
    UNITED STATES of America, Plaintiff-Appellee, Cross-Appellant, v. VITEK SUPPLY CORPORATION and Jannes Doppenberg, Defendants-Appellants, Cross-Appellees.
    Nos. 97-1254, 97-1255 & 97-1498.
    United States Court of Appeals, Seventh Circuit.
    Argued Oct. 8, 1997.
    Decided May 14, 1998.
    
      Eric J. Klumb (argued), Thomas P. Schneider, Office of the United States Attorney, Milwaukee, WI, Kenneth Jost (argued), Department of Justice, Washington, DC, for United States of America.
    Williams H. Theis (argued), Robert R. Henak, Shellow, Shellow & Glynn, Milwaukee, WI, for Vitek Supply Corp.
    James M. Shallow (argued), Robert R. Henak, Shellow, Shellow & Glynn, Milwaukee, WI, for Jannes Doppenberg.
    Before CUDAHY, COFFEY, and EVANS, Circuit Judges.
   CUDAHY, Circuit Judge.

Vitek Supply Corporation manufactured “premixes” for veal calves—that is, mixtures that feed companies and livestock growers add to animal feed. Certain premixes contained elenbuterol, avoparcine, zinc bacitracin or various nitrofurans. Some of these substances promote growth and increase meat-to-fat ratios; others treat and prevent scours (diarrhea). And they are all unapproved by the Food and Drug Administration (FDA), either for use in food-producing animals generally or veal calves specifically. Several of the drugs are carcinogens; one may lead to acute poisoning in humans; and another may increase human resistance to antibiotics.

Vitek smuggled these drugs into the United States with the help of its Dutch parent, Pricor B.V. In shipments from Pricor to Vitek, the companies either misdescribed the drugs in documents submitted to the United States Customs Service or failed to declare the substances altogether. The scheme began to collapse when an animal grower informed the government about the true content of Vitek’s products and when investigators found undeclared substances concealed in a shipment from Pricor. Eventually a jury convicted Vitek and its president, Jannes Doppenberg, of conspiracy to defraud Customs and the FDA, of smuggling or receiving smuggled merchandise and of distributing adulterated or misbranded animal drugs with intent to defraud or mislead.

On appeal, Vitek and Doppenberg challenge several decisions of the district judge, beginning with his refusal to suppress the fruits of the government’s search and ending with his application of the Sentencing Guidelines. The government also cross-appeals from the defendants’ sentencing. We affirm in all respects.

I. Search and Seizure

The warrant authorizing the search of Vitek’s premises permitted the seizure of (1) all tainted animal feed; (2) any and all misbranded drugs, to include elenbuterol and any of its derivatives; (3) any and all records from February 18, 1989, relating to the importation of merchandise and to the smuggling and illegal entry of tainted animal feed; and (4) any and all records from February 18, 1989, relating to the illegal entry and distribution of misbranded drugs in interstate commerce. The warrant further instructed that the evidence seized should indicate possible violations of 18 U.S.C. §§ 545 and 1001 and 21 U.S.C. § 331(a)—statutes prohibiting the smuggling and the distribution of misbranded drugs or adulterated food. The defendants assert the warrant lacked sufficient particularity and was not supported by probable cause. These are issues we review de novo. See United States v. Navarro, 90 F.3d 1245, 1251 (7th Cir.1996).

The Fourth Amendment requires that a warrant “particularly deserib[e] the ... things to be seized.” This requirement precludes the issuance of a warrant that permits a “general, exploratory rummaging in a person’s belongings,” Coolidge v. New Hampshire, 403 U.S. 443, 467, 91 S.Ct. 2022, 2038, 29 L.Ed.2d 564 (1971), and thereby ensures that the scope of á search will be confined to evidence relating to a specific crime that is supported by probable cause. See United States v. Leary, 846 F.2d 592, 600 (10th Cir.1988). To satisfy the demand for particularity, a warrant “must describe the objects of the search with reasonable specificity, but need not be elaborately detailed.” United States v. Shoffner, 826 F.2d 619, 630 (7th Cir.1987) (quoting United States v. Reed, 726 F.2d 339, 342 (7th Cir.1984)).

The Vitek warrant is broad, but not impermissibly so. See United States v. Vanichromanee, 742 F.2d 340, 347 (7th Cir.1984) (warrant authorized seizure of writings related to the conspiracy to import heroin but did not specify precise documents); Shoffner, 826 F.2d at 630 (warrant authorized seizure of “stolen motor vehicles, parts of stolen motor vehicles ... and documentation concerning the purchase, sale, ownership, titling and licensing of stolen motor vehicles”); United States v. Pritchard, 745 F.2d 1112, 1121 (7th Cir.1984) (warrant authorized seizure of electronic wiretapping equipment, including electronic meter and devices resembling telephone receivers; agents executing warrant seized every portable electronic item within appellant’s residence). This is not.a case like United States v. Spilotro, 800 F.2d 959 (9th Cir.1986), on which the defendants rely. In Spilotro, the search warrant’s only limitation was that the items seized be evidence of a violation of any one of thirteen statutes, some of exceptional scope. See id. at 965 (noting that one of the statutes was 18 U.S.C. § 371, conspiracy to commit an offense against or defraud the government). The Vitek warrant, in contrast, specified only three statutes and all are more narrowly focused than the statutes at issue in Spilotro.

