
    UNITED STATES of America, Plaintiff-Appellee, v. Johnny RIVERA, Elena Vila, Defendants-Appellants.
    No. 89-5228.
    United States Court of Appeals, Eleventh Circuit.
    March 22, 1991.
    
      Michael Cohen, Miami, Fla., for Johnny Rivera.
    Arthur Joel Berger, Miami, Fla., for Elena Vila.
    Dexter W. Lehtinen, June C. Seraydar, U.S. Attys., Eduardo Palmer, Linda Collins-Hertz, Asst. U.S. Attys., Miami, Fla., for plaintiff-appellee.
    Before HATCHETT and CLARK, Circuit Judges, and MORGAN, Senior Circuit Judge.
   CLARK, Circuit Judge:

Defendants Elena Vila and Johnny Rivera appeal from their convictions for conspiracy to import, importation of, conspiracy to possess with intent to distribute, and possession with intent to distribute in excess of 500 grams of cocaine. For the following reasons, we affirm these convictions.

I. BACKGROUND

On August 17, 1988, Vila, Rivera, and John Stroud arrived at Miami International Airport on a flight from Barranquilla, Colombia. Vila was traveling with her three-year old child. While picking up their baggage at the luggage carousel, this group was observed by Customs Inspector Sy Schor. Inspector Schor's attention was drawn to the group because they were all young, spoke English without an accent, and arrived from Colombia, a source country for cocaine, even though none of them appeared to be Colombian. Schor approached the group after they had retrieved their luggage and requested to see their passports, customs declarations, and airplane tickets.

Schor noticed that the tickets and other travel documents indicated that the group originally had intended to fly from New York City to Miami and on to Barranquilla on August 2, 1988 and to return along the same route on August 28. These travel plans, however, had been revised, and the group actually flew from New York to Barranquilla via Miami on August 5 and returned from Barranquilla on August 17. The tickets for the three adults and the child had been purchased through the same travel agency. The boarding passes indicated that the group sat together throughout the entire trip. The total cost of the tickets was $2,769. In addition, Schor noticed that the passport of Rivera had been issued on August 3, 1988 and that Stroud’s passport had been issued on August 4, 1988.

Schor asked the group what the purpose of their trip was, and Stroud responded that they had gone just to visit Barranquilla and not to see family or friends. This heightened Schor’s suspicion because he knew that that city was not a common destination for tourists. Upon further questioning, Schor learned that Vila was Rivera’s sister-in-law and that Stroud was a very good friend. Vila also claimed that she worked as a sales clerk in a shoe store, that Stroud worked part-time installing window glass, and that Rivera was currently unemployed. Schor testified that during this preliminary questioning, the group was “fairly deadpan" and did not appear to be angry or nervous about being questioned.

Due to the unusual circumstances surrounding the group’s travel, Schor decided to examine their luggage and directed them to a table in an inspection area. Prior to this examination, Schor had each of the three persons acknowledge their individual ownership of one of the three suitcases. Schor began by inspecting Stroud’s suitcase. Upon opening it, Schor noticed immediately that the bottom portion of the suitcase had been altered and that it was unusually thick. Schor testified that this false bottom was so obvious that “it jumped out at” him. He then punctured this portion of the suitcase with a screwdriver and after withdrawing it, noticed a white powder on it which was tested as being cocaine. Schor testified that the group showed no surprise, agitation, or protest while he was probing Stroud’s luggage.

Schor then placed the three into separate rooms along with their suitcases so that they could be individually examined. The suitcases of Rivera and Vila were virtually identical to that of Stroud and also had false bottoms constructed in the same manner which contained cocaine. After .examining these suitcases, Schor informed Stroud, Rivera, and Vila that they were under arrest and recited to them their Miranda rights.

