's VIN plate to the stolen car, take the stolen car to another state, and sell it. This type of operation is known as a "salvage switch."

A. Tommy Orr

Appellant Tommy Orr owned a used car lot business, Elite Motor Company in Warner Robins, Georgia. In connection with that business, he had a financing arrangement with Rudolph and Mark Flanders. On March 1, 1983, Orr and Mark Flanders met Ervin and Ali at the Albany Auto Auction. Orr discussed buying an Oldsmobile Regency that Ervin and Ali were attempting to register at the auction. Two days later, Ervin brought the car to Elite Motors and Orr purchased it. Ervin signed a blank bill of sale and gave Orr the Michigan salvage title, which was in the name of State Farm Insurance Company.

On March 6, 1984, Orr wrote to State Farm to determine whether he could obtain clear title to the car. In his letter, Orr described the Regency as "in excellent condition, requiring only minor repair." State Farm's representative replied that the car in question had been "stolen twice and stripped so that it was in worse condition than had it been totally wrecked."

Despite this reply, Orr sold the Regency to Carolyn Tidwell and completed the blank bill of sale. On the bill of sale, he stated he purchased the automobile from Ervin on March 26, 1984 for $4,800. Ervin testified that he had received much less than the stated amount. Orr also filled out the back of the Michigan salvage title indicating that he had purchased the car from the State Farm representative for $4,800.

Subsequently, Orr bought eleven more cars from Ervin and Ali. Each time Orr had Ervin sign a blank bill of sale. Orr would then fill in information to match the salvage titles of the automobiles he sold.

In April 1984, Orr gave Ervin a dealer's tag to facilitate transportation of the Michigan cars to Georgia. In June 1984, Orr told Ervin to retrieve a car that Orr had bought from him. Flanders had found papers in the car indicating it was a 1984 Cadillac, rather than a 1982 Cadillac. Ervin took the car back and later sold it to another buyer. When the government's investigation began in the summer of 1984, Orr told Ervin never to come back to Warner Robins because the police were "snooping around."

B. George Lada

Appellant George Lada owned and operated Petersburg Tractor Company, which was a licensed salvage vehicle dealer. Lada was required by law to maintain records of his salvage vehicle purchases and sales. Lada properly maintained his records until the end of 1983. In early 1984, however, Lada's records showed Petersburg Tractor Company as both the purchaser and seller of the salvage cars. In other words, one could no longer ascertain the chain of ownership by examining the record books. Lada claimed that he had adopted this mode of recordkeeping to sell cars at auctions.

Ervin testified that he purchased only the VIN plate and Michigan salvage title from Petersburg Tractor Company. He stated that he paid cash for these items and never saw the salvage car itself. Detective Bruce Saller of the Michigan State Police searched the Petersburg Tractor Company property in 1984. During that search, he found a truck that had had its vehicle identification number plate removed. He also found the burnt frame of an Oldsmobile Cutlass. When he ran a check on the vehicle identification number, he discovered that a stolen car bearing that same VIN had been sold in Georgia to Dewey Robinson in July 1984. Robinson had purchased a black Oldsmobile Cutlass from Ervin. Although the car was in excellent condition, it bore a Michigan salvage title marked "Not for Highway Use." The title indicated that the car had been bought from Petersburg Tractor Company. Lada had assured Robinson that the car bearing the salvage title was in good condition.

C. Mark and Tony Auk

Appellants Mark and Tony Auk operated M T Enterprises, a business in Detroit, Michigan. Ervin had known both Auks, but he dealt primarily with Tony. Ervin bought three vehicle identification plates and salvage titles from M T Enterprises.

Detective Saller also searched Mark Auk's farm, located near Detroit. The April 6, 1984 search yielded a van bearing a falsified registration form. The form listed M T Enterprises as the owner. Saller found a loose identification plate inside the van. The plate should have been attached to a Pontiac Grand Prix, but that automobile was not found on the premises. Saller discovered two cars that had been built using parts from recently stolen cars. Finally, he found a Michigan bill of sale that had been chemically altered to remove the "salvage" stamp.

II

A. Limitations on Cross-Examination of Ervin

John Ervin, a cooperating codefendant, entered into a plea agreement with the government under which he pled guilty to two counts in the indictment and testified for the government. In return, the government would recommend to other jurisdictions not to institute charges against him. The recommendation, however, was not binding.

