Defendants-Appellants Gustavo Diaz (Diaz), Richard J. Goldberg (Goldberg), Jesse Jaime Lopez (Lopez), and Dr. Arthur C. Bieganowski (Bieganowski) appeal their convictions and sentences for various charges arising out of a scheme to defraud medical-insurance companies, including mail fraud, conspiracy to commit mail fraud, aiding and abetting mail fraud, and conspiracy to money launder. For the following reasons, we affirm all the appellants’ convictions and sentences.
Background
As reflected by the trial evidence, physicians and medical service providers typically bill insurance companies by means of a standardized form known as a Healthcare Finance Administration (HCFA) Form No. 1500, the actual service for which a bill is submitted being designated on the HCFA Form by a Current Procedural Terminology (CPT) code, a numerical code that represents a specific service or procedure for which an insurance company will pay on behalf of an insured.2 On August 4, 1998, Diaz, Goldberg, Lopez, Bieganowski, and five others were charged in a twenty-three-count indictment with a series of offenses arising from a complex scheme to use these forms to defraud insurance companies. The essence of the scheme involved a conspiracy to submit bills for services that were either never performed, were known to be unneeded, or contained CPT codes that reflected a higher level of service than was actually provided.
Dr. Bieganowski began practicing medicine in Texas in 1979.. By the time of his arrest in 1996, he owned five medical clinics in El Paso: El Paso Pain & Stress Clinic (EPPSC), a clinic specializing in pain management and the center of Dr. Bieganowski’s' medical practice; El Paso Institute of Physical Medicine & Rehabilitation (EPIPMR), a physical therapy clinic; El Paso Doctors Medical Center (EPDMC), a chiropractic clinic; and El Paso Radiology Services (EPRS), a radiology clinic. As a licensed physician and owner of the various clinics, Dr. Bieganow-ski was the central figure in the conspiracy, with Diaz, Lopez, and Goldberg fulfilling secondary roles. Diaz worked as a physician’s assistant in Dr. Bieganowski’s primary clinic, while Lopez worked as a physical therapist at the El Paso Institute of Physical Medicine & Rehabilitation. Goldberg was nominally Dr. Bieganowski’s outside accountant, but actually served as the defacto business manager for the various businesses.
The operation of the conspiracy, as charged in the indictment, covered the period between 1989 and 1996, and can be divided into three operational stages, the first of which involved the solicitation of patients. To obtain patients, Dr. Biega-nowski initially engaged a self-styled telemarketer, Richard Griego, to solicit patients for the El Paso Pain & Stress Clinic. To avoid the appearance that he was soliciting directly for Dr. Bieganowski, Griego was later employed through EPDMC, Dr. Bieganowski’s chiropracty clinic. The connection, however, was only thinly veiled, as both Dr. Bieganowski and Goldberg met periodically with Griego to monitor his work, prepare scripts, and set quotas. Griego would obtain automobile accident reports from the El.Paso Police Department and then use those reports to contact the accident victims by telephone. Once *270Griego contacted victims and referred them to EPDMC for chiropractic care, they would then be referred again to Dr. Bieganowski for further medical treatment.
The second stage of the scheme was the heart of the conspiracy and involved the creation and submission of fraudulent bills and HCFA Forms to medical insurance companies for reimbursement. The Government presented evidence of a number of fraudulent acts, including double billing, billing for services performed by Dr. Bie-ganowski on days when he was not in El Paso, billing for treatments known to be unneeded, billing for treatments performed by a non-physidan at a physician’s rate, double billing, and billing for the use of equipment that the clinic never possessed. Lopez, for example, was convicted of billing for therapy provided in a device called a Hubbard Tank, when none of Dr. Bieganowski’s clinics actually possessed such a device.
The third aspect of the conspiracy involved money laundering, and the movement of the funds derived from the submission of the fraudulent HCFA Forms. In the early stages of the conspiracy, before 1994, payments from insurance companies were deposited directly into bank accounts maintained in the names of the various clinics at Norwest Bank in El Paso. After November 1994, the scheme increased in complexity and the billing operations for the various clinics were consolidated through Servicio de Facturación y Cobranza, S.A. de C.V. (Servicio), a Mexican Corporation established by Goldberg and located in Ciudad Juarez, Mexico.3 Under the direction of Lucy Campos, Dr. Bieganowski’s nominal office manager and a named co-conspirator, Servicio assumed the role of submitting bills for the clinics for reimbursement from various insurance companies. Insurance company reimbursements were then deposited into accounts held in the clinics’ names at the Bank of the West in El Paso. From there Campos, the sole signator on the Servicio account, would transfer the entire amount of the reimbursements into an account held in the name of Servicio, also at the Bank of the West. Once the funds were consolidated in the Servicio account, Campos shifted those amounts necessary to cover the clinics’ operating expenses back to the original clinic accounts maintained at Norwest Bank. The excess funds that remained in the Servicio account then followed the below described routes from the Bank of the West to Dr. Bieganowski’s pocket.
A certain amount of the surplus funds held in the Servicio account was delivered directly to Dr. Bieganowski. The remainder, however, was transferred to UTM Professional Management (UTM), a shell corporation established under Goldberg’s guidance, whose nominal owner and sole officer was a young college student and former nanny to Dr. Bieganowski’s children. Under Goldberg’s direction, the funds deposited in UTM’s name were moved by means of wire transfers from UTM’s account in El Paso to Barclays Bank in New York. From New York, the funds were transferred to a Barclays account held by International Medical Management, a limited partnership in the Cayman Islands, where they eventually became available for Dr. Bieganowski’s personal use.
*271In 1994, the Federal Bureau of Investigation (FBI) along with the Internal Revenue Service (IRS) began to investigate Dr. Bieganowski’s medical practice. An. undercover investigation soon followed, which, together with the results of a search executed in 1996, led to the appellants’ arrest in August of 1998. Shortly after his arrest, Dr. Bieganowski was diagnosed with cancer. Although incarcerated in El Paso, he began treatment and was briefly transferred to New York for medical attention. As a result of Dr. Biega-nowski’s condition and the volume of discovery, the case was considerably delayed, and did not proceed to trial until March 13, 2000.
A jury returned a guilty verdict on at least some counts for all four appellants. Goldberg was found guilty on two counts, conspiracy to commit mail fraud in violation of 18 U.S.C. §§ 1341 and 371, and conspiracy to money launder in violation of 18 U.S.C. § 1966(a)(1)(B)®, (a)(2)(B)®, and (h). A third count against Goldberg was dismissed on the government’s motion. He was sentenced to one hundred months’ imprisonment on the conspiracy to money launder count and to a sixty month concurrent term on the mail fraud conspiracy count. Lopez was charged in five counts of the indictment, was convicted on two counts of mail fraud, and was acquitted on the other three counts. He was sentenced to concurrent terms of forty-one months’ imprisonment and a two-year period of supervised release. Diaz was charged in two counts of the indictment. He was convicted of one count of conspiracy to commit mail fraud, and sentenced to a term of fifty-one months’ imprisonment. He was acquitted on the other count. Bie-ganowski, the central participant in the conspiracy, was charged in fifteen of the twenty-three counts- of the indictment. The jury returned a guilty verdict on ten of those counts, including nine counts of mail fraud and conspiracy to commit mail fraud, and one count of conspiracy to money launder.- He was acquitted on five counts. Bieganowski was sentenced to 168 months’ imprisonment.
All the defendants appeal.
Discussion
A. Voir Dire
Bieganowski’s first argument on appeal is that the district court erred by denying him the right to voir dire certain members of the venire individually out of the hearing of the rest of the venire and in overruling his motion for mistrial after one mentioned a prejudicial statement from a newspaper article.4
On the opening day of the trial, a story -appeared in the El Paso Times reporting a number of prejudicial allegations, including allegations that Dr. Bieganowski had threatened witnesses and agents of the FBI. Six of the venire panel indicated they may have seen the article, four stating that they had read part of it. Biega-nowski moved the district court to permit him to question those four panel members himself, individually and outside the hearing of the venire. The trial court denied the request _ and Bieganowski’s counsel questioned the panel openly. Of the six panel members who reported having seen the article, two could remember nothing *272about it; one saw it but did not read it; one started reading it and stopped; and one simply read the headline. None of these five recalled anything “prejudicial to Dr. Bieganowski.” However, venireperson Carr, when questioned by Bieganowski’s counsel about the article’s content, mentioned in front of the entire venire that according to the article Bieganowski “allegedly threatened witnesses, threatened to kill them.” Bieganowski moved for a mistrial and the district court overruled the motion. Bieganowski then concluded his voir dire by asking the panel “is there anyone who feels that they could not be fair and impartial, as you sit here today, to try this case, from any source, any conversation, any news, anything.” None responded. At no point did Bieganowski either seek to himself conduct further voir dire or ask the district court to conduct further voir dire or to issue supplemental instructions, nor did the district court, on its own initiative, ask further questions of the other venire members concerning either the article or Carr’s statements.