The defendants argue that the warrant did not advise government agents how to distinguish between legal and illegal substances. But a warrant must explicate the items to be seized only as precisely as the circumstances and the nature of the alleged crime permit. See Shoffner, 826 F.2d at 630. With respect to the misbranded drugs and adulterated animal feed, we are unaware of any readily-discernable characteristic that would have enabled the agents to identify the illegal substances. This is not a cáse' like United States v. Fuccillo or Mantilla Records of P. R., Inc. v. Morales, in which warrants were deemed invalid because they failed to mention features that made the illegal products easily identifiable. See Fuccillo, 808 F.2d 173, 176-77 (1st Cir.1987) (stolen clothing was máde by a specific manufacturer); Montilla Records, 575 F.2d 324, 325 (1st Cir.1978) (stolen records had a Motown label). Because the warrant could not have better informed the agents how to distinguish between legal and illegal substances, the instructions to seize “tainted animal feed” and “any and all misbranded drugs to'include clenbuterol and any of its derivatives” were sufficiently particular.

In light of the nature of Vitek’s crime, the instruction regarding the seizure of records also satisfied the requirements of the Fourth Amendment. Evidence of importing and distributing illegal substances is not likely to be confined to a single type of document. As the D.C. Circuit has noted, “specificity is even more difficult [when] evidence of the crimes can be found in almost every type of business document conceivable.” United States v. Dale, 991 F.2d 819, 848 (D.C.Cir.1993). Vitek and Doppenberg seek to analogize the Vitek warrant to the one in United States v. Leary, 846 F.2d 592 (10th Cir.1988), but the warrants are distinguishable. In Leary, the warrant authorized the search of an export company and included two limitations: that any documents seized (1) “fall within a long list of business records typical of the documents kept by an export company,” and (2) indicate a violation of the federal export laws. Id. at 600-01. The Tenth Circuit held that, in the context of a search of an export company, the Leary warrant placéd no limitation on the government. See id. at 601. Leary, however, differs from the ease at bar in at least two significant respects. First, unlike the Vitek warrant, the Leary warrant contained no date limitation. Second, and' more importantly, in Leary the government had information that it could have used to particularize its description of the documents to be seized. See id at 604. As with the misbranded drugs and tainted animal feed, we are not convinced that the government could have been more precise about the records it was seeking. Vitek and Doppenberg suggest several ways the government might have tailored its warrant, such as directing agents to seize records that related to particular customers. But, as we elaborate below, the warrant here was supported by broad probable cause. All of the defendants’ suggestions would have resulted in a warrant that was narrower than the'probable cause supporting it. We are also skeptical of Vitek and Doppenberg’s claim that, after the search, “[n]o records of any significance were left on the premises.” Appellants’ Br. at 25. The defendants’ brief asserts that the agents seized material that filled approximately 100 banker’s boxes; the record shows that agents seized approximately 20 boxes. See Tr. at 891. Indeed, Vitek had to produce additional documents in response to a grand jury subpoena. Because the warrant did not allow a dragnet seizure, and because the government could not have been more specific, the description of the records to be seized was sufficiently particular.

The warrant also was supported by probable cause. At the time the warrant was issued, the government had been informed that Vitek was importing and distributing animal feed tainted with clenbuterol. The government had also been informed that Pricor, Vitek’s Dutch parent, was shipping tainted animal feed to other customers in the United States. In a shipment from Pricor to Vitek, investigators had found hidden parcels containing oxytetraeycline hydrochloride, colistine sufaat [sic], furaltadone hydrochloride and liquid Baytril. Sutherland Aff. at para. 30. All the drugs were misbranded and had not been declared on Customs documents. Based on these facts, the government had probable cause to believe that Vitek had been importing unapproved and mislabeled drugs. The government also had probable cause to believe that Vitek was blending these drugs into premixes and animal feeds. In sum, we find no reason to invalidate the warrant that authorized the search of Vitek’s premises.

II. Evidentiary Issues

A. Prior Litigation in the Court of International Trade

The first of the defendants’ evidentiary challenges relates to the charge that they conspired to defraud the Customs Service and the FDA, in violation of 18 U.S.C. § 371. To prove its case, the government argued, in relevant part, that the defendants failed to pay certain duties to Customs. But after earlier civil litigation with Vitek in the Court of International Trade, the government had stipulated that certain shipments from Pricor to Vitek were duty-free. In the criminal trial against Vitek and Doppenberg, the government argued that these same shipments were part of a scheme to defraud Customs. When Vitek sought to admit the government’s prior stipulations, the district judge excluded this evidence pursuant to Federal Rule of Evidence 403, on the grounds that the stipulations would confuse the jury and cause undue delay. We review this ruling for an abuse of discretion. See United States v. York, 933 F.2d 1343, 1352, 1354 (7th Cir.1991).

The government made its stipulations in the course of litigating Vitek Supply v. United States, 17 C.I.T. 111 (Ct. Int’l Trade 1993). In the events leading up to that case, Vitek had imported shipments of veal premix—or rather, what it declared to be veal premix— from Pricor. The Customs Service imposed a duty on these shipments on the theory that animal feed loses its duty-free status if it contains vitamins and minerals that are suitable for human consumption. Vitek paid the duties under protest and then successfully challenged the policy of the Customs Service in the Court of International Trade. See id. After the court determined that the veal premix could enter the United States duty-free, Vitek sought a refund of the duties it had paid on other shipments that had been declared as veal premix. The government stipulated that these shipments were covered by the ruling of the Court of International Trade and granted the refund. During its criminal investigation, however, the government learned that its stipulations covered shipments that were in fact bulk vitamins, avoparcine and zinc bacitraein-not veal premix, as the government had been led to believe.