While each was being held in custody in a separate room, Schor decided to inspect the contents of each suitcase. Starting with Vila’s suitcase, Schor picked up a normal-looking can of aerosol hairspray and noticed that it weighed more than a normal hairspray can and that there was no shift in weight that should occur from the flow of liquid inside the can. Schor then detached the bottom of this can, probed with his screwdriver, and again discovered a white powder later identified to be cocaine. Schor testified that while he was searching the can, Vila had a “deadpan” reaction and did not appear to be interested or upset. A subsequent search of the suitcases of Rivera and Stroud disclosed that each also contained an aerosol can containing cocaine.

Stroud pled guilty prior to trial.

II. DISCUSSION

A.

Rivera first contends that the government violated the district court’s Standing Discovery Order and Fed.R.Crim.P. 16(a)(1)(A) by not producing his statement to Inspector Schor that one of the suitcases belonged to him. At trial, the government elicited the testimony of Inspector Schor that when Stroud, Rivera, and Villa were in the customs line, he asked whether each of them had a suitcase and that Rivera (along with the other two) identified his suitcase by saying “this is mine”. Rivera admits that this discovery violation on the part of the government was unintentional and that the government did disclose this statement on the first day of trial immediately prior to Rivera’s opening statement.

In order for this court to reverse a conviction based on the government’s violation of a discovery order, a defendant must demonstrate that the violation prejudiced his substantial rights. Substantial prejudice is established when the defendant shows that he was unduly surprised and did not have an adequate opportunity to prepare a defense or that the mistake had a substantial influence on the jury. After a review of the record, we find that Rivera has failed to establish either of these requirements.

We do not believe that Rivera could have been surprised by Schor’s testimony that Rivera had verbally claimed ownership of his suitcase. Rivera’s statement was made in response to a rather routine question that custom inspectors could ordinarily be expected to ask while questioning a citizen returning from abroad. In a trial in which all the issues revolved around whether the defendants knowingly possessed a cocaine-laden suitcase, it is doubtful that Rivera’s counsel would not anticipate or contemplate that such a statement might exist. In addition, the belated disclosure of Schor’s testimony involved Rivera’s own statement which he should have had some knowledge of making. More importantly, if Rivera had, in fact, been prejudiced by the delayed disclosure of this statement, he should have moved for a continuance. Rivera, however, did not do so and elected to proceed to trial.

Schor’s testimony concerning Rivera’s identification of his suitcase also did not have a substantial influence on the jury. The government introduced other substantial evidence linking the three members of the group to the three suitcases containing cocaine. For instance, the government introduced an airline ticket holder that had three claim checks attached which matched the claim checks fastened to the three suitcases. Since the group had spent ten days outside of the United States on their trip to Colombia, the jury could have reasonably inferred that each member had taken a suitcase on the trip. In addition, there was no confusion about whether only one of the members of the group possessed the contraband because cocaine was not found in just one suitcase, but relatively equal amounts were found in each piece of luggage. Rivera’s statement was cumulative of other evidence introduced by the government tending to show Rivera’s possession of one of the suitcases and therefore did not have a substantial effect on the jury.

B.

Vila next contends that her right to due process was violated when the government was allowed to comment at trial on her silence after having been arrested and given her warnings as required by Miranda v. Arizona. This argument is based on the accepted notion that implicit within the Miranda warnings is the assurance that a defendant’s silence “will carry no penalty.” In addition, silence in the wake of these warnings is “insolubly ambiguous because of what the State is required to advise the person arrested.” Thus, when the government has induced silence by assuring the defendant that she will suffer no penalty by being silent, the prosecution violates fundamental fairness if it then attempts to use that silence against her. Although Vila raises a substantial question about whether or not the government did in fact impermissibly comment on Vila’s silence, we find that the prejudice flowing from any constitutional violation would be harmless error.