In the district court’s initial questioning of the venire, before the lawyers commenced their questioning of the panel, the court read the entire indictment to the panel, emphasizing that it was not evidence, and then asked if any venirepersons knew anything about the case from any other source, including the newspaper. The questions were asked row by row for each of the three rows into which the thirty-four venirepersons were divided.5 Those who indicated they had heard or read about the case on the news or in the newspaper were asked by the court if they had formed any opinions, and the two who responded affirmatively were excused. The court then repeated that process with the following introductory comment:
“Okay, What I need to know, the fact that you’ve read something in the paper, the allegations in the paper, does that influence you one way or another?
You’re going to be asked to sit in judgment here in this court. The evidence is going to be presented by both sides. There will be witnesses here, exhibits. Now, what I need to know from you is, can you limit yourself, your deliberations, only on what is presented here, and not what’s in the papers?
If you’ve ever been involved in a situation, you know that the papers are not always correct. Okay? And that is not proof of anything, what you may have read in the papers. Any proof in this case has to come right here. It has to come here, in open court, presented by witnesses and exhibits.
So I need to ask you, if you are asked to sit on this jury, can you limit yourself, no matter what you have read in the paper, to only consider the evidence that is presented here in court and no other evidence at all?”6
“We review a district court’s determination of the scope and method of jury voir dire for abuse of discretion.” United States v. Beckner, 69 F.3d 1290, 1291 (5th Cir.1995). The decision to permit individual questioning lies within the district court’s discretion, and we will find *273an abuse of that discretion only “when there is insufficient questioning to allow defense counsel to exercise a reasonably knowledgeable challenge to unqualified jurors.” Id.
Questions as to the adequacy of voir dire frequently arise in situations where the trial is surrounded by significant publicity. Where a defendant claims that voir dire was inadequate given the nature of such publicity, we will reverse the conviction where the defendant can establish “(1) that pretrial publicity about the case raised a significant possibility of prejudice, and (2) that the district court’s voir dire procedure failed to provide a reasonable assurance that prejudice would be discovered if present.” Beckner, 69 F.3d at 1292.
As a threshold matter, we must determine whether the record in Bieganowski’s case contains sufficient evidence of prejudice. Bieganowski introduced the article from the El Paso Times into evidence before the court, and there is no question but that the article was inflammatory. The reported allegations involved not simply a threat of violence, but a threat of violence directed toward witnesses in the very trial the jurors were called to hear. See United States v. Davis, 583 F.2d 190, 196 (5th Cir.1978) (finding prejudice where pretrial publicity included the violent background of the defendant). In addition, the publicity was contemporaneous with the start of the trial and was, therefore, fresh in the mind of at least one panel member. Cf. United States v. Gerald, 624 F.2d 1291, 1298 n. 3 (5th Cir.1980) (noting that impressions and memories of any publicity had necessarily diminished in the eight months between arraignment and trial); Salemme v. Ristaino, 587 F.2d 81, 88 (1st Cir.1978) (finding that because the trial was held five years after the prejudicial publicity, “[a]ny publicity surrounding the event had long since passed from the public’s mind.”). We conclude that Bieganowski has satisfied his burden in demonstrating that the record contains sufficient pretrial publicity to raise a significant possibility of prejudice.
It remains for us to determine, however, whether the voir dire in Bieganowski’s case was sufficient for Bieganowski to identify unqualified jurors. We have held repeatedly that “because jurors exposed to pretrial publicity are in a poor position to determine their own impartiality ... district courts must make independent determinations of the impartiality of each juror.” Beckner, 69 F.3d at 1291; United States v. Davis, 583 F.2d 190 (5th Cir.1978). We have also held, however, that “[wjhile examination of each juror out of the presence of the other prospective jurors is sometimes preferable, it is not necessarily required.” Beckner, 69 F.3d at 1292.
Once Venireperson Carr revealed that he had read the prejudicial article, the district court did pose additional questions to him in the presence of the entire veni-re.7 However, the district court did not thereafter question the remainder of the panel members individually about the contents of the article that they had heard Carr relate. Undoubtedly, the district court would have been better advised to have granted Bieganowski’s request to conduct individual voir dire, of those who indicated they had read the particular arti*274cle, outside the hearing of the panel. The court also would have been better advised to have engaged in further questioning of the entire venire after Carr’s statement in the presence of the panel about the contents of the article. Equally important, however, is Bieganowski’s failure to request such additional questioning by the court (or otherwise). We must ask, therefore, whether the district court’s failure to conduct individual voir dire after Carr’s statement, in the absence of that failure being brought to the court’s attention, so affected Bieganowski’s substantial rights as to merit reversal. See Fed.R.Crim.P. 52(b). We conclude that it did not.
Carr, the only panel member who had actually read the article, did not ultimately serve on the jury (the defense did not challenge Carr for cause but exercised a peremptory strike to remove him).8 To say that Carr never served on the jury, however, does not answer the charge that his statements prejudiced the entire veni-re. Nevertheless, three additional observations indicate that the venire was not infected with such a degree of prejudice as to require reversal in the present setting. First, as above indicated, the district court had previously strongly instructed the ve-nire not to consider what they had read in the papers and that “the papers are not always correct,” and in the presence of the venire openly instructed Carr, after his mention of what the article stated, that “what the newspaper says has nothing to do with this trial” (see note 7 above). And at the conclusion of voir dire the court instructed the panel that “anything you may have seen or heard outside the courtroom is not evidence and must be totally disregarded. You are to decide this case solely on the evidence presented here in court.” Second, the jury returned a guilty verdict on only ten of the fifteen counts of the indictment charging Bieganowski, acquitting him of the other five, indicating that the jury methodically assessed each of the charges against him. Third, the prosecution presented overwhelming evidence of Bieganowski’s guilt at trial. Thus, in light of the volume of evidence against him and Bieganowski’s failure to request individual voir dire by the court (or otherwise) after venireperson Carr’s statement about the article, and the district court’s overall handling of the voir dire, we decline to hold that the court’s failure to engage in such individual questioning amounted to a deprivation of Bieganowski’s substantial rights.
B. Sufficiency of the Evidence
1. Lopez: Mail Fraud
Both Lopez and Goldberg challenge the sufficiency of the evidence to sustain their convictions. We address both Lopez’s and Goldberg’s arguments in turn.
Lopez was convicted on two counts of mail fraud for submitting HCFA Forms that reflected the use of á physical-therapy device known as a Hubbard Tank.9 Although Lopez concedes that none of Dr. Bieganowski’s clinics ever contained a Hubbard Tank, he maintains that the evidence failed to show either that billing for a Hubbard Tank was a material misstatement or that he possessed the requisite intent to commit mail fraud.
*275“The standard of review in assessing a challenge to the sufficiency of the evidence in a criminal case is whether a ‘reasonable trier of fact could have found that the evidence established guilt beyond a reasonable doubt.’ ” United States v. Smith, 296 F.3d 344, 346 (5th Cir.2002). In evaluating the evidence, we view “all evidence and all reasonable inferences drawn from it in the fight most favorable to the government.” Id. (quoting United States v. Mergerson, 4 F.3d 337, 341 (5th Cir.1993)). “It is not necessary that the evidence exclude every reasonable hypothesis of innocence or be wholly inconsistent with every conclusion except that of guilt.” United States v. Henry, 849 F.2d 1534, 1536 (5th Cir.1988); United States v. Lechuga, 888 F.2d 1472, 1476 (5th Cir.1989). However, in a case depending on circumstantial evidence if “the evidence viewed in the fight most favorable to the prosecution gives equal or nearly equal circumstantial support to a theory of guilt and a theory of innocence,” a defendant is entitled to a judgment of acquittal. United States v. Brown, 186 F.3d 661, 664 (5th Cir.1999) (quoting United States v. Schuchmann, 84 F.3d 752, 754 (5th Cir.1996)).
Lopez was ultimately convicted on two counts of mail fraud in violation of 18 U.S.C. § 1341. To prove mail fraud under 18 U.S.C. § 1341, the government must show: (1) a scheme to defraud; (2) the use of the mails to execute the scheme; and (3) the specific intent to defraud. United States v. Peterson, 244 F.3d 385, 389 (5th Cir.2001). In addition, the Supreme Court has interpreted section 1341 to require that the misstatement made in the course of the scheme to defraud be a material one. See Neder v. United States, 527 U.S. 1, 119 S.Ct. 1827, 1841, 144 L.Ed.2d 35 (1999).