As the district judge recognized, admitting the government’s stipulations into evidence would have opened the door to a panoply of issues surrounding the litigation in the Court of International Trade. In order to digest the import of the stipulations, the jury would have had to consider various Customs classifications, whether the information before the Court of International Trade was accurate and sufficient, and whether certain sworn statements were truthful. The nature of the questions addressed by the Court of International Trade would have only compounded the difficulty of the jury’s task; the district judge candidly admitted that he did not “get a handle” on the documents the defendants sought to present to the jury until he had the benefit of oral argument. Tr. at 3642. This is not a simple case like United States v. Fisher, 106 F.3d 622 (5th Cir.1997), on which Vitek and Doppenberg rely. In Fisher, the defendants sought to admit evidence that they had prevailed in an arbitration proceeding that involved an issue relating to their criminal prosecution. See id. at 633. The district court excluded the evidence under Rule 403 after the government objected on the grounds that the arbitrator had not detailed the reasons for the result and that the jury may not understand that it was not bound by the arbitrator’s decision. See id. The court of appeals reversed, explaining that the evidence went to the “heart of the case” and that the government could easily address its concerns during cross-examination See id. In the case at bar, however, the district judge may have found himself presiding over a complex mini-trial that focused on the significance of the Court of International Trade’s opinion and the actions the parties took in its aftermath. In light of these circumstances, the district judge did not abuse his discretion when he decided that admitting evidence of the government’s prior stipulations would result in confusion and unnecessary delay.

As a practical matter, we also question whether the evidence would have benefitted Vitek and Doppenberg. They argue that the stipulations were important because the jury would question how the defendants could have deceived the Customs Service with respect to shipments that the government had stipulated were duty-free. But after the jury heard all the facts relating to the stipulations, they would perceive the defendants as trying to ride the coattails of an earlier, successful deception. We doubt that this would have given the jury reason to acquit the defendants of a charge of conspiracy to defraud the Customs Service.

B. Testimony of the Defense Expert

The defendants further contend that the district judge erred when he declined to allow a defense expert to testify about the effects of avoparcine and zinc bacitracin. Part of the government’s ease depended upon its proving that these substances are drugs. Under 21 U.S.C. § 321(g)(1)(C), a substance is a drug when it is intended to affect the structure or function of the body, and is not food. A defense expert allegedly was prepared to testify that avoparcine and zinc bacitracin do not affect the body’s structure or function. The district judge did not allow the testimony because it was not sufficiently set forth in a summary the defendants submitted in response to a scheduling order. The defendants’ summary stated, “[The expert] will testify that avoparcine and zinc bacitracin are considered safe and effective as feed additives for calves and cattles.” Vitek argues that it was “implicit” in this summary that the expert would testify that the substances are feed additives, not drugs. But neither the district court nor the government should have to parse the summary of expert testimony, searching for subtle nuances and relying on uncertain inferences. We agree with the district court that the summary failed to give adequate notice that the expert would testify .that avoparcine and zinc bacitracin are not drugs.

It is well-established that in a civil case, a district judge has the discretion to exclude evidence as a means of sanctioning one of the parties for an inadequacy in its "case, such as the summary at issue here. See, e.g., Mid-America Tablewares, Inc. v. Mogi Trading Co., 100 F.3d 1353, 1363 (7th Cir.1996). In a criminal case, however, the district court’s power to levy such sanctions is less unconstrained. Although “[f]ew rights are more fundamental than that of an accused to present witnesses in his own defense,” Taylor v. Illinois, 484 U.S. 400, 408, 108 S.Ct. 646, 652, 98 L.Ed.2d 798 (1988), the Supreme Court has allowed the imposition of sanctions when a criminal defendant has willfully violated a discovery order. See id. at 414, 108 S.Ct. at 655-56. But it is not certain whether sanctions are permissible if the violation is not egregious—specifically, when “the excluded witnesses would undoubtedly have been at least somewhat helpful to the defense and violation of the [court’s] order was not willful.” Tyson v. Trigg, 50 F.3d 436, 445 (7th Cir.1995); see also United States v. Harvey, 117 F.3d 1044, 1047-48 (7th Cir.1997). Here, while the summary was sloppy and inadequate, it is not clear that the defendants intended to willfully violate the district court’s order.

We have not yet had to define the limits of the district court’s power to use the exclusion of evidence as a sanction in a criminal trial, see Harvey, 117 F.3d at 1047, and we need not decide that question today. If the district judge did err in excluding the expert’s testimony, the error was harmless. As previously explained, under 21 U.S.C. § 321(g)(1)(C), a substance is a drug if it is intended to affect the structure or function of the body. With respect to avoparcine, the expert’s proffered testimony stated only that avoparcine did not have an effect on the structure of the body. The expert would not have stated that avoparcine did not affect the function of the body. See Tr. at 3515. Indeed, the expert would have testified that avoparcine was a dilution of an “antibiotic” used in “nutritive doses to improve animal performance.” Tr. at 3515. We think this testimony supports, the conclusion that avoparcine affects the function of the body and thus falls squarely within the definition of § 321(g)(1)(C). In regard to zinc bacitracin, the expert similarly would have referred to it as an antibiotic. See Tr. at 3518. And even if the expert’s testimony had persuaded the jury that avoparcine and zinc bacitracin do not affect the structure or function of the body, § 321(g)(1)(C) is concerned with intended, not actual, effect. See 21 U.S.C. § 321(g)(1)(C) (“The term drug means ... articles (other than food) intended to affect the structure or any function of the body ----”) (emphasis added). The jury saw letters written by Doppenburg himself that (i) referred to avoparcine as “a growth promotant” used to “promote liver function,” Gov.’s Ex. 357; (2) discussed “drugs ... which work at the gut level (like Bacitracin[) ],” Gov.’s Ex. 358; and (3) explained that “with ... the FDA’s crackdown on Zinc Bacitracin, the veal industry is ... scared to lose all its (few) antibiotics,” id. The expert’s testimony would not have refuted the overwhelming evidence that the defendants intended avoparcine and zinc bacitracin to affect the structure or function of the body. Therefore, even if the judge erred in excluding the expert’s testimony, his error was harmless.

