Defendant-appellant Ralph Hernandez (Hernandez) appeals his conviction, following a jury trial, of one count of conspiracy to distribute marihuana and four counts of possession of marihuana with intent to distribute. He challenges the sufficiency of the evidence, complains of the denial of his request for a severance, claims a fatal variance between the indictment and the evidence, and contends that a witness was improperly allowed to assert her privilege against self-incrimination. He also challenges his sentence. We affirm.

In January 1989, the police in Plano, Texas began an investigation of a man named John Bass (Bass) on suspicion of drug trafficking. Their investigation entailed almost daily surveillance during the early months of 1989.

On the afternoon of April 4, 1989, Bass left his home and drove a pickup truck to the parking lot of a local Bennigan's restaurant. A short time later a woman arrived in a rented Ryder van. Bass got into the passenger side of the van and conversed with the driver, whom the police later determined to be Denise Pero (Pero). Soon thereafter a white Lincoln Continental pulled into the parking lot, and Bass went over to talk with the driver, later determined to be defendant-appellant Hernandez. Bass then got back into his pickup truck and drove away. Hernandez got into the van with Pero, and they drove to a Holiday Inn in McKinney, Texas, about fifteen miles north of Plano.

About ten minutes later, Bass arrived driving the pickup truck. Pero dropped Hernandez off at the Holiday Inn, and followed Bass further northward on the highway. About five miles away, they stopped at a service station, filled the vehicles with gas, and switched vehicles: Bass continued on in the Ryder van, and Pero drove back toward McKinney in Bass's pickup truck. Bass drove the van to a ranch near Trenton, Texas belonging to his brother-in-law Scott King (King), and pulled the van into King's garage. When Bass left King's house and drove the van back onto the highway, the police arrested him and took custody of the van. They detected a strong odor of raw marihuana in the van and found a partially smoked marihuana cigarette in the ash tray. In the back of the van were a suitcase and a cardboard box sealed with duct tape. After obtaining a search warrant, they opened the box in the back of the van and found a set of heavy-duty scales. In the suitcase were a number of smaller duffel-type bags. The police obtained and executed a search warrant on King's residence in the early morning hours of April 5. They found in the garage eight large boxes containing marihuana--with a total net weight of slightly less than 300 pounds--and another large triple-beam scale. In the house itself they found $8,050 in currency, several loaded handguns, and several plastic bags containing marihuana. Pero and Hernandez were arrested in the Bennigan's parking lot on the evening of April 4.

Bass cooperated with the government and provided information about his drug trafficking activities dating back to 1986.

On August 15, 1990, Hernandez and eight other persons, including Pero, were named in a 35-count indictment. Hernandez was named in five counts: (1) Count 1, charging all nine defendants with conspiring, from October 1986 to the date of the indictment, to distribute, and possess with intent to distribute, in excess of 1,000 kilograms of a substance containing a detectable amount of marihuana, in violation of 21 U.S.C. §§ 841(a)(1) and 841(b)(1)(A)(vii); (2) Count 6, charging Hernandez and Pero with possession with intent to distribute, and distribution of, between 180 and 200 pounds of marihuana on or about November 29, 1988; (3) Count 11, charging Hernandez, Pero, and two others with possession with intent to distribute, and distribution of, 200 pounds of marihuana on or about January 29, 1989; (4) Count 14, charging Hernandez, Pero, and one other defendant with possession with intent to distribute, and distribution of, 200 pounds of marihuana on or about March 9, 1989; and (5) Count 16, charging Hernandez and Pero with possession with intent to distribute, and distribution of, approximately 315 pounds of marihuana on or about April 4, 1989.

By the time of trial, Pero and several others named in the indictment had entered into plea agreements, and Hernandez was tried jointly with four codefendants. The district court denied his pretrial motion for a severance. Bass's trial testimony described the overall operations of the conspiracy. He testified that marihuana brought into the country in El Paso was brought by courier to him in Plano (a small town near Dallas). Bass utilized a number of locations, including the rural homes of King and of one Fred Harrington (Harrington), to inspect and weigh the marihuana, and to store it until it could be sold to various persons who distributed it in Ohio, Indiana, and Mississippi. Bass testified that in the spring of 1988 Pero called him and told him that she could bring some marihuana to Dallas, if he was interested in selling it. Bass was receptive, because he was experiencing difficulties with one of his regular suppliers, and he began to purchase marihuana regularly from Pero. He testified that on one occasion in September or October of 1988 she was accompanied by Hernandez, whom Pero said worked for the man who actually owned the marihuana and was there to ensure that all of the money was paid and returned safely to the owner. Hernandez helped load the marihuana into Bass's car on that occasion. Bass testified that thereafter during the fall of 1988, Hernandez accompanied Pero several times on the drug transactions, that he participated in the delivery of the marihuana, and that on at least one occasion Bass paid Hernandez directly.