Lopez argues that billing for Hubbard Tank treatment could not have been a material misstatement since" the billing rate for the use of a Hubbard Tank was lower than the rate at which Lopez could have billed for the treatment that he actually delivered. Specifically, Lopez maintains that although he submitted bills with CPT code 97220, the code for Hubbard Tank treatment, he could have billed under the more expensive CPT code 97420, the code used for supervised pool therapy or Hubbard Tank therapy with exercises.10
On closer examination, however, Lopez’s argument fails. First, the evidence indicates that billing for Hubbard Tank therapy includes not only a representation that the clinic possessed a Hubbard Tank, but also the implicit representation that the Tank was used to deliver certain professional services. The evidence further indicated that a physical therapist may only bill for pool therapy under CPT code 97420 where the therapy is supervised. Ample evidence, however, was introduced to establish that such supervision was lacking in Lopez’s clinic, and that no professional *276services were being provided to Lopez’s patients while they were in the clinic’s pools.11
Lopez’s defense that he could have billed for the services he provided as pool therapy under CPT code 97420, therefore, is unsupported by the evidence. Lopez’s argument essentially amounts to the claim that his misrepresentation was not material since, by making an additional misrepresentation, he could have charged for a different service at an equal or higher rate. We find this reasoning unconvincing.
Moreover, there was at least some evidence presented that insurance companies found the representation that the clinic possessed a Hubbard Tank to be material regardless of any actual charges billed. Lisa Hannusch, an expert witness from the Texas Workers Compensation Insurance Fund, testified that in order for the Fund to pay a bill for a Hubbard Tank, the clinic submitting the bill must actually have a Hubbard Tank. Hannusch also testified that had she known that there was no such tank at Lopez’s clinic, she would not have reimbursed his bills. Finally, Hannusch testified that- a pool such as Lopez’s — a pool used to treat multiple individuals, with no window access, no aide present, and no physical therapist available to supervise the patients — would not be billable as a Hubbard Tank or as pool therapy.
We also find that the evidence supported the jury’s finding that Lopez possessed the requisite intent to defraud. Lopez was active in selecting billing codes, he adjusted the billing codes submitted by other employees, and at least on one occasion, he received and annotated billing statements from insurance companies. When viewed in the light most favorable to the verdict, we find this evidence sufficient to support the conclusion that Lopez intended to submit bills containing material misstatements to the insurance companies for reimbursement.
After reviewing the record, therefore, we find that the evidence is sufficient to establish both that billing for a Hubbard Tank was a material misstatement and that Lopez possessed the requisite intent to support his conviction for mail fraud.
2. Goldberg: Mail Fraud
Goldberg also challenges the sufficiency of the evidence to support his convictions. Goldberg was convicted on one count of conspiracy to commit mail fraud and one count of conspiracy to commit money laundering in violation of 18 U.S.C. § 1956. Goldberg makes the related arguments that the evidence failed to show that he possessed the requisite intent to commit mail fraud, and that since the offense of money laundering requires knowledge that the laundered funds are the proceeds of unlawful activity, he can therefore be found guilty neither of mail fraud nor money laundering. In addition, Goldberg maintains that the Government failed to' prove that the funds transferred to the Cayman Islands were the proceeds of unlawful activity.
A section 371 conspiracy comprises the following elements: (1) an agreement between the defendant and a co-conspirator to violate a law of the United States; (2) an overt act by one conspirator in furtherance of the conspiracy; and (3) the specific intent to further an unlawful objective of the conspiracy. United States v. Sharpe, 193 F.3d 852, 863 (5th Cir.1999). The requirement of an agree*277ment is the central element and the agreement, therefore, must be arrived at knowingly. United States v. Holcomb, 797 F.2d 1320, 1327 (5th Cir.1986); United States v. Ballard, 663 F.2d 534, 543 (5th Cir.1981). “[M]ere association with those involved in a criminal venture is insufficient to prove participation in a conspiracy.” Id.; United States v. Alvarez, 610 F.2d 1250, 1255 (5th Cir.1980), aff'd 625 F.2d 1196 (5th Cir.1980) (en banc). The existence of an agreement, however, may be proved by circumstantial evidence, see Holcomb; 797 F.2d at 1327, and even minor participation in the conspiracy may serve as the basis for a conviction. United States v. Prieto-Tejas, 779 F.2d 1098, 1103 (5th Cir.1986). Moreover, in a conspiracy case: “[a]n agreement may be inferred from ‘concert of action,’ ” “[v]oluntary participation may be inferred from ‘a collocation of circumstances,’ ” and “Knowledge may be inferred from ‘surrounding circumstances.’ ” United States v. Lechuga, 888 F.2d 1472, 1476-77 (5th Cir.1989).
Inasmuch as the circumstantial evidence in this case tends to prove that Goldberg knew that Dr. Bieganowski’s clinics were engaged in fraudulent billing practices, we conclude that there was sufficient evidence to establish Goldberg’s participation in the conspiracy. Goldberg’s affiliation with Dr. Bieganowski’s practice far exceeded the limits of an ordinary professional relationship, and involved him in nearly every aspect of the operation of the clinics. He spent almost every afternoon at Dri Bieganowski’s clinic and attended multiple meetings with the clinic staff, including meetings addressing such mundane administrative matters as employee dress codes. The evidence supports the conclusion that he was the de facto business manager of Dr. Bieganowski’s practice, with day to day supervision of and extensive familiarity with it. The fraudulent billing practices were widespread, pervasive and virtually continuous throughout the clinics. From an internal perspective, they were neither concealed nor secret.
A portion of the Government’s conspiracy case also involved allegations that Dr. Bieganowski’s clinics knowingly obtained authorization for, provided, and billed for unnecessary services, including an expensive procedure known as a facet block injection. Although Goldberg maintains on appéal that he was not involved in the mechanics of creating bills or demanding payment, the record indicates that Goldberg was involved with efforts to obtain certification from insurance companies for these treatments. For example, he closely monitored those employees who were responsible for obtaining precertification for facet block injections, and he directed that the precertification quota for injections- be increased, first from ten to fifteen patients per day, and later to twenty patients per day. An employee responsible for the precertification of injections, Rene Moreno, testified that when she told Goldberg that patients were reluctant to receive the injections, Goldberg instructed her to do whatever was necessary to get the patients to the hospital. Although this evidence ' does not prove that Goldberg knew that any particular, single injection was not medically necessary, or that a particular precertification request contained fraudulent representations, it illustrates the extent to which Goldberg was involved in the preparation and submission of bills. More important, it, together with the other evidence, tends to support an inference that Goldberg knew that some bills contained fraudulent representations.
The record also indicates that Goldberg was closely involved with Dr. Bieganow-ski’s solicitation efforts. He not only attended meetings with Robert Griego, Bie-ganowski’s telemarketer, but also reviewed *278the script that Griego used to solicit new patients. Goldberg knew that Griego told reluctant patients that they could increase their automobile-insurance settlements by-generating higher medical bills, and he knew that Griego advised patients to obtain medical examinations even when those same patients told Griego that they were not injured. More important, when Griego suggested to Goldberg that Griego might have to begin staging accidents in order to meet his quota, Goldberg simply responded: “Well, you know, whatever you have to do.”
Also damaging to Goldberg’s protestations of ignorance was the testimony of Rosa Cordova and Lucy Campos. Campos testified that she had given Goldberg a copy of the Medical Fee Guidelines, a manual that contained the various CPT billing codes, further undermining Goldberg’s claim that he was not involved with creating bills. Cordova, an employee in the precertification department, testified that Dr. Bieganowski had directed her to generate false fee tickets and to submit fee tickets even when patients had left without being treated. When asked about how much Goldberg knew about her activities, Cordova replied, “[Goldberg] knew exactly what my job was and he wanted to make sure that I was doing it.”
Further, Goldberg’s extensive efforts in setting up and overseeing an elaborate virtual labyrinth of bank accounts for Dr. Bieganowski’s clinics, which concealed both the clinics’ and Dr. Bieganowski’s relationship to the accounts and the ultimate disposition of the funds, is plainly suggestive of guilty knowledge. Goldberg correctly points out that each piece of evidence against him, viewed separately, may admit of an innocent explanation. That, however, is not determinative. As we observed in Lechuga, 888 F.2d at 1476: “the United States Supreme Court remarked long ago, ‘[cjircumstances altogether inconclusive, if separately considered, may, by their number and joint operation, especially when corroborated by moral coincidences, be sufficient to constitute conclusive proof.’ Coggeshall v. United States (the Slavers, Reindeer), 69 U.S. (2 Wall.) 383, 17 L.Ed. 911, 914-15 (1864).” Thus, although no individual piece of evidence against Goldberg is dispositive, taken together the evidence as a whole suffices to establish an adequately clear picture of Goldberg’s role in the conspiracy. The cumulative effect of this evidence is sufficient to support the inference that Goldberg was aware of the fraudulent billing practices, and we therefore decline to hold that the evidence was insufficient to support Goldberg’s conviction for conspiracy to commit mail fraud.