C. The Daubert Hearing

At trial, an expert witness for the government testified that scientific testing had revealed that Vitek’s premixes contained illegal substances. Vitek and Doppenberg maintain that this testimony is inadmissible under Daubert v. Merrell Dow Pharmaceuticals, Inc., 509 U.S. 579, 113 S.Ct. 2786, 125 L.Ed.2d 469 (1993). When a party challenges the admissibility of scientific testimony, we first conduct a de novo review to ensure that the district court followed the Daubert framework. See Cummins v. Lyle Indus., 93 F.3d 362, 367 (7th Cir.1996).

In Daubert, the Supreme Court determined that, when a district judge is faced with expert scientific testimony, the judge must decide “whether the expert is proposing to testify to (1) scientific knowledge that (2) will assist the trier of fact to understand or determine a fact in issue.” Daubert, 509 U.S. at 592, 113 S.Ct. at 2796; cf. Fed.R.Evid. 702. The Court set forth several factors that are “pertinent” to the district judge’s determination whether testimony is scientifically valid: (1) whether the theory or technique can be and has been tested; (2) whether the theory or technique has been subject to peer review and publication; (3) whether the theory or technique has a known or potential rate of error; and (4) whether the theory or technique is generally accepted. See Daubert, 509 U.S. at 593-94, 113 S.Ct. at 2796-97. However, the Court emphasized that it did “not presume to set out a definitive checklist or test,” id. at 593, 113 S.Ct. at 2796, and that the district, judge’s inquiry should be “flexible.” Id. at 594, 113 S.Ct. at 2797.

Before allowing the government’s expert to testify at trial, the district judge held a five-hour Daubert hearing to evaluate the scientific validity of the expert’s testimony. Vitek and Doppenberg assert that the district judge strayed beyond the bounds of Daubert when he analyzed the material presented at the hearing. Specifically, they argue that the district court did not assess whether the expert’s techniques were generally accepted, ignored error rates and placed undue emphasis on the qualifications of the government’s expert. We disagree.

We first address the contention that the district judge failed to determine whether the techniques used to ascertain the content of Vitek’s premixes are generally accepted. All the chemical testing took place at a FDA laboratory, where analysts performed four procedures—fourier transform infrared spectrometry, gas chromatography/mass spectrometry, high performance liquid chromatography and electrospray liquid chromatography tandem mass spectrometry. Each of these procedures reveals a substance’s “spectrum” or “fragmentation pattern”—a sort of chemical fingerprint. Analysts then identify a substance by comparing its spectrum with spectra from known standard samples or from a computer library. These procedures, and the tools used to perform them, are widely used and generally accepted in the fields of analytical and forensic chemistry. See Tr. at 259394, 2603, 2606, 2613. Vitek and Doppenberg, however, argue that the district court did not inquire whether the procedures are generally accepted for the specific purpose of determining the content of animal feed. But we have suggested that when tests involve the application of well known instruments “to a particular and not-out-of the-ordinary application,” some of the Daubert factors may be worthy of less emphasis. See Cummins, 93 F.3d at 367 n. 2. Because the FDA’s testing procedures were not dependent on “abstract or novel scientific theory,” id., and because of the controls discussed below, the district court did not err by failing, to focus on the narrow question whether the procedures- were generally accepted as means of ascertaining the content of animal feed.

The defendants further argue that the district court should not have allowed the government’s expert to testify because he was unable to identify’ the error rate of his testing methods. But the purpose of an inquiry into error rates is to determine whether tests are accurate and reliable. See United States v. Pierre, 47 F.3d 241, 243 (7th Cir.1995). Here the district court heard evidence that the analysts controlled for false positives with “blanks” (samples known to contain none of the relevant chemical) and for false negatives with “spiked samples” (samples known to contain a specific amount of the chemical). Depending on the circumstances, this may be an appropriate means of ensuring both reliability and accuracy. See id. (“[P]erhaps [to test the reliability of a laboratory), the government submits an assortment of samples containing different drugs (and the statistically appropriate number of samples known not to be contaminated) to see how well the lab distinguishes among them.”). The same sample was also submitted to multiple procedures by different analysts to ensure that the result was accurate. In light of these controls, the district judge found that “while the plaintiff’s chemists may not have used every standard possible to control and test the operation of then-techniques, they did employ proper standards.” Tr. at 2727. We agree that there was ample evidence for the district judge to conclude that the government’s tests were accurate and reliable.