The record indicates that Inspector Schor testified about Vila’s demeanor as he observed it at three different points during the initial confrontation in the customs line and the subsequent search. First, Schor testified that when he initially encountered the group at the luggage carousel and began to question them, all three members of the group were “fairly deadpan,” expressionless, and without any visible signs of agitation or nervousness about being singled out for questioning. Second, Schor stated that the group again expressed no reaction or protest after he began inspecting Stroud’s suitcase, pierced its construction with a screwdriver, and discovered the cocaine. After this point in the confrontation, the group was separated into different rooms, arrested, and given their Miranda warnings. Finally, Schor testified that while he inspected the contents of Vila's suitcase and discovered the cocaine in the aerosol can, she did not appear to be physically upset. In her closing statement, government counsel noted that the group had been consistently indifferent throughout the encounter and asked the jury to infer that this had been a prearranged reaction among the group in the event that their smuggling operation was detected. Vila’s counsel objected to Schor’s testimony and the prosecutor’s closing argument as an impermissible comment on her silence and moved for a mistrial, which was denied by the district court. At no point during the trial, however was the jury ever told that any of the defendants had been given Miranda warnings,

We note initially that some of Inspector Sehor’s testimony, even if construed as comments on Vila’s silence, do not raise constitutional difficulties. The government may comment on a defendant’s silence if it occurred prior to the time that he is arrested and given his Miranda warnings. Schor’s testimony about Vila’s reaction to his initial questioning prior to inspection of the group’s luggage falls within this category and therefore was not improper. In addition, the government may comment on a defendant’s silence when it occurs after arrest, but before Miranda warnings are given. The record does not state whether Vila was in custody at the time that she and the others had been directed by Schor to an inspection area. Yet, even if she was in custody at that time, the government could comment on her silence as she viewed Schor’s inspection of Stroud’s suitcase because she had not yet been given her Miranda warnings.

Thus, the only government comment on Vila’s silence that may be constitutionally problematic are those descriptions of her demeanor after she had been arrested, given her Miranda warnings, and while she observed Schor’s examination of her own suitcase. Vila argues that Schor’s testimony was a direct comment on her silence and therefore constitutionally impermissible. The government, however, contends that the prosecutor did not comment on Vila’s silence, but only on her facial expressions, mannerisms, and demeanor during the examination of the aerosol can in her suitcase. Specifically, the prosecution invited the jury to infer that Vila’s “deadpan” expression was inconsistent with the reaction of an innocent traveler with no knowledge that her luggage contained contraband. We are therefore confronted with the rather inscrutable problem of determining whether there exists a rational distinction between impermissible comments showing that the defendant is being silent and permissible comments indicating that the defendant is acting silent.

It is well-established that “it is not proper ... for the prosecutor to ask the jury to draw a direct inference of guilt from silence — to argue, in effect, that silence is inconsistent with innocence.” The complexity posed in this case is deciding what actually is “silence” within the context of the Miranda warnings. Although both logic and common sense dictate that “silence” is more than mere muteness, there is no definite outer boundary in determining what types of nonverbal conduct or demeanor, whether assertive or nonasser-tive, a prosecutor may permissibly comment on without running afoul of the dictates of Miranda. Rather, there are difficult levels of gradation between types of human behavior that constitute a purely physical act and behavior that is solely a communication. For instance, in this case, Schor’s testimony about Vila’s demeanor after exercising her right to remain silent is perhaps probative of her state of mind; a suspect can act silent in many ways that may be inconsistent with innocent knowledge. On the other hand, if the government’s position was accepted, we might force future defendants into the unenviable predicament of expressing their innocence nonverbally through flailing arms, shaking heads, furtive glances or the like, lest the government draw negative inferences from a defendant’s passive silence.