3. Goldberg: Money Laundering
For his role in the conspiracy, Goldberg was also convicted of conspiracy to money launder in violation of 18 U.S.C. § 1956(h). The substantive offense of money laundering requires that the defendant knew that the funds in question represented the proceeds of unlawful activity. See United States v. Burns, 162 F.3d 840, 847 (5th Cir.1998). Goldberg maintains that since he did not know that Bieganowski’s clinics were submitting fraudulent claims, he could not have known that the funds deposited into the various clinic accounts represented the proceeds of unlawful activity, and that he therefore cannot be found guilty of money laundering. Because we find that the evidence supports the conclusion that Goldberg was aware that the reimbursements from the insurance companies represented the proceeds of fraudulent billing practices, see section 11(B)(2), supra, we reject this argument.
Finally, we address Goldberg’s claim that the Government failed to prove that the funds transferred to the Cayman Is*279lands in fact represented the proceeds -of unlawful activity. In this case, the indictment charged a conspiracy to commit two types of money laundering: (1) engaging in a financial transaction designed to conceal the source or control of the proceeds of unlawful activity in violation of section 1956(a)(l)(B)(i), and (2) transporting or attempting to transport funds from a place in the United States to a place outside the United States in order to conceal the source or control of the proceeds of unlawful activity, in violation of section 1966(a)(2)(B)®.
The offense of money laundering under section 1956(a)(l)(B)(i), requires that the government prove that the defendant: (1) conducted or attempted to conduct a financial transaction, (2) that the defendant knew involved the proceeds of unlawful activity, and (3) that the defendant knew was designed to conceal or disguise the nature, location, source, ownership, or control of the proceeds of the unlawful activity. 18 U.S.C. § 1956(a)(1)(B)(i); United States v. Burns; 162 F.3d 840, 847 (5th Cir.1998), cert. denied, August v. United States, 526 U.S. 1076, 119 S.Ct. 1477, 143 L.Ed.2d 560 (1999). An offense under section 1956(a)(2)(B)(i) is almost identical, with the exception that the transaction in question must be from a place in the United States to a place outside the-United States. See 18 U.S.C.A. § 1956(a)(2)(B)(i).
Agent Hivie of the IRS testified that between November, 1994,12 and January, 1997, over six million dollars of insurance company reimbursements were deposited in-the various clinics’ accounts. All of that six million dollars was then transferred from the clinics’ accounts at the Bank of the West to the Servicio account, also located at the Bank of the West. Of that six million dollars, a little over two million was eventually transferred to the Cayman Islands.
Goldberg’s argument proceeds from the premise that the Government failed to prove that all of Dr. Bieganowski’s billings were fraudulent. If some billings were legitimate, then at least some of the money that was deposited into the clinic accounts at the Bank of the West and then consolidated in the Servicio account was also legitimate. Consequently, Goldberg maintains that the Government never established that Bieganowski earned less than two million dollars through legitimate billing and that the Government cannot, therefore, prove that the funds transferred to the Cayman Islands were the proceeds of fraudulent activity. The government maintains that it produced sufficient evidence that all the funds deposited to the Servicio account — and certainly more than four million dollars thereof — were the product of fraudulent billings. The government also argues that if some funds in the Servicio account were legitimate their commingling with illegitimate funds there allows treatment of the Cayman Island funds as illegitimate.
Accepting, arguendo, Goldberg’s position as valid — that the Government failed to establish that the funds transferred to the Cayman Islands were illegitimate— this failure does not undermine Goldberg’s conviction. The Government charged Goldberg with a conspiracy to violate both section 1956(a)(l)(B)(i) and (a)(2)(B)®, and the jury charge authorized conviction upon either theory.13 Goldberg’s argument con*280cerning the funds transferred to the Cayman Islands, if valid, would only undermine a conviction based on a conspiracy to commit money laundering under section 1956(a)(2)(B)(i), laundering by transferring illegitimate funds out of the United States. The evidence to support a conviction for section 1956(a)(l)(B)(i), on the other hand, was more than sufficient.
The indictment and the jury charge include a series of overt acts tracing the entire money laundering operation, including the transfer of funds involving the proceeds of unlawful activity from the clinics’ accounts at the Bank of the West to Servicio’s bank account. That transfer to Servicio alone satisfies the requirements of section 1956(a)(l)(B)(i). The entire six million dollars deposited into the clinics’ accounts was thereafter transferred to the Servicio account. Therefore, even assuming that the Government only proved that a portion of those six million dollars represented the proceeds of fraudulent activity, the prosecution nevertheless satisfied its burden of demonstrating that the transfer involved the proceeds of specified unlawful activity. See 18 U.S.C. § 1956(a)(1). There is also little doubt that the transfers from the clinics’ accounts to the Servicio account were designed to conceal the source of the unlawful funds. A casual observer would not have immediately linked the contents of the Servicio account to Bieganowski as neither Dr. Bieganowski nor Goldberg were listed as shareholders (or officers or directors or authorized agents or account signatories) of Servicio. See United States v. Willey, 57 F.3d 1374, 1387-89 (5th Cir.1995) (noting that a transfer from one third party to another supports an inference of a design to conceal).
Because the jury could have convicted Goldberg for conspiracy to violate 18 U.S.C. § 1956(a)(l)(B)(i), and because the evidence supports a finding that the transfers from the clinic’s accounts to Servicio involved the proceeds of unlawful activity and were designed to conceal the source of those proceeds, we hold that the evidence is adequate to sustain Goldberg’s conviction for conspiracy to money launder.
C. Speedy Trial
Lopez argues that the indictment should have been dismissed for undue delay under the Speedy Trial Act, 18 U.S.C. §§ 3161-3174, and that the eventual delay between his arrest and trial violated his right to a speedy trial under the Sixth Amendment.14 *281We turn first to the Speedy Trial Act claim. We review factual findings under the Speedy Trial Act- (the Act) for clear error, and legal conclusions de novo. United States v. Narviz-Guerra, 148 F.3d 530, 538 (5th Cir.1998).
The Act requires that a defendant be brought to trial “within seventy days from the filing date (and making public), of the information or indictment, or from the date the defendant has appeared before a judicial officer of the court in which such charge is pending, whichever date last occurs.” 18 U.S.C. § 3161(c)(1). Where a defendant is not brought ,to trial within this period, the indictment, must, be dismissed. Id. § 3161(a)(2).
Under section 3161(h), however, certain delays are excluded from the calculation of the seventy-day limit, including -
“[a]ny period of delay resulting from a continuance granted by any judge on his own motion or at the request of the defendant or his counsel or at the request of the attorney for the Government, if the judge granted such continuance on the basis of his findings that the ends of justice served by taking such action outweigh the best interest of the public and the defendant in a speedy trial.” Id. § 3161(h)(8)(A).
Section 3161(h) also excludes a “reasonable period of delay when the defendant is joined for trial with a codefendant as to whom the time for trial has not run and no motion for severance has been granted.” Id. § 3161(h)(7). Thus, the Act excludes from the calculation of the seventy-day limit any delay resulting from the proper grant of a continuance requested by a co-defendant. United States v. Bermea, 30 F.3d 1539, 1567 (5th Cir.1994) (“[T]he ex-dudable delay of one defendant may be attributed to all defendants.”).
It is undisputed that the seventy-day period in the case sub judice began on August 5, 1998, the date of the appellants’ arrest and arraignment, and that the trial began one.-and-a-half years later on March 13, 2000. From August 5, 1998, the date of the appellants’ first appearance, until October 2, 1998, the trial court found that only twenty-three days expired on the speedy trial clock. Lopez does not dispute this calculation. Lopez also concedes that the entire time from October 2, 1998, until the first trial setting for February 22, 1999, was properly excluded from the seventy-day limit. Only at issue on appeal, therefore, are three orders continuing the trial past February 22, 1999. The first continuance, granted on February 11, 1999, and followed by a written order issued on February 12, 1999, continued the trial until August 23, 1999. The second issued on August 12, 1999, when the district court set the case for trial on November. 1, 1999; the third was granted on September 2, 1999, memorialized in an order on October 5, 1999, and set the trial for March 13, 2000. We examine each continuance in turn. Although the Act excludes from the seventy-day limit the period of a continuance, such period is only excluded where the court “sets forth, in the record of the case, either orally or in writing, its reasons for finding that the ends of justice served by the granting of such continuance outweigh the best interests of the public and the defendant in a speedy trial.” 18 U.S.C. § 3161(h)(8)(A). Lopez argues on appeal that the district court failed, on each of the three occasions listed above, to engage in an ends-of-justice analysis or to state adequately its *282reasons for granting the three continuances.