With respect to the defendants’ argument that the district court gave undue emphasis to the expert’s qualifications, it is true that the court misspoke when it stated that one of the “nonexclusive guideposts” set forth in Daubert is whether the expert is qualified. Tr. at 2725. In fact, Daubert did not include the expert’s qualifications in its list of pertinent considerations. Daubert, however, did not intend to set forth “a rigid or exclusive list.” See United States v. Hall, 93 F.3d 1337, 1341 (7th Cir.1996). And we have no doubt that an expert’s qualifications bear upon the scientific validity of his testimony. In United States v. Benson, 941 F.2d 598 (7th Cir.1991), we stated, “An expert’s opinion is helpful only to the extent the expert draws on some special skill, knowledge, or experience to formulate that opinion; the opinion must be an expert opinion (that is, an opinion informed by the witness’ expertise) rather than simply an opinion broached by a purported expert.” Id. at 604. Because an expert’s qualifications bear upon whether he can offer special knowledge to the jury, the Daubert framework permits—indeed, encourages—a district judge to consider the qualifications of a witness. Cf. Braun v. Lorillard Inc., 84 F.3d 230, 234-35 (7th Cir.1996) (determining that jury could not hear testimony that plaintiff’s lung tissue contained asbestos fibers, when purported expert was not experienced in the testing of human tissue and spent 99.9 percent of his time engaged in administrative and marketing activities for his consulting firm). Despite the district judge’s inaccurate statement about Daubert, the district judge did not err when he gave weight to the expert’s qualifications.

When the district court’s analysis is within the parameters of Daubert, we affirm its decision to admit scientific evidence unless the decision is manifestly erroneous. See Cummins, 93 F.3d at 367. Here we find no such error. As we have explained, the district judge had reason to believe that the government’s tests were reliable and accurate. The defendants argue that the district court did not give adequate weight to their expert, who testified at the Daubert hearing that the government had not properly validated its testing methodology. But, as the district judge noted in his oral ruling, the government’s analysis was qualitative, ■ not quantitative-—that is, the government only needed to establish that an unapproved substance was present; it did not need to determine how much of the substance was present. See Tr. at 2726. The validation methods recommended by the defendant’s expert were necessary only for a quantitative analysis. Moreover, the defense expert had little “hands-on” experience with the testing methodologies used to determine the content of Vitek’s premixes. In sum, the district judge’s oral ruling makes clear that he pondered the testimony given at the Daubert hearing, evaluated it within the parameters of Daubert and concluded that the government’s evidence was scientifically valid. He did not err in doing so.

III. Jury Instructions

Counts Seven, Nine, Eleven, and Twelve of the indictment charged Vitek and Doppenberg with introducing misbranded drugs in interstate commerce in violation of 21 U.S.C. § 333(a)(2). Counts Eight and Ten charged the defendants with introducing adulterated drugs in interstate commerce, also in violation of § 333(a)(2). The indictment specified that the drugs were “adulterated” because they were “new animal drugs”they had not been approved by the FDA and recognized as safe and effective for then-intended use of promoting growth and feed efficiency in veal calves. In order to be guilty of Counts Seven-Twelve, the defendants had to have acted with “intent to defraud or mislead.” 21 U.S.C. § 333(a)(2). To act with this intent, Vitek and Doppenberg must have had “knowledge of the essential nature of the alleged fraud.” United States v. Hiland, 909 F.2d 1114, 1128 (8th Cir.1990).

Vitek and Doppenberg argue that the district court failed to instruct the jury that the government was required-to prove such knowledge. The district- court charged the jury, in relevant part,

To act with intent to defraud means to act voluntarily and intentionally to deceive or cheat. The intent to defraud may be established by proof that, with respect to the specific count in question, the defendant intended to deceive or cheat another person, a business entity, or a government agency. To act with intent to defraud a government agency means to act with the intent to interfere with or obstruct a lawful government function by deceit or trickery, or at least by means that are dishonest—
To act with the intent to mislead means to act voluntarily and intentionally to conceal a material fact and thereby create a false impression, or-' to omit or withhold information from a statement and thereby cause a portion of the statement to be misleading. An intent to mislead may be established by proof that the defendant intended to mislead a person, an entity with whom he was doing business, or a government agency.

Our review of these instructions “is limited to the determination of whether the jury was misled in any way and whether it had understanding of the issues and its duty to determine these issues.” United States v. Dack, 987 F.2d 1282, 1284 (7th Cir.1993) (internal quotation marks and citations omitted). In making this determination, we cónsider how the jury perceived the instructions in light of all the evidence and arguments presented at trial. See EEOC v. AIC Sec. Investigations, Ltd., 55 F.3d 1276, 1283 (7th Cir.1995). We reverse only if “the jury’s comprehension of the issues is so misguided that it prejudiced the complaining party.” Dack, 987 F.2d at 1284.

Given the allegations against Vitek and Doppenberg, the government needed to show that the defendants: (1) knew they were distributing a “new animal drug”; and (2) knew their labeling omitted any mention of unapproved substances. See Hiland, 909 F.2d at 1128; United States v. Industrial Lab. Co., 456 F.2d 908, 910 (10th Cir.1972). Here the district court’s instructions, when considered in their larger context, adequately advised the jury of these requirements. The district judge gave comprehensive instructions regarding the definition of “new animal drug,” making clear that the term refers to a drug that is not approved by the FDA and not recognized as safe and effective for its intended use. See Tr. at 4072. The judge also defined “misbranded.” See Tr. at 4070. And while the instructions regarding the definition of “act with intent to defraud or mislead” did not explictly state that the defendants had to know that they were distributing new animal drugs or misbranded products, the instructions were given on the heels of closing arguments that were replete with references to the defendants’ knowledge. For example, the defendants’ counsel cautioned the jury, “[U]nless you can say beyond a reasonable doubt we think these folks knew exactly what was required and exactly what was prohibited, then you should not be entering ... a verdict that' they engaged in schemes to defraud, or did certain things with the intent to defraud.” Tr. at 39994000. The prosecutor also made repeated references to Doppenberg’s knowledge. See, e.g., Tr. at 383940 (referencing letters presented at trial and asserting that they showed Doppenberg knew the illegality of avoparcine, zinc bacitracin and nitrofurazone); Tr. at 3847 (urging that when Doppenberg spoke with government investigators, he knew certain substances were illegal); Tr. at 4035 (asking rhetorically whether Doppenberg thought certain substances were food instead of drugs). In -light of these closing arguments and the evidence presented at trial, the jury understood that one of the issues was whether Vitek and Doppenberg knew that they were distributing “new animal drugs” and that their labeling omitted information about the presence of unapproved substances. And finally, as a practical matter, the guilty verdict on the charge of conspiracy against the FDA and Customs is a “clear indication” that the jury believed that Vitek and Doppenberg were aware of the illegal nature of their activities. See Hiland, 909 F.2d at 1129.