We may, however, refrain from tackling this thorny issue at this juncture because assuming that it was error for the government to comment on Vila’s demean- or after her Miranda warnings, any prejudice would be harmless beyond a reasonable doubt. Although the prosecutor did deliberately elicit Schor’s testimony on Vila’s various episodes of silence and later highlighted them in her closing argument, as our discussion above indicates, she was clearly entitled to comment on Vila’s demeanor when she was first approached by Schor at the luggage carousel and later as Stroud’s suitcase was being searched. Thus, the prosecutor still could argue in closing that Vila’s demeanor prior to arrest was not consistent with her claim of innocence. Considering that the prosecutor’s comment on Vila’s post-Miranda silence was cumulative of other permissible evidence of her “deadpan,” expressionless demeanor, any potential error on the part of the government in this case was not so harmful as to require reversal of Vila's conviction. This conclusion is further fortified when the degree of prejudice from this constitutional error is juxtaposed against the strength of the evidence of Vila’s guilt. The manner and method of the smuggling attempt and the circumstances of Vila’s arrest provided substantial evidence that Vila had knowledge of the cocaine in her suitcase. In addition, there was no countervailing evidence to suggest that Vila had no prior knowledge of the cocaine or the attempt to smuggle it in her luggage. In light of these considerations, we conclude that the government’s comment on Vila’s silence was harmless error beyond a reasonable doubt.

C.

Both Rivera and Vila contend that the district court erred in giving the jury a “deliberate ignorance” instruction. Both defendants objected to the instruction at trial, but the trial court held that the evidence was sufficient to warrant the instruction and delivered the deliberate ignorance, “conscious avoidance,” or “ostrich” instruction from this Circuit’s Pattern Jury Instructions. The defendants moved for a mistrial on the grounds that this instruction was erroneous, and the district court denied these motions.

The deliberate ignorance instruction is based on the alternative to the actual knowledge requirement at common law that “ ‘if a party has his suspicion aroused but then deliberately omits to make further enquiries, because he wishes to remain in ignorance, he is deemed to have knowledge.’ ” It is premised on the belief that acts conducted under the guise of deliberate ignorance and acts committed with positive knowledge are equally culpable. “To act ‘knowingly,’ therefore, is not necessarily to act only with positive knowledge, but also to act with an awareness of the high probability of the existence of the fact in question.”

Courts which have adopted deliberate ignorance instructions have properly cautioned that such a charge should not be given in every ease in which a defendant claims a lack of knowledge, “but only in those comparatively rare cases where ... there are facts that point in the direction of deliberate ignorance.” The danger of overly liberal use of such an instruction in an inappropriate case is that juries will convict on a basis akin to a standard of negligence: that the defendant should have known that the conduct was illegal. Thus, the important safeguard of the law that a criminal defendant must be shown to have had knowledge of culpable behavior, subjectively viewed, may be watered down in those cases in which a deliberate ignorance instruction is incongruous with the facts of a crime.

In determining whether a deliberate ignorance instruction is proper in a particular case, we have held that “it must be based upon facts which would point in the direction of deliberate ignorance.” Although broadly descriptive of the necessary factual predicate that must be established by the government before such an instruction may be given, the statement is somewhat circular and therefore insufficiently precise in identifying those cases in which an instruction would not be appropriate. We note that the Ninth Circuit— which has been primarily responsible for innovating the use of such instructions and whose decisions we have previously relied on in this area—has spelled out more specifically that such an instruction is warranted only when:

the facts ... support the inference that the defendant was aware of a high probability of the existence of the fact in question and purposely contrived to avoid learning all of the facts in order to have a defense in the event of a subsequent prosecution.

We find that this standard is more descriptive of the constitutive elements of the concept of “deliberate ignorance” and adopt it in the analysis of this case.