Bass stated that on the day of his arrest, April 4, 1989, he had met with Pero and Hernandez at the Bennigan's restaurant and told them to go to the Holiday Inn in McKinney. At the Holiday Inn he suggested to Pero that in order to avoid attracting attention, Hernandez remain there while the two of them drove the van containing the marihuana to King's ranch.

After the seventh day of the trial, at which point Bass was testifying for the government during its case-in-chief, Hernandez's four codefendants pleaded guilty. At the beginning of the court proceedings the next morning, the district court instructed the jury as follows:

"Ladies and gentlemen of the jury, you will notice that the Defendants, Fred Joseph Harrington, Brigitte Gaon Harrington, Stanley Diers and Morris Patterson are no longer present in Court.

The reason these Defendants are not [sic] longer present here in Court is because of a ruling made by this Court. The reasons for the Court's ruling are not your concern. The absence of these Defendants should not be considered by you as affecting in any way your determination of the guilt or innocence of the Defendant, Ralph Hernandez who remains in Court."

A short time later, Hernandez unsuccessfully moved for a mistrial, arguing that notwithstanding the court's instruction, it was perfectly clear to the jury that the other defendants had pleaded guilty, and that it unfairly prejudiced his defense.

Pero also testified for the government at the trial. She stated that an acquaintance of hers named Henry Barragan (Barragan) had told her in early 1988 that he was going to have marihuana at his disposal in Dallas, and that he was looking for someone to sell it for him. Pero, who had met Bass through her ex-husband's drug activities, called Bass for this reason and arranged the initial sale. She testified that Barragan told her on this initial occasion that he had 50 pounds of marihuana for her and 50 pounds for someone else, whom she learned to be Hernandez when Barragan introduced them in the spring of 1988. She and Hernandez flew to Dallas together and checked into a hotel. The marihuana was driven to Dallas by Barragan's brother and delivered to them at the hotel. Bass came to the hotel and purchased the 50 pounds from Pero. Hernandez then asked Pero if she could also sell his 50 pounds to Bass, so Pero called Bass again, and Bass returned to the hotel and purchased the second 50 pounds from Pero.

Pero testified that she and Hernandez continued to make periodic trips to Dallas to sell marihuana to Bass throughout 1988 and spring of 1989, and that on those occasions Bass and Hernandez met face-to-face, and Bass paid both of them for their marihuana. On a few occasions, King came to meet them instead of Bass. She and Hernandez always flew to Dallas, and a third person would drive the marihuana from El Paso to Dallas and deliver it to them. Pero testified that the driver was frequently Barragan's cousin Teresa Chavez (Chavez). On a few occasions, Pero and Hernandez went to Dallas simply to pick up from Bass money Bass owed to Barragan from a previous marihuana transaction. Credit card slips produced by the government earlier at trial established the dates of these trips by Pero and Hernandez as those charged in the indictment.

Pero testified that on April 4, 1989, she and Hernandez had come to Dallas to sell 300 pounds of marihuana belonging to Hernandez. She stated that at Hernandez's direction they went to a convenience store, where they met two men who had driven the Ryder van containing the marihuana from El Paso, and that Hernandez instructed her to drive the van to the Bennigan's in Plano to meet Bass.

At the beginning of Hernandez's defense, his attorney informed the court that he wished to call Chavez as a witness. Chavez had pleaded guilty to one count of interstate travel in aid of a racketeering enterprise (18 U.S.C. § 1952) charged in the indictment, and was awaiting sentencing. Hernandez's attorney later informed the court that after conferring with Chavez's attorney, he believed that Chavez intended to invoke her Fifth Amendment privilege against self-incrimination. The court called Chavez to the stand, and she informed the court that on advice of counsel she would exercise her privilege against self-incrimination if summoned to testify. Defense counsel then proffered the questions he intended to ask Chavez and argued that given the limited scope of his questioning, she could not have a valid Fifth Amendment right to refuse to answer. The district court disagreed and excused Chavez.