Lopez’s assertion with respect to the February 11, 1999, continuance is patently unsound. The district court’s February 12th order clearly satisfied the requirement of section 1361(h)(8) that the court articulate reasons recognized under the Act for granting a continuance. Section 1361(h)(8)(B) sets forth a number of grounds that a court shall consider in granting a continuance, including “[wjhether the case is so unusual or so complex ... that it is unreasonable to expect adequate preparation ... within the time limits established by this section.” Id. § 3161(h)(8)(b)(ii). The district court’s order not only explicitly referenced subsections 3161(h)(8)(B)(i) and (ii), but also described the case as “unusual and complex.” Moreover, the order stressed that because of Dr. Bieganowski’s illness and the high volume of discovery, the continuance was necessary to permit Bieganowski to assist his attorney to prepare for trial.15
Lopez’s claim that the district court failed to perform the required ends-of-justice analysis on August 12, 1999, when it continued the case until November 1, 1999, however, has some arguable merit. The record of the August 12th hearing contains reference neither to the ends-of-justice nor to the complexity of the case. The district court, however, had previously designated the case as complex, and the record of the August 12th hearing contains repeated reference to both the volume of discovery and the numerous logistical constraints on Dr. Bieganowski’s ability to cooperate in his defense.
We decline to decide, however, whether the August 12th continuance satisfied the requirements of the Act. Even if the August 12th order failed to stop the clock, the September 2, 1999, continuance did. In its order of October 6, 1999, memorializing the September 2, 1999, continuance, the district court found, after “giving all due consideration to the interest of the public and the defendants to a speedy trial and to the Constitutional rights of [the] defendants ... that the ends of justice are served by continuing the ... action.” In addition, the district court in that same order again entered a finding that the case was complex due to the number of defendants and the nature of the prosecution.16 Between August 23, 1999, the date for which trial, was set in the February 12th order, and September 2, 1999, only another ten days expired on the speedy trial clock, bringing the total number of expired days to thirty-three, and well below the seventy days mandated by the Act.
Finally, Lopez presents two additional arguments in support of his Speedy Trial Act claim. First, Lopez maintains that the *283district court’s October 5, 1999, order does not constitute a contemporaneous finding as required by the Act. Second, he contends that the delay • of the trial until March 13, 2000, even if supported by the requisite findings, was not reasonable. We reject both of these arguments.
In arguing that the Speedy Trial Act requires contemporaneous findings to support an ends-of-justiee continuance, Lopez mistakenly relies on language from this Court’s decision in United States v. Blackwell, 12 F.3d 44, 48 (5th Cir.1994) (“In the absence of contemporaneous, articulated on-the-record findings for extending the time for trial past seventy days ... Defendanb-Appellant is entitled to have his case dismissed.”). The word “contemporaneous” in Blackwell upon which Lopez relies, however, was dicta. See United States v. Jones, 56 F.3d 581, 585 n. 9 (5th Cir.1995). Moreover, we declined in Jones to elevate Blackwell’s statement about contemporaneity to the status of a rule of law, noting instead that “virtually every Circuit has held that the entry of findings after granting the continuance is not reversible error so long as the findings were not actually made after the fact.” Id. Today, we adopt the position toward which we moved in Jones and reject the Blackwell dicta. Rather than contemporaneous findings, section 3161 merely requires that a district court enter on the record, at some point (presumably prior to trial), the necessary findings to support an ends-of-justice continuance. Id. The only requirements for such an order are that the order memorializing the continuance indicate when the motion was granted, and that the reasons stated be and can be fairly understood as being those that actually motivated the court at the time it granted the continuance. Id. Those conditions are clearly met here.17
Finally, turning to the reasonableness of the delay, we first note that the nineteen-month delay between Lopez’s arrest and trial was substantial. We decline to hold, however, that such a delay was unreasonable under the circumstances.
Section 3161(h)(7) provides for the exclusion from the seventy-day speedy trial period of a “reasonable period of delay when the defendant is joined for trial with a codefendant as to whom the time for trial has not run and no motion for severance has been granted.” 18 U.S.C. § 3161(h)(7). Given the fact-intensive nature of the reasonableness inquiry, we review subsection (h)(7) exclusions on a case-by-case basis, United States v. Franklin, 148 F.3d 451, 457 (5th Cir.1998), and examine both the totality of the circumstances of the case prior to trial and the “actual prejudice suffered by the appellant as a result of the subsection (h)(7) exclusion.” Id. In examining the totality of the circumstances of the case, our inquiry focuses on the necessity of the delay, giving proper consideration “to the purpose behind subsection (h)(7) — ‘accommodating the efficient use of prosecutorial and judicial resources in trying multiple defendants in a single trial.’ ” Id. In weighing prejudice, on the other hand, “relevant considerations include whether the delay impaired the appellant’s ability to defend himself or resulted in excessive pretrial incarceration.” Franklin, 148 F.3d at 457.
Neither prong of our subsection (h)(7) analysis supports the conclusion that Lopez’s delay was unreasonable. The trial in this case followed almost four years of investigative work, involved thousands of *284medical and financial documents, and lasted nearly two months. To have tried Lopez separately would necessarily have involved a substantial additional expenditure of judicial' and prosecutorial resources. Nor does the record indicate that the delay in any way impaired Lopez’s ability to defend himself. Finally, the delay did not result in excessive incarceration as Lopez remained free on bond during the pen-dency of his trial.
In addition to his Speedy Trial Act claim, Lopez also alleges a violation of his Sixth Amendment right to a speedy trial. “The Sixth Amendment guarantees that ‘in all criminal prosecutions, the accused shall enjoy the right to a speedy ... trial.’ ” United States v. Neal, 27 F.3d 1035, 1042 (5th Cir.1994). It will be the unusual case, however, where the time limits under the Speedy Trial Act have béen satisfied but the right to a speedy trial under the Sixth Amendment has been violated. See United States v. O’Dell, 247 F.3d 655, 666-67 (6th Cir.2001); United States v. Munoz-Amado, 182 F.3d 57, 61 (1st Cir.1999); United States v. Nance, 666 F.2d 353, 360 (9th Cir.1982). Lopez’s case is no exception.
In analyzing a Sixth Amendment speedy trial claim, we balance, among other relevant circumstances, (1) the length of the delay; (2) the reason for the delay; (3) whether the defendant timely asserted his right; and (4) any prejudice resulting to the defendant because of the delay. Barker v. Wingo, 407 U.S. 514, 92 S.Ct. 2182, 2192-93, 33 L.Ed.2d 101 (1972). Here, the Government concedes that the delay was substantial enough to trigger the remaining Barker factors, and that Lopez timely asserted his rights. Our focus, therefore, must be on the remaining two factors of the Barker test.
In assessing the reasons for the delay, we observe at the outset that “pretrial delay is often both inevitable and wholly justifiable.” Doggett v. United States, 505 U.S. 647, 112 S.Ct. 2686, 2693, 120 L.Ed.2d 520 (1992). We also recognize that the extent to which this observation rings true will necessarily vary with the complexity of the case. Thus, “the delay that can be tolerated for an ordinary street crime is considerably less than for a serious, complex conspiracy charge” such as the one in which Lopez found himself enmeshed. Barker, 92 S.Ct. at 2192-93. This was a complex case, and we hesitate to say that the reasons for the delay were unreasonable. The volume of discovery and the number of defendants involved justified some delay, as did Dr. Bieganow-ski’s illness and consequent inability to assist in his defense. Moreover, Lopez has not demonstrated that the delay was occasioned by the prosecution, or that the “government ... intentionally held back in its prosecution ... to gain some impermissible advantage at trial.” Neal, 27 F.3d at 1043 (quoting Doggett v. United States, 505 U.S. 647, 112 S.Ct. 2686, 2693, 120 L.Ed.2d 520 (1992)).