In addition, a necessary corollary to this standard is that a district court should not instruct the jury on “deliberate ignorance” when the relevant evidence points only to actual knowledge, rather than deliberate avoidance. In cases involving the smuggling of controlled substances in which we have upheld the use of deliberate ignorance instructions, the government established only that the defendant was probably aware that he was in the possession of contraband, but purposely avoided learning all the facts necessary to obtain positive knowledge. For example, in United States v. Batencort, a case with similar facts in which the former Fifth Circuit upheld the use of a deliberate ignorance instruction, the defendant was arrested attempting to smuggle cocaine in the false bottom of his suitcase. The defendant, formerly a street peddler in Colombia, testified at trial that he was hired by an unknown individual he met on the street to bring appliances to the United States for a large sum of money and who furnished him with false travel documents. In addition, the defendant admitted in interrogation that “ ‘he had something in the suitcase that he shouldn’t, but he didn't know exactly.' ” Similarly, in United States v. Aleman, the defendant’s briefcase was inspected by customs agents as he arrived from Colombia because it had unusually thick sides and upon examination, the case was found to contain cocaine. This court upheld the use of a deliberate ignorance instruction because the defendant stated that he had been approached by a mystery man who asked him to take the briefcase to a person in New York City, that he did not know the name of the person to whom the briefcase was to be delivered, and that no arrangements had been made for actual delivery of the briefcase.

In this case, we conclude that the district court erred in instructing the jury on deliberate ignorance because the relevant evidence presented at trial was consistent only with a theory supporting the defendants’ actual knowledge, rather than conscious avoidance on their part. More importantly, there is no evidence at all in the record suggesting that Rivera and Vila purposely contrived to avoid learning that their luggage contained contraband. Unlike Batencort and Aleman, there was no suggestion that the defendants had come into possession of their suitcases under suspicious circumstances which put them on notice of any potential illegality. The prosecution did not demonstrate that the defendants were aware of the unusual construction of their suitcases or the contents of the spray cans, but also averted any investigation that would have given them positive knowledge of the true contents. The government’s contention that the defendants should have known of the cocaine because of the false bottoms in the suitcases and the weight distribution of the hairspray cans skates dangerously close to a negligence standard under which Rivera and Vila ought to be convicted based on information that they should have had knowledge of.

Although the district court erred in giving a deliberate ignorance instruction, we conclude that the error was harmless beyond a reasonable doubt. Under the facts of this case, the jury could only find either that the defendants had actual or no knowledge of the cocaine in their suitcases; there is no evidence suggesting a middle ground of conscious avoidance. However, because the jury was also instructed that it could convict based on a theory of actual knowledge, any error is harmless if there was sufficient evidence to support the convictions under that theory. Evaluating the record as a whole, it appears to us that the district court’s error in instructing on deliberate ignorance did not affect the jury’s verdict. The evidence shows that each of the defendants, traveling as a group under very unusual circumstances, admitted ownership to one of the three suitcases in which relatively equal amounts of cocaine were found. Luggage claim tickets were also found in the possession of the defendants that corresponded to those attached to the suitcases. The jury had no reasonable factual basis upon which it could infer that the defendants had innocent knowledge and thereby cast doubt on the government’s case. We therefore conclude that the evidence was so overwhelming that a guilty verdict on all counts is compelled.

By granting the requested instruction on deliberate ignorance, the district court failed to restrain an overzealous prosecution from putting forth an alternate theory of mens rea that was not supported by the evidence. This, however, does not detract from the government’s overwhelming proof that the defendants acted with actual knowledge.

For the foregoing reasons, the convictions of Rivera and Vila are AFFIRMED. 
      
      . See United States v. Barragan, 793 F.2d 1255, 1259 (11th Cir.1986).
     
      
      . See id.
      
     
      
      . Rivera’s statement arises in the following colloquy with Inspector Schor elicited by the government’s counsel at trial:
      Q: When you had the three people in the Customs line, did you ask them if each of them had a suitcase, you know, one suitcase went to a person?
      A: Yes.
      Q: And what kind of responses did you get?
      A: "This is mine. This is mine and this is mine,” each one.
     
      
      
        .See United States v. Silien, 825 F.2d 320, 323 (11th Cir.1987).
     
      
      . 384 U.S. 436, 86 S.Ct. 1602, 16 L.Ed.2d 694 (1966).
     
      
      . See Wainwright v. Greenfield, 474 U.S. 284, 290, 106 S.Ct. 634, 637, 88 L.Ed.2d 623 (1986) (citation omitted).
     