IV. Sentencing

After four days of hearings, the district judge sentenced Doppenberg to 44 months of imprisonment for conspiring to defraud the FDA and Customs and for smuggling and receiving smuggled merchandise (Counts One-Six), and to 36 months of imprisonment for introducing misbranded and adulterated drugs into interstate commerce (Counts Seven-Twelve), to run concurrently. Doppenberg also received three years of supervised release for Counts One-Six, and one year of supervised release for Counts Seven-Twelve, also to run concurrently. In addition; he was ordered to pay a special assessment of $600 and a fine of $25,000. Vitek was placed on probation for four years and fined $350,000. Both defendants, and a co-conspirator who pleaded guilty, were made jointly liable for a restitution payment of $735,266.65. Of this amount, $29,452.65 was for duties owed to the Customs Service; the remaining $705,814 was for a meat processor that destroyed its calves upon learning that they had been fed Vitek’s tainted products.

These sentences satisfy neither the defendants nor the government. Both appeal from the court’s application of U.S.S.G. § 2F1.1, which captures the “intended, probable, or otherwise expected loss” from a defendant’s fraud. United, States v. Schneider, 930 F.2d 555, 558 (7th Cir.1991). The defendants argue that the losses of the meat processor should not count toward the § 2F1.1 calculation and that all of Vitek’s shipments were duty-free under Vitek Supply Co. v. United States, the decision rendered by the Court of International Trade. For its part, the government asserts that the district court erred when, in applying § 2F1.1, it rejected evidence of competitor and consumer losses. After considering these arguments, we are satisfied that the district judge meted out appropriate sentences.

A. The Defendants’ Arguments

Vitek and Doppenberg contend that, for purposes of § 2F1.1, Swissland, the meat processor, has not suffered a “loss” and is not a “victim.” The definition of these two terms is a question of law that we review de novo. See United States v. Barrett, 51 F.3d 86, 89 (7th Cir.1995). As an initial matter, we reject the contention that Swissland has not incurred a “loss” within the meaning of § 2F1.1. After the FDA became aware that Swissland’s herds had ingested a banned nitrofuran, Swissland sought assurance that the FDA would not initiate an enforcement action if Swissland sold the meat from its calves. The FDA refused to provide such an assurance but did not order Swissland to destroy the meat. Instead the FDA informed Swissland that it was free to pursue judicial resolution of the issue, and that any decision to destroy the meat “would be purely voluntary.” Defs.’ Sup. Sent. Mem., Ex. G3. Anxious to capitalize on the FDA’s selection of an adjective, the defendants argue that the decision to destroy the meat was voluntary because Swissland could have argued in court that the meat was safe for human consumption and that the FDA misconstrued the applicable regulations. The defendants then cite United States v. Marlatt, 24 F.3d 1005 (7th Cir.1994), for the principle that the “voluntary decision to take a loss, even if reasonable in terms of business strategy, does not result in legal liability for the defendant under § 2F1.1(b)(1).” Appellants’ Br. at 62. The defendants’ argument fails for at least two reasons. First, we would not use the word “voluntary” to describe the choice between destroying meat and judicially challenging a federal agency’s interpretation of its regulations. Second, and more fundamentally, the defendants have misunderstood Marlatt. That case distinguishes between direct and consequential damages, see Marlatt, 24 F.3d at 1007, and reiterates the unsurprising requirement that a defendant must have legally caused a loss before he can be held accountable for it, see id. at 1006. But Marlatt does not hold that the cost of measures to rectify harm caused by the defendánt (here the ingestion of an unapproved substance by Swissland’s herds) falls outside the purview of § 2F1.1, when those measures may (in some perverse way) be considered voluntary.

We also reject the assertion that Swissland was not a victim for purposes of § 2F1.1. As Vitek and Doppenberg point out, Swissland was not a victim unless it was in fact defrauded—i.e., unless it did not know that Vitek’s produpt contained a banned nitrofuran. To bolster their claim, that Swiss-land was a knowing consumer of Vitek’s tainted product, the defendants rely on the law of agency. In Barrett we suggested that, under § 2F1.1, the knowledge of an agent is imputed to the agent’s employer when the agent is acting at least in part for the benefit of the employer. See 51 F.3d at 89 (quoting United States v. One Parcel of Land, 965 F.2d 311, 316 (7th Cir.1992)). Vitek and Doppenberg argue that the knowledge of Dr. Dan Shields should be imputed to Swissland. The contention is that Shields is the vice-president of American Feeds and Livestock (AF & L), the animal feed company that Swissland employed to recommend feeds and feed additives. There is no question that Shields knew that Vitek’s product, dubbed “Apple First Start,” contained nitrofurans; indeed, Shields helped Doppenberg develop the product. According to the defendants, Shields encouraged Swissland to use Apple First Start because it prevented scours; thus Shields was “acting for the benefit” of Swissland and his knowledge is imputed to the meat processor.