In the final step of the Barker calculus, we examine the degree of prejudice that attached to Lopez because of the delay and find that insofar as Lopez fails to make a convincing show of prejudice, this remaining Barker factor also weighs heavily against him. Lopez argues that as a result of the delay, he suffered “psychological and' economic prejudice,”- and that the Government gained additional time for its expert to review certain documents. During the period of the delay the Government did uncover additional documentary evidence that supported the charges against Lopez. Specifically, the Government located additional bills for Hubbard Tank treatments that included Lopez’s handwritten signature. Lopez, however, was acquitted on two Hubbard Tank *285charges and does not demonstrate that these newly discovered billing records were the ones used to support the charges for which he was ultimately convicted. Moreover, since the Government already had documentary evidence of numerous bills that bore Lopez’s signature stamp, it is difficult to see how these additional documents resulted in prejudice. Lopez’s claims of psychological and economic strain are also insufficient to establish the prejudice necessary to find a violation of his Sixth Amendment rights. The Sixth Amendment is concerned with “reducing the ‘anxiety and concern of the accused.’ ” Cowart v. Hargett, 16 F.3d 642, 647 (5th Cir.1994). “Anxiety about one’s reputation and private life during pretrial delay, however, will not alone suffice to warrant a reversal of a conviction.” Id. Consequently, we find that Lopez did not suffer a degree of prejudice sufficient for us to find a violation of his Sixth Amendment rights.18
D. Sufficiency of the Indictment
Lopez also raises a challenge to the sufficiency of the indictment, arguing that those counts of the indictment charging him with representing that the clinic possessed a Hubbard Tank were insufficient to support an inference of materiality.19
We review the sufficiency of an indictment de novo. United States v. Fitzgerald, 89 F.3d 218, 221 (5th Cir.1996). To be sufficient, an indictment must conform to minimal constitutional standards, United States v. Threadgill, 172 F.3d 357, 373 (5th Cir.1999), standards that are met where the indictment alleges every element of the crime charged and in such a way “as to enable the accused to prepare his defense and to allow the accused to invoke the double jeopardy clause in any subsequent proceeding.” Id. (quoting United States v. Webb, 747 F.2d 278, 284 (5th Cir.1984)).
Where the government charges a defendant with mail fraud, it must prove the materiality of the fraudulent statement as an element of the offense. See Neder v. United States, 527 U.S. 1, 119 S.Ct. 1827, 1841, 144 L.Ed.2d 35 (1999). The failure to employ the word “material” in the language of the indictment, however, is not fatal. See United States v. Richards, 204 F.3d 177, 191 (5th Cir.2000) (“In determining the sufficiency of the indictment, ‘[t]he law does not compel a ritual of words.’ ” (quoting United States v. Wilson, 884 F.2d 174, 179 (5th Cir.1989))). Instead, an allegation of fraud in an indictment will be sufficient so long as “the. facts alleged in the indictment warrant an inference that the false statement is material.” United States v. McGough, 510 F.2d 598, 602 (5th Cir.1975).
Lopez’s argument here largely mirrors his challenge to the sufficiency of the evidence to support his conviction.20 The misstatement charged against Lopez in this case was the submission of bills representing that patients received physical therapy in a Hubbard Tank, when, in fact, the clinic never possessed such a device.21 *286Lopez argues that because the billing rate for the therapy that was actually provided was the same as the billing rate -that would have been charged had the therapy been provided in a Hubbard Tank, the misstatement that a Hubbard Tank was used could not have been material. His real argument, however, is that at trial the Government did not focus on the false statement alleged in the indictment, that the clinic employed a Hubbard Tank, but instead argued that the bills were fraudulent because they misstated the degree of supervision the patients were given while in therapy.
The flaw in Lopez’s argument lies in his failure to distinguish between a challenge to the sufficiency of the indictment and a challenge to the evidence produced at trial. See, e.g., United States v. McGough, 510 F.2d 598, 603 (5th Cir.1975) (holding that an indictment “need only allege materiality ‘in substance,’ ” and warning against the failure to “draw a clear distinction between an allegation of materiality and proof of materiality.”). In determining whether an allegation of materiality in an indictment is sufficient, the proper inquiry is whether the allegation is “potentially capable of being proved material by the government at trial,” and whether the allegation is sufficient to support an inference of materiality. Id. at 602. Accordingly, it would be inappropriate to test the validity of the indictment from the perspective of the evidence eventually produced at trial.. That the Government produced proof demonstrating that Lopez did not provide individualized supervision to his patients has no bearing on the issue of whether the indictment provided Lopez with notice that the Government intended to, and eventually did, prove that the bills submitted for Hubbard Tank therapy were fraudulent.
The allegation in the indictment that Lopez committed fraud by falsely describing his services as including the use of a Hubbard Tank formed a sufficient basis from which Lopez could infer that the Government would attempt to prove that such a misstatement was material. The indictment, therefore, satisfied minimal constitutional standards and we find Lopez’s argument to be without merit.
E. Constructive Amendment
Lopez also maintains that the district court permitted the Government to constructively amend the indictment. Lopez first raised this issue in a Rule 34 motion for Arrest of Judgment.22 The district court ruled that Lopez’s claim was not cognizable under Rule 34. Lopez attempts to bring this claim within the purview of Rule 34 by casting the alleged amendment as a jurisdictional defect. Since the Supreme Court’s decision in United States v. Cotton, however, it is clear that “defects in an indictment do not deprive a court of its power to adjudicate a case.” 535 U.S. 625, 122 S.Ct. 1781, 1785, 152 L.Ed.2d 860 (2002), overruling Ex parte Bain, 121 U.S. 1, 7 S.Ct. 781, 30 L.Ed. 849 (1887); see also United States v. Longoria, 298 F.3d 367, 372 (5th Cir.2002). A claim of con*287structive amendment, then, is not the equivalent of a charge of a jurisdictional defect. Lopez, therefore, did not properly raise his charge of constructive amendment on motion to the district court, but instead raises it for the first time on appeal.
Where a claim of constructive amendment is raised for the first time on appeal, review is for plain error. United States v. Delgado, 256 F.3d 264, 278 (5th Cir.2001). Accordingly, a defendant must show: “(1) an error; (2) that is clear or plain; (3) that affects the defendant’s substantial rights; and (4) that seriously affects the fairness, integrity or public reputation of judicial proceedings.” United States v. Longoria, 298 F.3d 367, 371 (5th Cir.2002).
There is some indication that the Government shifted its focus at trial from the actual billing code numbers for Hubbard Tank treatment to the lack of individual supervision afforded patients while in the clinic’s pool. This shift in emphasis, however, does not necessarily mean that there was a constructive amendment to the indictment. As discussed above, at least some evidence at trial indicated that billing for a Hubbard Tank included the implicit representation that patients were supervised. Proof of the absence of supervision, therefore, was relevant to the Government’s claim that billing for a Hubbard Tank was a material misrepresentation. The Government’s closing argument also indicates that the evidence regarding the lack of supervision was introduced not as part of a shift in the Government’s theory, but in order to negate Lopez’s claim of mistake. Given that there were two plausible bases, other than a constructive amendment, for introducing evidence regarding lack of supervision, we hold that the district court’s denial of Lopez’s motion for arrest of judgment did not amount to plain error.23
F. Severance
Lopez next argues that the district court erred when it denied his motion for a severance.24 We review a denial of a motion to sever for an abuse of discretion. United States v. Cortinas, 142 F.3d 242, 247 (5th Cir.1998).
We also review Lopez’s argument with an eye to two general principles, namely, that a court should order separate trials only where “[i]t appears that a defendant ... is prejudiced by a joinder of offenses,” Fed.R.Crim.P. 14, and second, that “persons jointly indicted in a conspiracy case should generally be tried together.” United States v. Scott, 795 F.2d 1245, 1250 (5th Cir.1986). Lopez fails to make the requisite showing.
Lopez looks for the necessary prejudice in his case in the volume of the evidence presented against Dr. Bieganowski and the subsequent “spillover” effect of that evidence on the jury. Lopez’s spillover argument is unconvincing. A spillover effect, by itself, is an insufficient predicate for a motion to sever. See United States v. Williams, 809 F.2d 1072, 1085 (5th Cir.1987) (“[A]dditional evidence adduced at joint trials does not constitute compelling prejudice by itself.”). Nor does Lopez’s reliance on United States v. Cortinas lend much support to his attempt to demonstrate prejudice. Cortinas in*288volved a drug conspiracy in which the evidence against some of the co-conspirators included evidence of the activities of a violent criminal gang. 142 F.3d 242, 248 (5th Cir.1998). Prejudice was found in that case because the defendants were never associated with the gang, and because the evidence of the gang’s activities was “highly inflammatory” and included evidence of a shooting. Id. Lopez’s situation is different. The evidence against Dr. Bieganowski was not as inflammatory as evidence of a shooting, and Lopez was undeniably a longtime associate of Dr. Bie-ganowski’s.
Finally, even if the volume and nature of the evidence against Dr. Bieganowski had the potential to cause Lopez some prejudice, Lopez fails to show “that he did not receive adequate protection ... through the court’s instructions to the jury.” United States v. Posada-Rios, 158 F.3d 832, 863 (5th Cir.1998). The district court instructed the jury that
“A separate crime is charged against one or more of the defendants in each count of the indictment. Each count, and the evidence pertaining to it, should be considered separately. The case of each defendant should be considered separately and individually. The fact that you may find one or more of the accused guilty or not guilty of any of the crimes charge[d] should not control your verdict as to any of [sic] other crime or any other defendant. You must give separate consideration to the evidence as to each defendant.”