Before trial, Ervin had telephoned Tony Auk and Auk tape-recorded the conversation. The appellants sought to question Ervin on the stand about statements he made during the telephone conversation. Although the court allowed counsel to question Ervin about his understanding of his plea agreement and his expectations of sentencing, the court refused to admit the tape-recorded conversation for impeachment. The court concluded that the tape constituted impeachment on an irrelevant and collateral matter. Appellants assert that they were prejudiced by the trial court's refusal to admit the tape-recording.

A trial court has broad discretion in controlling the scope and extent of cross-examination. Delaware v. Van Arsdall, 475 U.S. 673, 106 S.Ct. 1431, 1435, 89 L.Ed.2d 674 (1986); United States v. Cameron, 814 F.2d 403, 406 (7th Cir. 1987); United States v. Bulman, 667 F.2d 1374, 1381 (11th Cir.), cert. denied, 456 U.S. 1010, 102 S.Ct. 2305, 73 L.Ed.2d 1307 (1982). That discretion is limited, of course, by a defendant's sixth amendment right to cross-examine a witness. Van Arsdall, 106 S.Ct. at 1435; Bulman, 667 F.2d at 1381 n. 9.

The appellants had ample opportunity to cross-examine Ervin regarding his plea agreement with the government. On cross-examination, defense counsel questioned Ervin about the terms of the plea agreement and the agreement itself was introduced into evidence. The court allowed them to prove Ervin's possible motivation to falsify his testimony. We hold that the court met the constitutional requirements for permitting cross-examination. Further, the court did not abuse its discretion in refusing to admit the tape-recording into evidence. In view of the fact that the jury was well aware of the plea agreement under which Ervin testified, the potential for further impeachment is speculative and minimal, at best. The exclusion of the tape recording was well within the district court's discretion.

B. Statement of Non-Testifying Witness

George Ali, Ervin's partner in the stolen car operation, also entered into a plea agreement with the government that required him to testify if called at trial. Prior to the plea agreement, Ali disclosed to the government his knowledge and activities in the stolen car enterprise. The government did not call Ali to testify at trial. Although the court made Ali available to defense counsel for interviewing, Ali refused to be interviewed. Also, Ali was available to the defense as a witness, but defense counsel did not call him to testify. Prior to the close of the government's case-in-chief, the defense requested that the government produce Ali's statements. The government presented Ali's statement to the court for review in camera. The court concluded that the statement did not contain any Brady material and refused to order disclosure.

The appellants argue that they were entitled to receive the statements Ali made to the government. They urge us to read Fed.R.Crim.P. 16(a)(1)(A) and Fed.R.Evid. 801(d)(2)(E) in pari materia. Combining these two rules, they reason that because the appellants could be held vicariously liable for statements made by coconspirator Ali, Ali's statements would be essentially their own admissions. Rule 16(a)(1)(A) provides for pretrial discovery of the defendant's statements. Therefore, appellants assert, Rule 16(a)(1)(A) should allow discovery of Ali's statements.

The Fourth Circuit had led the way on this issue, holding that defendants were entitled to discover coconspirator's statements under Rule 16(a)(1)(A). United States v. Jackson, 757 F.2d 1486, 1491 (4th Cir.), cert. denied, 474 U.S. 994, 106 S.Ct. 407, 88 L.Ed.2d 358 (1985). However, the Fourth Circuit sitting en banc recently reconsidered that issue and concluded that Rule 16(a)(1)(A) was not intended to apply to coconspirators' statements. United States v. Roberts, 811 F.2d 257, 258 (4th Cir. 1987) ( en banc); see also United States v. Warren, 772 F.2d 827, 837 (11th Cir. 1985), cert. denied, ___ U.S. ___, 106 S.Ct. 1214, 89 L.Ed.2d 326 (1986) (did not directly rule on the matter due to harmless error finding, but deemed the interpretation of Rule 16(a)(1)(A) a "novel claim"); 8 J. Moore, Moore's Federal Practice ¶ 16.04(1) at 16-54 (2d ed. Nov. 1986 Rev.) (statements of coconspirators not available to defendant under Rule 16).

We agree with the Fourth Circuit that Rule 16(a)(1)(A) does not apply to coconspirator's statements. Besides, Fed.R.Evid. 801(d)(2)(E) applies to statements made in furtherance of the conspiracy. Ali's statement to the government was in support of his plea agreement — not in furtherance of the conspiracy. Thus, his statement would not have been admissible as non-hearsay under Rule 801(d)(2)(E). Moreover, Ali did not testify at trial and his statement was not read into evidence or used to impeach the appellants. The district court found no exculpatory evidence in Ali's statement. Consequently, the fact that the appellants were unable to gain access to his statement was harmless error, if error at all.