The defendants gloss over several points that distinguish Shield’s connection with Swissland from the straightforward employer/agent relationship discussed in Barrett. Shields was not a simple agent of Swissland. Instead, he was the employee of one of Swissland’s independent contractors. As a general matter, an employer is less likely to be held vicariously liable for the acts of its independent contractors than for the acts of its employees. See Stephan D. Sugarman, A Restatement of Torts, 44 Stan. L.Rev. 1163, 1195 (1992). But it is not necessary for us to determine the import of AF & L’s independent contractor status, as there is yet another factual complication which convinces us that Shields’ knowledge cannot be imputed to Swissland. Shields had his own feed supply business, Fancy Calf, which was unconnected to AF & L and was not an independent contractor of Swissland. Fancy Calf, not AF & L, purchased Apple First Start from Vitek. Thus, strictly speaking, we cannot say that Swissland received Apple First Start from one of its independent contractors. And Shields was simply wearing too many hats— co-creator of Apple First Start, vice-president of AF & L, and proprietor of Fancy Calf—for us to impute his knowledge to Swissland with any degree of confidence about the fairness of the result. We therefore affirm the district court’s decision to include Swissland’s $705,814 loss in the § 2F1.1 calculation.

In applying § 2F1.1, the district court also included a $29,452.65 loss suffered by Customs. Vitek and Doppenberg, however, argue that under the decision rendered by the Court of International Trade, Vitek Supply Co. v. United States, 17 C.I.T. 111 (Ct. Int’l Trade 1993), Vitek’s shipments were duty-free. Therefore, the defendants contend, although' Customs was defrauded, it incurred no loss. But the defendants’ interpretation of Vitek is untenable. Vitek explained that, in order for a shipment to be duty-free under the applicable regulation, it must be a preparation used in feeding animals and contain at least six percent grain product. See id. at 112. The remainder of the preparation must consist of feedstuff's—sources of nutrition. See id. at 114. The unapproved substances in Vitek’s premixes were not sources of nutrition. Accordingly, Vitek’s shipments are dutiable and Customs has indeed suffered a loss within the meaning of § 2F1.1.

B. The Government’s Cross-Appeal

At sentencing, the government asked the district court to include the losses of Vitek’s competitors and downstream consumers in its § 2F1.1 calculation. The district court refused to do so because it would “involve too much conjecture and speculation” and “the evidence in this case is [in]sufficient [to provide] a firm foundation for such a finding.” Sen. Tr. at 210. While we review the definition of “loss” de novo, we review the district court’s factual determination regarding losses for clear error. See United States v. Andersen, 45 F.3d 217, 220 (7th Cir.1995).

With respect to competitor losses, the government first looked to other sellers of premixes for veal calves—Vitek’s direct competitors. The government assumed that these sellers suffered losses when feed companies and livestock growers purchased Vitek’s tainted premixes, and sought to use Vitek’s gain from its premix sales as a proxy for that loss. This approach is not without support; the application notes to § 2F1.1 allow a district court to use the defendant’s gain to calculate a victim’s loss when a more precise measure is unavailable. See U.S.S.G. § 2F1.1, comment (n.8); Andersen, 45 F.3d at 221. But gain may be used only if “there is in fact a loss, and [the] use of the gain results in a ‘reasonable estimate of the loss.’ ” Andersen, .45 F.3d at 221 (quoting U.S.S.G. § 2F1.1 comment (n.8)). We agree with the district judge that, in this case, the government has not presented sufficient evidence to allow us to determine whether the criteria set forth in Andersen are satisfied. And even if the government had proved the existence of a loss, and that Vitek’s gain was a reasonable estimate of that loss, the government has not proved that Vitek’s sale of unadulterated products caused the loss.

The government has done nothing more than establish the mere fact that other companies sell premix. See Gov.’s Sent. Mem. at 7 (citing to an exhibit that refers to Qualitech, another premix company). It is true, as the government argues, that in Andersen we declined to "find a loss because we had no reason to believe that competitors were selling the same or similar products. See 45 F.3d at 221. But whether the defendant has competitors is the beginning, not the end, of the inquiry. Here, while there is proof that some customers knew the content of Vitek’s products, there is no evidence that the presence of illegal ingredients drew customers to Vitek from its competitors. And even if we assume that Vitek’s competitors suffered a degree of loss-—that at least some of Vitek’s customers would have gone elsewhere had Vitek’s premixes not contained illegal substances—the government has provided us with no means of determining whether Vitek’s gain is a reasonable estimate of that loss. Vitek’s conduct was not pervasively illegal; it sold legal products as well as illegal ones. We have every reason to believe that if Vitek had not sold illegal premixes, it would have sold similar, legal products. Presumably, then, in the absence of Vitek’s fraud, not all of its sales would have gone to other sellers. On the record before us, however, we have no method of estimating how many sales would have gone elsewhere. For example, we do not know how many competitors Vitek has. We do not know the market shares of any of its competitors, or, for that matter, Vitek’s market share for its illegal or legal products. We do not know whether purchasers of feed additives frequently change suppliers. In sum, we cannot even begin to determine whether Vitek’s gain was a reasonable estimate of its competitors’ losses. The district judge did not err when he refused to use Vitek’s gain as a proxy for the losses of its direct competitors.