We have previously stated that because a jury is presumed to follow the court’s instructions, instructions such as those given here are generally sufficient to cure the possibility of prejudice. See Posada-Rios, 158 F.3d at 863-64. We also note that Lopez was charged in five counts of the indictment and was acquitted on three, namely count one, in which he, Bieganow-ski and others were charged with conspiracy to commit mail fraud (Bieganowski was convicted on this count), and counts three and, four (mail fraud counts in which he was charged with Bieganowski, who was also acquitted on those counts). He was convicted on counts two and. five (mail fraud counts in which he was jointly charged with Bieganowski, who was also convicted on those counts). Where, as here, a jury returns a verdict of not guilty on some counts and as to some defendants, “the presumption that the jury followed the court’s instructions is even stronger.” Id. at 864.
We therefore find that Lopez has failed not only-to show prejudice, but also to demonstrate that the district court’s instructions were insufficient to protect him from possible prejudice. Consequently, we reject Lopez’s claim that the district court committed reversible error when it denied his motion to sever.
G. Deliberate Ignorance
Dr. Bieganowski claims that the district court erred in including a deliberate ignorance instruction25 in the jury charge.26
*289“We review jury instructions to determine “whether the court’s charge as a whole, is a correct statement of the law and whether it clearly instructs jurors as to the principles of law applicable to the factual issues confronting them.’ ” United States v. Faulkner, 17 F.3d 745, 766 (5th Cir.1994). “The charge must be both legally accurate and factually supportable.” United States v. Cartwright, 6 F.3d 294, 300 (5th Cir.1993).
Dr. Bieganowski does not challenge the deliberate ignorance instruction as an incorrect statement of law. Rather, drawing on language from Faulkner, he contends that the evidence adduced at trial does not support the inclusion of the instruction. In pursuing this track, however, Dr. Bie-ganowski faces a high hurdle. In deciding whether there is sufficient evidence to support a jury instruction, we “examine the evidence and all reasonable inferences therefrom in the fight most favorable to the government.” Cartwright, 6 F.3d at 300-301; see also Glasser v. United States, 315 U.S. 60, 62 S.Ct. 457, 469, 86 L.Ed. 680 (1942).
Although a deliberate ignorance instruction should rarely be given, Faulkner, 17 F.3d at 766, we have permitted its use “ ‘to inform the jury that it may consider evidence of the defendant’s charade of ignorance as circumstantial proof of guilty knowledge.’ ” United States v. Threadgill, 172 F.3d 357, 368 (5th Cir.1999) (quoting United States v. Lara-Velasquez, 919 F.2d 946, 951 (5th Cir.1990)). “It is only to be given when a defendant claims a lack of guilty knowledge and the proof at trial supports an inference of deliberate indifference.” Id. The instruction is proper, therefore, where the evidence shows “(1) subjective awareness of a high probability of the existence of illegal conduct, and (2) purposeful contrivance to avoid learning of the illegal conduct.” Threadgill, 172 F.3d at 368.
We find that this case satisfies this test. Dr. Bieganowski maintained in his testimony,27 in his closing statement below,28 and in his brief on appeal, that what the Government characterized as fraud, was no more than “extensive errors [] in his billing procedure.”
The second prong of the test also finds support in the record. Bieganowski admits on appeal that he was aware of certain billing errors. His practice was the subject of a televised investigative report into billing fraud, and he was aware of enough problems to prompt him to hire an outside billing consultant. When that billing consultant did eventually report the presence of systematic billing errors, Bie-ganowski, rather than evincing a desire to learn the nature and extent of those problems, simply directed the consultant to fix them. Finally, Bieganowski’s nurses testified that they were given a script to follow in filling out progress notes and fee tickets, and openly and regularly remained behind in the clinic after it closed to fill out billing materials.
A jury could certainly infer from this evidence that Bieganowski could have been *290aware of the presence of fraud, but instead deliberately closed his eyes to it. We reject Bieganowski’s claim that the record does not support a deliberate ignorance instruction.
Bieganowski, however, also maintains that the district court’s instruction, even if supported by the record, prejudiced him by unfairly singling him out from his co-defendants. We initially note that Biega-nowski’s contention in this respect has some arguable merit. We are aware of the risk inherent in a deliberate ignorance instruction, see United States v. Soto-Silva, 129 F.3d 340, 345 (5th Cir.1997), and we have noted that in a multiple-defendant case where only some of the defendants justify a deliberate ignorance charge, “singling out the defendant who merits the instruction, based, perhaps, on disputed or equivocal evidence, may be unfairly prejudicial to that defendant.” United States v. Reissig, 186 F.3d 617, 619 (5th Cir.1999). It is equally true, however, that “giving the instruction generally, without naming a specific defendant,” may prejudice those co-defendants who do not merit the instruction. Id. Thus, we have indicated that the better approach in this situation is to “give the instruction and indicate that [it] may not apply to all of the defendants.” Id. at 619-20.
In Reissig this Court considered the appeal of five jointly tried defendants convicted of participating in a fraudulent telemarketing scheme. They each contended that the district court erred in giving a deliberate ignorance instruction because the evidence did not warrant it. We held that as to one defendant the evidence did warrant the instruction, but agreed that it did not as to any of the other defendants. Id. at 619. We nevertheless affirmed their convictions because the instruction was one which “indieate[d]” that it “may not apply to all of the defendants.” Id. at 619-20.29 We stated that the district court’s approach was that “followed by the First Circuit in United States v. Brandon, 17 F.3d 409, 453 (1st Cir.1994)” and expressed our agreement with the First Circuit. Reissig, 186 F.3d at 620. We do not read Reissig as purporting to state a general rule requiring district courts to always follow the approach which the district court did there, or as holding that it would be error to restrict the deliberate ignorance instruction to one or less than all of several defendants. What we held in Reis-sig was that it was not error to fail to restrict the instruction to the sole defendant as to whom the evidence supported it. Id. at 619-20. That, too, is precisely what the First Circuit held in Brandon. There the court plainly indicated that the matter was one generally within the discretion of the trial court, stating:
‘We do not exclude the possibility that, on particular facts, it might so mislead a jury to give a general instruction, rather than one tailored to a specific defendant or rather than no instruction at all, as to be an abuse of discretion, but we emphasize that judgments of this kind are ‘primarily entrusted in the trial judge who inevitably has a superior feel for the dynamics of the trial and the likely reaction of the jury.” Brandon, 17 F.3d at 453 (emphasis added).
We agree. The law in this Circuit is well established that “[a] district court has *291broad discretion in framing instructions to the jury, and this Court will not reverse unless the instructions taken as a whole do not correctly reflect the issues and the law.” United States v. Alarcon, 261 F.3d 416, 424 (5th Cir.2001) (internal quotations omitted); United States v. Davis, 226 F.3d 346, 357-58 (5th Cir.2000); United States v. Moser, 123 F.3d 813, 825 (5th Cir.1997); United States v. McKinney, 53 F.3d 664, 676 (5th Cir.1995). Here the charge correctly reflected the issues and the law and we find no abuse of discretion in the district court’s framing of the deliberate ignorance instruction under the circumstances presented.
We reject Bieganowski’s complaints as to the deliberate ignorance instruction.
H. Prosecutorial Misconduct
Appellants Diaz and Bieganowski contend that the Government engaged in prosecutorial misconduct with respect to Linda Howard, an expert witness for the defense.30 After the close of the Government’s case in chief, both Diaz and Biega-nowski moved for a mistrial on the grounds of prosecutorial misconduct, alleging that the prosecution had improperly attempted to intimidate a defense expert witness, Linda Howard. The challenged comments included a warning issued by the prosecutor, the Assistant United States Attorney, to counsel for Bieganow-ski, to the effect that the Government was considering charging Howard with misprision of a felony and perjury.
The Sixth Amendment guarantees a criminal defendant the right to present witnesses to “establish his defense without fear of retaliation against the witness by the government.” United States v. Dwpre, 117 F.3d 810, 823 (5th Cir.1997); see also Washington v. Texas, 388 U.S. 14, 87 S.Ct. 1920, 1923, 18 L.Ed.2d 1019 (1967). In addition, the Fifth Amendment protects the defendant from improper governmental interference with his defense. Thus, “substantial governmental interference with a defense witness’ choice to testify may violate the due process rights of the defendant.” Id. (quoting United States v. Whittington, 783 F.2d 1210, 1219 (5th Cir.1986)). Whether a defendant has made a showing of substantial interference is a fact question, and we therefore review a claim of prosecutorial intimidation for clear error. United States v. Thompson, 130 F.3d 676, 686-87 (5th Cir.1997).