The jury convicted Hernandez on all counts. The presentence report (PSR) on Hernandez calculated a base offense level of 28 and recommended a three-level upward adjustment under U.S.S.G. § 3B1.1(b) for Hernandez's role as a supervisor in the charged offenses. Hernandez objected to the three-level increase on the basis that the trial evidence showed him merely to have been an accomplice to Pero. The district court overruled Hernandez's objection, adopted the PSR's calculation of a total offense level of 33,1 and sentenced Hernandez to concurrent terms of 135 months' imprisonment and a five-year period of supervised release on each count of conviction. Hernandez brings this appeal.

Hernandez first challenges the sufficiency of the evidence. Because he failed to move for a judgment of acquittal at any stage of the trial, we review the sufficiency of the evidence only to determine whether affirmance of his conviction would result in a manifest miscarriage of justice. United States v. Pruneda-Gonzalez, 953 F.2d 190, 193 (5th Cir.1992).

For his conviction under Count 1 of the indictment, Hernandez argues that other than the testimony of Bass and Pero, who were testifying for the government in exchange for leniency, there was nothing to show that he was involved in a conspiracy to distribute marihuana; the police were only able to corroborate Bass and Pero's account with credit card receipts showing that Hernandez had travelled to Dallas, not with evidence independently showing that he had engaged in illegal activity.

There is no requirement that testimony by a co-conspirator fulfilling a plea bargain be corroborated by independent evidence. The jury is entrusted with the responsibility of evaluating the witness's credibility, and uncorroborated testimony of a co-conspirator will sustain a guilty verdict unless, as is not the case here, the testimony is incredible or otherwise insubstantial on its face. United States v. Osum, 943 F.2d 1394, 1405 (5th Cir.1991); United States v. Gardea Carrasco, 830 F.2d 41, 44 (5th Cir.1987).

In the present case, the existence of plea agreements by Bass and Pero was fully disclosed to the jury during direct examination of those witnesses, and the jury was instructed that testimony from an alleged accomplice who has entered into a plea agreement "is always to be received with caution and weighed with great care," and that "[y]ou should never convict a Defendant upon the unsupported testimony of an alleged accomplice unless you believe that testimony beyond a reasonable doubt." The jury nonetheless credited Bass and Pero's version of events, a decision we will not disturb, because their testimony was far from incredible or insubstantial. Bass and Pero's testimony was more than sufficient to establish the requisite elements for a conspiracy conviction under 21 U.S.C. § 846, i.e., (1) the existence of an agreement between two or more persons to violate the narcotics laws, (2) that Hernandez knew of the agreement and intended to join it, and (3) that Hernandez did participate in the conspiracy. See, e.g., United States v. Juarez-Fierro, 935 F.2d 672, 677 (5th Cir.), cert. denied, --- U.S. ----, 112 S. Ct. 402, 116 L. Ed. 2d 351 (1991).

Hernandez challenges his convictions for the substantive counts of possession with intent to distribute primarily on the same basis--that they rest on the uncorroborated testimony of Bass and Pero. For the reasons set forth above, this argument is unavailing. Hernandez also notes that neither Bass nor Pero was specific as to the dates when the supposed transactions took place. Although he is correct that in many cases Bass or Pero could recall only a general time frame for the transactions, the jury was aided by the credit card records and hotel receipts showing exactly when Pero and Hernandez had travelled to Dallas. Moreover, when the indictment uses the "on or about" terminology employed in this case, the prosecution is not obligated to prove the precise date of the offense. See United States v. Tunnell, 667 F.2d 1182, 1186 (5th Cir.1982).

Hernandez has demonstrated no possibility of a manifest miscarriage of justice in affirmance of his convictions based on the evidence produced at trial. Indeed, the evidence was clearly more than sufficient to sustain the convictions under any standard.

Hernandez next argues that the joinder of his case with those of the codefendants was prejudicial, and that the district court therefore erred in denying his motion for severance, made pursuant to Federal Rule of Criminal Procedure 14. The basis for his argument is that his codefendants were people such as Harrington who cooperated with Bass in storing the drugs in the Dallas area and preparing them for distribution and resale, and that Hernandez never had any occasion to deal directly with them or conspire with them for any common purpose.