C. Deliberate Ignorance Instruction

The district court gave the following instruction:

Speaking further of knowledge, the element of knowledge may be satisfied by inferences drawn from proof that a defendant deliberately closed his eyes to what would otherwise have been obvious to him. A finding beyond reasonable doubt of a conscious purpose to avoid enlightenment would permit an inference of knowledge. Stated another way, a defendant's knowledge of a fact may be inferred from willful blindness to the existence of the fact.

Record on Appeal Vol. 11 at 18. The appellants argued that there was insufficient evidence to justify this instruction.

A conscious avoidance instruction must be based upon facts that would "point in the direction of deliberate ignorance." United States v. Aleman, 728 F.2d 492, 494 (11th Cir. 1984) (quoting United States v. Batencort, 592 F.2d 916, 918 (5th Cir. 1979)). Orr had been a used car dealer for over ten years and he purchased twelve cars from Ervin and Ali. The first car he bought from Ervin and Ali, a 1980 Oldsmobile Regency was represented as a 1981 Oldsmobile Regency and it carried a salvage title that stated the car was not for highway use. Orr attempted to obtain a clear title for the car by writing to the insurance company listed as owner of the salvage. Orr wrote that the car had only minor damage and had never been repainted. State Farm Insurance Company's representative responded that the car had been stolen and stripped so that it was in worse condition than if it had been wrecked. Despite the disparity between the appearance of the car he possessed and State Farm's description, Orr sold the car and bought more cars from Ali and Ervin. Seven of the twelve he purchased carried salvage titles marked "Not for highway use." Yet, the cars were in good condition.

The evidence against Lada showed he had sold VIN plates and titles to Ervin. Further, Lada's bookkeeping had changed so that the chain of ownership was impossible to determine. Lada also admitted to falsifying an affidavit in reference to one of the cars.

The evidence against both Orr and Lada pointed in the direction of deliberate ignorance. The trial court properly gave the instruction.

D. Defense Theory Instruction

The appellants requested that the trial court charge the jury on the relationship of buyer and seller and on multiple conspiracies. The court refused to give either instruction.

A defendant is entitled to have the court instruct the jury on the theory of the defense, as long as it has some basis in the evidence and has legal support. United States v. Gold, 743 F.2d 800, 819 (11th Cir. 1984), cert. denied, 469 U.S. 1217, 105 S.Ct. 1196, 84 L.Ed.2d 341 (1985). The district court has broad discretion in constructing its charge within the confines of the law and the facts at hand. Id. We will reverse a trial judge's refusal of a requested instruction only if the rejected instruction was substantively correct; the actual charge to the jury did not substantially cover the proposed instruction, and the failure to give it substantially impaired the defendant's ability to present an effective defense. Id.

Appellants requested the following instruction on the buyer-seller relationship:

You are instructed that the relationship of buyer and seller of goods without any prior or contemporaneous understanding beyond the mere sales agreement does not establish a conspiracy.

Supplemental Record on Appeal, Vol. 1 at 185.

The trial court instructed the jury on the elements of conspiracy. After reviewing the judge's charge as a whole, we find that it substantially covered the proposed instruction. Therefore, the trial court did not abuse its discretion in denying the requested charge. See United States v. Padilla-Martinez, 762 F.2d 942, 952 (11th Cir.), cert. denied, 474 U.S. 952, 106 S.Ct. 320, 88 L.Ed.2d 302 (1985); United States v. Borders, 693 F.2d 1318 (11th Cir. 1982), cert. denied, 461 U.S. 905, 103 S.Ct. 1875, 76 L.Ed.2d 807 (1983).

Defense counsel also requested the Fifth Circuit's Pattern Jury Instruction on multiple conspiracies and the appellants assert that the court erred in refusing this charge. We reject this claim, as well. The appellants have failed to demonstrate the likelihood that multiple conspiracies existed. United States v. Barlin, 686 F.2d 81, 89 (2d Cir. 1982) (appellants must show likelihood of multiple conspiracies and substantial prejudice from denial of charge to justify reversal).

Appellants contend that the government only showed the existence of two or more different schemes primarily because none of the codefendants knew of each other. A single conspiracy, however, does not fragment into multiple conspiracies simply because particular members do not know the identities of other members of the conspiracy. United States v. Wilkinson, 754 F.2d 1427, 1434 (2d Cir.), cert. denied, 472 U.S. 1019, 105 S.Ct. 3482, 87 L.Ed.2d 617 (1985). Moreover, the evidence did not show separate networks operating independently of each other. Id.; Barlin, 686 F.2d at 89. Therefore, failure to charge the jury on multiple conspiracies does not warrant reversal.