The government also asserts that the district judge should have included the losses of another class- of “competitors”: upstream drug suppliers. There are legal drugs that promote growth and feed efficiency in veal calves and prevent scours. The manufacturers of these drugs competed with Pricor, Vitek’s Dutch parent. The government argues (and this is ironic, in light of our preceding discussion) that, if Vitek had not included unapproved substances in its premixes, it would have included similar, legal substances. Therefore, the government contends, upstream drug suppliers suffered a loss as a result of Vitek’s illegal activities. See Gov.’s Sent. Mem. at 6-7 and Ex. A. The government again proposed using Vitek’s gain as a measure of these upstream losses; to this end, the government determined how much Vitek “marked up” the drugs it included in its premixes. In support of the theory that the district court should use Vitek’s gain as proxy for upstream losses, the government submitted a publication entitled “1993 Feed Additive Compendium,” which establishes that approved drugs serve the same purposes as the drugs used by the defendants. The government also submitted evidence that Vitek purchased one legal substance from Pfizer, Inc. But we have no means of estimating, among other things, whether Vitek’s mark-up on illegal substances is equivalent to the mark-up on legal substances. We do not know whether Vitek could have obtained some, or all, of the legal drugs from its parent company. As with direct competitors, the government simply has failed to provide evidence that enables us to determine the extent of upstream losses and whether Vitek’s gains are a reasonable measure of these losses.

Finally, the government argues that the § 2F1.1 calculation should include the losses of downstream consumers. Unlike Swissland, most of Vitek’s direct customers were aware that the premixes contained unapproved drugs. Therefore, as the government concedes, these customers were not defrauded and the defendants cannot be held hable for their losses. However, the government argues, at some point innocent purchasers consumed the meat of veal that had been treated with Vitek’s tainted products. The government contends that these innocent purchasers suffered a loss, which should be measured by Vitek’s gross sales of its tainted products.

This was the approach taken in United States v. Marcus, 82 F.3d 606 (4th Cir.1996). In Marcus, the defendant conspired to defraud the FDA by failing to notify or seek approval for a drug he modified to treat a heart condition. See id. at 607. The defendant’s gross sales from the unapproved drug were more than ten million dollars. In determining that consumers had suffered a loss, the Fourth Circuit reasoned

The marketing of a drug employing an unapproved and untested formula, when the modification presents the potential to affect the safety, therapeutic value, or bioequivalence of the drug, renders the drug of unknown efficacy and safety; the sale of a drug represented to possess FDA approval under those circumstances does not provide consumers with the benefit of their bargain---- Given the unchallenged finding that consumers would not purchase a drug of unknown safety and efficacy at any price, the district court correctly concluded that ... gross sales were the appropriate measure of the actual loss suffered by consumers____

Id. at 610. As this quotation indicates, the Fourth Circuit’s reasoning rests largely on the assumption that a knowing consumer would not pay anything for the product that the Marcus defendant sold.

In some cases, a product may be so inherently harmful that a court can confidently conclude that it is worthless. At oral argument, the government stated that knowing consumers would have left the meat from veal treated with Vitek’s products “rotting on the shelves.” Perhaps the government is correct. But perhaps it is not. People take a wide variety of health risks; for instance, the knowing ingestion of certain carcinogens can be considered almost commonplace. Maybe some purchasers would have risked consuming the meat. If so, the proper measure of the consumer’s losses would be the difference between what the consumer would have paid if she had all the facts, and the price the consumer actually paid. Cf. U.S.S.G. § 2F1.1 app. n. 7(a). The problem, of course, is that these issues can only be addressed by speculation. This is not a case like Marcus, where the district court made an unchallenged finding that consumers would not purchase the defendant’s product at any price.

We do not wish to minimize the conduct of Vitek and Doppenberg. The government’s basic proposition is correct: innocent purchasers did not receive the , benefit of the bargain when they purchased meat from veal calves treated with Vitek’s premixés. As we explained in Andersen, “The FDA is in the business of protecting the public____ [T]he defendants :.. caused harm to the public through their violations of FDA rules.” 45 F.3d at 222. We also suggested that the district court may wish to consider making an upward departure to account for “nonmonetizable risk to human and animal health.” Id. But the district court cannot punish the defendants for this harm by including speculative losses in its § 2F1.1 calculation. Accordingly, the sentences of Vitek and Doppenberg, and their underlying convictions, are AFFIRMED. 
      
      . In an argument that hardly merits discussion, the defendants contend that the district judge misapplied the concept of peer review. They argue that the district court decided that "there must have been peer review since the testing took place over the course of many months.” Appellants’ Br. at 46. However, review of the district judge’s oral comments makes clear that he believed that there had not been enough time for extensive peer review. And because the tests used well-established technology to detect the presence of unapproved substances, the district judge felt that peer review was less critical. Daubert encoúrages exactly this kind of flexibility-
     
      
      . The defendants also contend that the district court should have instructed the jury that 21 U.S.C. § 333(a)(1), which does not require intent to defraud or mislead, is a lesser included offense of § 333(a)(2). But this argument does not warrant discussion, since the defendants did not request an instruction on lesser included offenses until after the government began its closing argument. Accordingly, the request was untimely and the district court had the discretion to reject it. See Fed.R.Crim.P. 30; United States v. Watson, 894 F.2d 1345, 1349 (D.C.Cir.1990).
     
      
      . The defendants also argue that circumstantial evidence established that Swissland knew the true content of Vitek’s products. The district judge, however, was convinced that Swissland had been defrauded. Because we do nol find this conclusion clearly erroneous, we do not further discuss the circumstantial evidence.
     
      
      . Here the district court denied the government's request for'such a departure. The government did not appeal from this ruling.
     