The decision of whether to sever the trials of persons who are indicted together is within the discretion of the trial court, and the denial of a severance will not furnish grounds for reversal unless the defendant can demonstrate specific compelling prejudice against which the district court was unable to afford protection. United States v. Capote-Capote, 946 F.2d 1100, 1104 (5th Cir.1991), petition for cert. filed (1-23-92); United States v. Massey, 827 F.2d 995, 1004 (5th Cir.1987). Any possible prejudice must, moreover, be balanced against the public's interest in efficient judicial administration. United States v. Lindell, 881 F.2d 1313, 1319 (5th Cir.1989), cert. denied, 496 U.S. 926, 110 S. Ct. 2621, 110 L. Ed. 2d 642 (1990); United States v. Fortna, 796 F.2d 724, 737 (5th Cir.), cert. denied, 479 U.S. 950, 107 S. Ct. 437, 93 L. Ed. 2d 386 (1986).

Hernandez's general assertions of prejudice arising from the joinder with other co-conspirators fall well short of the required showing of specific and compelling prejudice. Although we have recognized the possibility of prejudice from a "spillover effect" if there is "a quantitative and qualitative disparity in the evidence among the co-defendants," United States v. Rocha, 916 F.2d 219, 228 (5th Cir.1990), cert. denied, --- U.S. ----, 111 S. Ct. 2057, 114 L. Ed. 2d 462 (1991), Hernandez has not demonstrated such a disparity. Indeed, he does not base his argument on any specific evidence admitted at trial that would have been inadmissible against him alone. Limited involvement in a conspiracy does not by itself entitle a defendant to severance. Id.; Fortna, 796 F.2d at 738. Although he claims that he was prejudiced by the mid-trial withdrawal of the other defendants, he again fails to specify how that prejudice arose, and we find no support for that view in the record. The district court gave an explanation for the departure of the other defendants that was calculated to prevent prejudice to Hernandez, and the jury was also instructed before retiring that "[t]he Defendant is not on trial for any act, conduct or offense or offenses not alleged in the indictment," and that the jury should not be "concerned with the guilt or [sic] any other person or persons not on trial as a Defendant in this case." The court further instructed the jury that once a defendant was determined to have been part of a conspiracy, acts done in knowing furtherance of the conspiracy were evidence against him even if he had not been aware of them, but that the jury had to make the initial determination of membership in the conspiracy based solely on the particular evidence against the defendant:

"In determining whether a Defendant was a member of an alleged conspiracy, however, you should consider only the evidence, if any, pertaining to his own acts and statements. He is not responsible for the acts or declarations of other alleged participants until it is established beyond a reasonable doubt first that a conspiracy existed, and second, that the Defendant was one of the members."

Hernandez has failed to demonstrate how these precautions by the district court were ineffective to protect him against prejudice, and accordingly he has demonstrated no abuse of discretion in the district court's refusal to sever the cases initially or grant a mistrial after the guilty pleas of his codefendants.

At trial Hernandez requested an instruction clarifying the government's burden to prove the single conspiracy alleged in the indictment. His requested instruction read in part as follows:

"In order to sustain its burden of proof for this charge, the government must show that the single conspiracy alleged in Count 1 of the indictment existed. Proof of separate or independent conspiracies is not sufficient.

....

Even if the evidence in the case shows that Defendant was a member of some conspiracy, but that this conspiracy is not the single conspiracy charged in the indictment, you must acquit Defendant.

Unless the government proves the existence of the single conspiracy described in the indictment beyond a reasonable doubt, you must acquit Defendant."

The district court declined the requested instruction and overruled Hernandez's objection to its omission. The instructions given to the jury did not address the question of multiple conspiracies. Hernandez contends on appeal that the instructions permitted conviction despite a material variance between the single conspiracy alleged in the indictment and the multiple conspiracies he claims were shown by the evidence at trial.