E. Sufficiency of the Evidence

The appellants argue that the evidence against them was insufficient to convict them of conspiracy or of aiding and abetting interstate transportation of stolen automobiles. On review, we must view the evidence and the inferences in the light most favorable to the government. Jackson v. Virginia, 443 U.S. 307, 319, 99 S.Ct. 2781, 2789, 61 L.Ed.2d 560 (1979); United States v. Bertram, 805 F.2d 1524, 1531 (11th Cir. 1986); United States v. Smith, 700 F.2d 627, 632 (11th Cir. 1983).

Regarding the conspiracy conviction, once the government establishes the existence of the conspiracy, only slight evidence may suffice to connect a particular defendant to the conspiracy. United States v. Udey, 748 F.2d 1231, 1236 (8th Cir. 1984), cert. denied, 472 U.S. 1017, 105 S.Ct. 3477, 87 L.Ed.2d 613 (1985); United States v. Green, 735 F.2d 1018, 1023 (7th Cir. 1984). It is well-settled that the government need not produce direct evidence to prove participation in a conspiracy. Conspiracy can be proved by the accused's actions or by inferences from circumstantial evidence of a scheme. United States v. Carter, 760 F.2d 1568, 1582 (11th Cir. 1985). Also, each conspirator need not know all the details of the conspiracy, or be aware of the other conspirators, or participate in every phase of the scheme. Id.

With these principles in mind, we have reviewed the record. We conclude that a reasonable trier of fact could have found each of the appellants was involved in the conspiracy. With respect to the aiding and abetting convictions, we find the evidence also sufficient to support the convictions.

F. Evidence of the Search

The appellants claim that the district court erred in admitting evidence that they characterize as evidence of crimes outside the scope of the conspiracy. They objected to evidence from the search of Mark and Tony Auk's farm in Michigan and to testimony of an aide from the Michigan Secretary of State's Office. The aide testified regarding two Michigan salvage title documents that she said Tony Auk presented to her office. The documents had been chemically altered to remove the salvage vehicle stamps. The government asserts that it offered the evidence to prove intent, knowledge, and knowing participation in the conspiracy.

A district court has broad discretion to determine the admissibility of evidence. We will reverse only when a district court abuses that discretion. United States v. Williford, 764 F.2d 1493, 1497 (11th Cir. 1985). Under Fed.R.Evid. 404(b), evidence of extrinsic acts may come in as evidence of scheme or intent. The admitted evidence concerned altered car titles, loose VIN plates, and stolen car parts. The indictment against the appellants charged a conspiracy to deal in stolen cars. The evidence would tend to prove the scheme, or at least the intent to deal in stolen cars. The district court also determined that the probative value of this evidence outweighed its prejudicial effect. We find no abuse of discretion in the admission of this evidence.

G. Aiding and Abetting Instruction

Appellants also contend that the trial court erred in its jury instruction on the elements of aiding and abetting. They take issue with the example the judge gave in describing aiding and abetting. They claim that the charge omitted the element of knowledge. Taking the charge as a whole, however, it is clear that the remaining charge included the element of knowledge. We find no merit in the appellants' argument on this issue.

H. Possible Admission of the Search Warrant

At trial, the district court heard evidence outside the jury's presence that concerned the search of Mark Auk's property. During that conference, the government offered into evidence a certified copy of the Michigan search warrant. No one objected to the admission of the warrant. The government contends that the warrant was admitted on the issue of the legality of the search and that the warrant was not for the jury's consideration. The government claims that the warrant did not go out with the jury.

The appellants, however, assert that the warrant did go to the jury room. They base their assertion on examination of the exhibit list. It is unclear whether the warrant did in fact go out with the jury.

At oral argument, counsel for the government pointed out, and the Auks' counsel conceded, that before the exhibits went to the jury room, the court asked the attorneys to examine them. Therefore, in addition to not objecting when the government moved for admission of the warrant, defense counsel also had the opportunity to prevent what they now claim as error. Because of the lack of objection at the trial level, we must review this issue for plain error.

Several hundred documents, made up of several thousand pages, were admitted for the jury's consideration. The contents of the search warrant were never discussed before the jury. Moreover, the affidavit contained within the warrant merely stated that the Auks were dealing in stolen car parts and the jury had already heard testimony to that effect. We find that the possible inadvertent admission of the warrant was not plain error.

Finding no error in the district court's rulings, we AFFIRM the jury verdict.