The Government does not dispute that it considered prosecuting defense expert Howard for misprision of a felony. The record is equally clear, however, that by the time Howard was to testify, the Government had further reviewed the evidence in the case and had assured Howard that she would not be so charged, an assurance that the district court conveyed to Howard. The Government also concedes that it told counsel for Bieganowski that it would consider prosecuting Howard for perjury if she were, in fact, to perjure herself. Diaz and Bieganowski both attempt to demonstrate that these comments amounted to a substantial interference with Howard’s choice to testify.
*292When judged against our prior cases, it becomes clear that the prosecution’s comments did not rise to the level of substantial interference. In United States v. Viera, 889 F.2d 1113 (5th Cir.1988) (en banc), the prosecution publicly stated that if a defense witness testified and provided incriminating evidence against himself, then that witness would be indicted. Id. at 1115. This Court, however, declined to find that there had been substantial interference even where the witness subsequently failed to testify.31 By contrast, Howard, after receiving assurances from the district court and from the Assistant United States Attorney, did testify.32 If the comments in Viera did not amount to a substantial interference, then the comparatively benign comments in this case certainly did not.
It is equally clear that the prosecution’s comments regarding perjury did not amount to a substantial interference. The prosecution did no more than to advise Howard that she could be prosecuted if she perjured herself in her testimony by stating she had previously worked for the FBI, a matter which was, at most, collateral to the subject matter of her intended testimony. There is no substantial interference in such a statement. On the contrary “[a] prosecutor is always entitled to attempt to avert perjury and to punish criminal conduct.” Viera, 839 F.2d at 1115; United States v. Thompson, 130 F.3d 676, 687 (5th Cir.1997) (“[T]he government told the witnesses . that they had to testify truthfully.... That procedure, however, even if carried out in a caustic manner, is no cause to dismiss the indictment against the defendants.” (quoting United States v. Hayward, 6 F.3d 1241, 1257 (7th Cir.1993))). Accordingly, we find that the prosecution’s comments did not amount to substantial interference and we reject the claim of Diaz and Bieganowski that their' Fifth or Sixth Amendment rights were, in any way, violated.
I. Evidence of the Prosecution’s Threats
In addition to arguing that the prosecution’s threats violated his Fifth and Sixth Amendment rights, Bieganowski also maintains that the district court erred when it prohibited him from introducing evidence of those threats to the jury, relying on United States v. Lowery, 135 F.3d 957 (5th Cir.1998). We disagree.
Lowery is wholly inapposite. There the defendant, Lowery, was charged with obstruction of justice by attempting to influence Taylor to testify falsely in a then pending criminal tax case against Lowery’s girlfriend, Sanders. Lowery’s defense was that he understood that in the Sanders case the IRS had begun “to pressure witnesses to testify in a manner consistent with the IRS position,” that Taylor had previously made statements “consistent with ... [Sanders’] innocence, and he feared the IRS was intimidating Taylor to state otherwise.” Id. at -958. We held that the exclusion of evidence of the IRS witness intimidation in the Sanders case “was error, because any evidence that the IRS was intimidating witnesses in the Sanders case would be relevant to Lowery’s case, given that his theory of defense was that he was trying to encourage wit*293nesses to tell the truth in the face of IRS pressure to do otherwise.” Id. at 959. In Lowery the government witness intimidation sought to be shown occurred before and was a cause of the defendant’s charged conduct and was relevant to show his state of mind in engaging in that conduct. Here, by contrast, the alleged witness intimidation occurred more than a year after the conduct charged in the indictment and had no relevance to it or to the state of mind of Diaz or Bieganowski in engaging in such conduct. In Lowery we applied an “abuse of discretion” review to the trial court’s exclusion of the evidence. Id. at 959. Applying that same standard here, it is clear that the trial court did not abuse its discretion in excluding the evidence.
J. Instructions in response to jury note
In his final point of error, Bieganowski argues that the district court reversibly erred when it issued a supplemental jury instruction without first notifying counsel for the defense.
On May 5, 2000, after the case had gone to the jury, the jury delivered a note to the court, the relevant portion of which read: “Also on counts 2, 3, 4, & 5 we’ve not been able to locate HCFA’s for counts 3 & 4. Do we or can we rely on [wjitness [tjesti-mony?” Upon receiving this note, and without first advising counsel for the defense of it, the district court responded to it by instructing the jury:
“In response to jury note 1, you are advised that, in my preliminary instruction to you at the beginning of the trial, I instructed you on the following as to evidence: ‘The evidence from which you will find the facts will consist of the testimony of witnesses, documents, and other things received into the record as exhibits.... ’
Thus, in answer to your question, I once again remind you that witness testimony is evidence.”
Federal Rule of Criminal Procedure 43 guarantees a defendant the right to be present at every stage of the trial. That right requires that “[w]hen a communication is received from the jury, counsel should be informed of its substance and afforded an opportunity to be heard before a supplemental charge is given.” United States v. McDuffie, 542 F.2d 236, 241 (5th Cir.1976). The Government in this case concedes that this right was violated. The only remaining question, therefore, is whether the violation was harmless or constitutes reversible error. See United States v. Sylvester, 143 F.3d 923, 928 (5th Cir.1998).
Here, the district court did not issue a true supplemental instruction. Rather, it simply resubmitted to the jury a portion of the original jury charge, an instruction to which Bieganowski had not previously objected. Bieganowski presents the same argument that was rejected in Sylvester, namely that prejudice resulted when the district court reread only a portion of the original instructions to the jury. Sylvester, 143 F.3d at 929. Beginning with the proposition that the failure to notify defense counsel of a jury communication is harmless when an “answer to the jury’s inquiry [is] distinctly responsive, ... clearly state[s] the law, and no prejudice is shown,” Sylvester, 143 F.3d at 928, this Court concluded that rereading a portion of the original instructions in response to a jury question was harmless error. Id. at 929; see also United States v. Breedlove, 576 F.2d 57, 60 (5th Cir.1978) (finding the court’s error in answering a jury note without first notifying the defense to be harmless).
Bieganowski, however, attempts to distinguish Sylvester by arguing that the dis*294trict court in that case did not simply issue a supplemental instruction, but also tempered that instruction by reminding the jury to keep the court’s original instructions in mind, and to apply all the instructions during its deliberations. Sylvester, 143 F.3d at 929. Although the district court’s supplemental instruction here did not clearly admonish the jury to rely on the original instructions, the supplemental instruction nevertheless referenced the original instructions. It was therefore evident from the language of the supplemental instruction that the original instructions remained in full force.
Diaz and Bieganowski also fault the court’s response to the jury note on the basis that it suggests to the jury that they need not be concerned with being unable to find the HCFA forms on which counts three and four were based or at least improperly minimized the importance of the HCFA forms in respect to counts three and four. However, it is clear that there was no prejudice, for none of the appellants were convicted of either of those counts.33
K. Sentencing
In his final point of error, Lopez challenges the evidentiary basis for the district court’s application of the Sentencing Guidelines. Specifically, Lopez disputes the district court’s finding that he was accountable for $961,287.50 in losses under section lB1.3(a)(l)(B) of the Sentencing Guidelines.34
We review a district court’s interpretation and application of the Sentencing Guidelines de novo, and its factual findings for clear error. United States v. Ismoila, 100 F.3d 380, 394 (5th Cir.1996). Having reviewed the basis for the district court’s finding, we conclude that Lopez’s claim has no merit.
Findings of fact for sentencing purposes need only be established by a preponderance of the evidence. United States v. Hull, 160 F.3d 265, 269 (5th Cir.1998). In this case, the Presentence Report attributed $43,084,042.27 in losses, a figure representing the entire amount billed to insurance companies during the course of the conspiracy, to Lopez. The district court, however, elected to hold Lopez responsible only for those bills that reflected charges for Hubbard Tank treatment, and accordingly departed from the Presentence Report to reduce the dollar value of Lopez’s conduct from $43,084,042.27 to $961,287.50.
The guilty verdicts returned against Lopez, together with the Presentence Report constitute a sufficient evidentiary basis for this finding. See, e.g., United States v. Lghodaro, 967 F.2d 1028, 1030 (5th Cir.1992) (“The PSR is considered reliable and may be considered as evidence by the trial judge in making factual sentencing determinations.”). We decline to hold, therefore, that the district court was clearly *295erroneous in holding Lopez responsible for the entire $961,287.50.
Conclusion
For the foregoing reasons, the convictions and sentences of each appellant are in all things
AFFIRMED.