We have held that a variance between the offense charged in the indictment and the proof relied upon at trial constitutes reversible error if it affects the substantial rights of the defendant. United States v. Lokey, 945 F.2d 825, 832 & n. 1 (5th Cir.1991); United States v. Guerra-Marez, 928 F.2d 665, 671 (5th Cir.), cert. denied, --- U.S. ----, 112 S. Ct. 322, 116 L. Ed. 2d 263 (1991). The concerns underlying our cases on variance are to ensure that the indictment notifies a defendant adequately to permit him to prepare his defense, and does not leave the defendant vulnerable to a later prosecution because of failure to define the offense with particularity. Lokey, 945 F.2d at 832-33; United States v. Richerson, 833 F.2d 1147, 1155 (5th Cir.1987). In cases dealing with an alleged variance between a single-conspiracy indictment and evidence showing multiple conspiracies, this concern focuses on the danger of transference of guilt, i.e., the danger that despite demonstrating his lack of involvement in the conspiracy described in the indictment, a defendant may be convicted because of his association with, or conspiracy for other unrelated purposes with, codefendants who were members of the charged conspiracy. See Guerra-Marez, 928 F.2d at 672; Richerson, 833 F.2d at 1155. Accordingly, a multiple conspiracy instruction forcefully reminds the jury that it must acquit the defendant if it concludes that he was not a member of a conspiracy charged against him, even if it finds that he was a member of an uncharged conspiracy. See Guerra-Marez, 928 F.2d at 672 n. 7; United States v. Toro, 840 F.2d 1221, 1236 (5th Cir.1988).

In the present case, several factors minimize the concern that transferred guilt contributed to the jury's guilty verdict for Hernandez. First, Hernandez's defense at trial was not directed to establishing the separateness of his dealings with Bass from any of Bass's other operations; the defense that Hernandez presented for the jury to accept or reject was that he had never had any knowing involvement in any marihuana or other drug trafficking and was not a part of any conspiracy. Second, because all of the other defendants had dropped out of the case before the government's case-in-chief was completed, there is strong reason to presume that the jury's attention was properly focused only on Hernandez's conduct when the case was submitted to it.

Hernandez argues on appeal that the government proved only a series of component conspiracies between Bass and his various suppliers and distributors, but that no reasonable jury could have inferred a single agreement among the various codefendants. We disagree. Whether the evidence shows one or multiple conspiracies is a factual determination principally based on three factors: (1) the existence of a common goal or purpose, (2) the nature of the scheme, and (3) overlapping of participants in the various dealings. Guerra-Marez, 928 F.2d at 671; Richerson, 833 F.2d at 1153. Hernandez's protestation that he had no dealings with some of his codefendants, even if correct, is not dispositive: the overlapping of participants contemplated by the factors above may be fulfilled if a pivotal figure such as Bass directs and organizes the illegal activity and has extensive dealings with each of the parties. See Lokey, 945 F.2d at 833; United States v. DeVarona, 872 F.2d 114, 119 (5th Cir.1989); Richerson, 833 F.2d at 1154.

Moreover, the consideration that this Court found decisive in Lokey, DeVarona, and Richerson--whether the activities of one aspect of the scheme were necessary to or advantageous to the success of other aspects or of the overall venture--is present in this case. As must have been obvious to Hernandez, Bass's willingness and ability to pay him cash for large quantities of marihuana in their frequent sales depended upon Bass's continued ability to steadily move the marihuana further along in the chain toward the eventual consumer.2 2]

That the evidence supported the existence of a single conspiracy, however, does not necessarily preclude the possibility that a jury could rationally have found multiple conspiracies to be present, and thus does not necessarily resolve the issue of the district court's refusal to give the requested jury instruction; a defendant is generally entitled to an instruction on any defensive theory for which the evidence is sufficient for a reasonable jury to rule in favor of the defendant on that theory. United States v. Stowell, 953 F.2d 188, 189 (5th Cir.1992) (per curiam), cert. denied, --- U.S. ----, 112 S. Ct. 1269, 117 L. Ed. 2d 497 (1992); see also United States v. Erwin, 793 F.2d 656, 663 (5th Cir.), cert. denied, 479 U.S. 991, 107 S. Ct. 589, 93 L. Ed. 2d 590 (1986). However, we are not convinced that the refusal here warrants reversal. For a refusal to give a requested jury instruction to constitute reversible error, the instruction (1) must have been substantially correct, (2) must not have been substantially covered in the charge given to the jury, and (3) must have concerned an important issue so that the failure to give it seriously impaired the defendant's ability to present a given defense. United States v. Allison, 953 F.2d 870, 876 (5th Cir.1992); United States v. Terrazas-Carrasco, 861 F.2d 93, 95 (5th Cir.1988). As noted above, the absence of an instruction on multiple conspiracies did not seriously impair Hernandez's ability to present, as he did through his own testimony, his already chosen defense of total lack of involvement in any conspiracy or criminal conduct whatever. Further, under the evidence and with the case in the posture that it was when it went to the jury, it is simply inconceivable that the jury would have failed to convict Hernandez for his conspiracy with Bass and Pero but would have nevertheless at the same time found him guilty of being a member of some separate conspiracy between Bass and out of state distributors no part of which included Hernandez's marihuana dealings with Bass and Pero. So far as the evidence showed, Hernandez was either guilty of nothing or guilty of being a member of a marihuana distribution conspiracy that included himself, Bass, Pero and others. No uncharged third alternative was suggested by the evidence. Moreover, it is highly questionable whether Hernandez's proposed instruction was substantially correct. The instruction quoted above did not adequately explain that proof of separate or independent conspiracies did not mandate acquittal so long as one of those conspiracies fit the description contained in the indictment, and Hernandez's participation in that conspiracy was established by the evidence. See Guerra-Marez, 928 F.2d at 671-72.

We conclude that because the evidence so strongly supported a finding of a single conspiracy, and because under these facts any arguable variance from the indictment could not have prejudiced Hernandez's substantial rights, Hernandez's claim of a material variance is unavailing. We further conclude that because his requested jury instruction was not substantially correct, and because its absence did not seriously impair the defense presented at trial, it was not reversible error for the district court to refuse to give Hernandez's instruction.3IV. Chavez's Invocation of the Fifth Amendment

Hernandez's fourth claim of error is that the district court erroneously permitted Chavez to invoke the Fifth Amendment, because, having entered a guilty plea, Chavez no longer enjoyed a privilege against self-incrimination.

It is well settled that a defendant's Sixth Amendment right of compulsory process to obtain witnesses in his favor must yield to a witness's Fifth Amendment privilege against self-incrimination. See, e.g., Roussell v. Jeane, 842 F.2d 1512, 1516 (5th Cir.1988); United States v. Khan, 728 F.2d 676, 678 (5th Cir.1984). The trial judge, moreover, "necessarily is accorded broad discretion in determining the merits of a claimed [Fifth Amendment] privilege." United States v. Lyons, 703 F.2d 815, 818 (5th Cir.1983).

Hernandez relies on the principle that once a defendant has been convicted of, or has pleaded guilty to, an offense, the privilege ceases to apply as to that offense and as to any other charges in an indictment that the government promises to dismiss as part of the plea agreement. See, e.g., United States v. Pardo, 636 F.2d 535, 543 (D.C.Cir.1980). However, Chavez had not been sentenced at the time of Hernandez's trial. As other courts of appeals have held, impending sentencing may furnish grounds for a legitimate fear of incurring additional criminal liability from testifying, in which case the privilege should remain in effect. See United States v. Lugg, 892 F.2d 101, 102 (D.C.Cir.1989); United States v. Tindle, 808 F.2d 319, 325 (4th Cir.1986); Bank One of Cleveland, N.A. v. Abbe, 916 F.2d 1067, 1075-76 (6th Cir.1990); United States v. Trejo-Zambrano, 582 F.2d 460, 464 (9th Cir.), cert. denied sub nom., Fierro-Soza v. United States, 439 U.S. 1005, 99 S. Ct. 618, 58 L. Ed. 2d 682 (1978). From the record before us, we cannot preclude that reasonable possibility, and we therefore find no abuse of discretion in the district court's deferral to Chavez's invocation of the Fifth Amendment.

Hernandez's final contention is that the district court erred in increasing his offense level by three levels based on the PSR's finding that he was a supervisor within the meaning of U.S.S.G. § 3B1.1(b). Hernandez has not provided this Court with a transcript of the sentencing hearing, or offered any justification for not doing so. We therefore consider this contention waived. See United States v. Hinojosa, 958 F.2d 624, 632-33 (5th Cir.1992).

Because we find all of Hernandez's contentions unavailing to establish reversible error, the judgment and sentence of the district court are

AFFIRMED.