      
      . Doyle v. Ohio, 426 U.S. 610, 617, 96 S.Ct. 2240, 2244, 49 L.Ed.2d 91 (1976).
     
      
      . See Greenfield, 474 U.S. at 290-91, 106 S.Ct. at 637-38; Doyle, 426 U.S. at 618-19, 96 S.Ct. at 2245; cf. United States v. Hale, 422 U.S. 171, 180, 95 S.Ct. 2133, 2138, 45 L.Ed.2d 99 (1975).
     
      
      . During Schor’s testimony about this third instance, he stated initially about Vila’s reaction to the search of the contents of her luggage that "[njothing verbal was said.” This answer was sturck by the trial court as an obvious comment on Vila’s silence after having been given Miranda warnings.
     
      
      . See Jenkins v. Anderson, 447 U.S. 231, 100 S.Ct. 2124, 65 L.Ed.2d 86 (1980).
     
      
      . See Fletcher v. Weir, 455 U.S. 603, 102 S.Ct. 1309, 71 L.Ed.2d 490 (1982).
     
      
      . The record indicates that Vila was not arrested or given her Miranda warnings until after Schor first discovered the cocaine in Stroud’s suitcase. The vital distinction for our purposes, however, is not when Vila was arrested or technically in custody, but when she was given her Miranda warnings and thereby given the implicit assurance that her silence would not be used against her. See id. 455 U.S. at 606-07, 102 S.Ct. at 1311-12. Because she had not yet received such affirmative assurances when Stroud’s suitcase was being searched, the government could unquestionably comment on her silence during that phase of the encounter.
     
      
      . See United States v. Elkins, 774 F.2d 530, 537 (1st Cir.1985) (stating that a comment on silence "occurs not only when the objectionable comments explicitly refer to a defendant's failure to answer questions put to him or her, but when the reference to defendant’s silence is more oblique"); cf. Hale, 422 U.S. at 177, 95 S.Ct. at 2137 (stating that “the inherent pressures of in-custody interrogation ... compound the difficulty of identifying the reason for silence”); United States v. Cummiskey, 728 F.2d 200, 205 (3d Cir.1984) (stating that "when the action of remaining silent occurs after the witness has received Miranda warnings, that action is not relevant as a prior inconsistent assertion”), cert. denied, 471 U.S. 1005, 105 S.Ct. 1869, 85 L.Ed.2d 162 (1985); State v. Vild, 155 Ariz. 374, 746 P.2d 1304 (Ariz.Ct.App. 1987).
     
      
      . The government argues that the decisions of this circuit establish that evidence concerning a defendant's actions does not constitute a comment on silence. See United States v. Rosenthal, 793 F.2d 1214, 1243 (11th Cir.1986), cert. denied, 480 U.S. 919, 107 S.Ct. 1377, 94 L.Ed.2d 692 (1987); United States v. Nabors, 707 F.2d 1294 (11th Cir.1983), cert. denied, 465 U.S. 1021, 104 S.Ct. 1271, 79 L.Ed.2d 677 (1984). Both these cases, however, are factually distinguishable and conceptually distinct. In Nabors, the prosecution’s comments involved not only a defendant’s prearrest silence, but also questions directed to the defendant by a private party and not the government. See 707 F.2d at 1297-1300. In Rosenthal, the prosecution did not seek to comment on the defendant’s silence, but the conduct of the defendant’s husband while in the her presence during custodial interrogation. See 793 F.2d at 1241-43.
      We note, however, that other courts have held that evidence of a defendant’s nonresponsive demeanor is admissible after he has waived his Miranda rights. See United States v. Shaw, 701 F.2d 367, 384-85 (5th Cir.1983); People v. McReavy, 436 Mich. 197, 210-17, 462 N.W.2d 1, 7-10 (1990).
     
      
      . Doyle, 426 U.S. at 634-35, 96 S.Ct. at 2252-53.
     
      
      . See Greenfield, 474 U.S. at 295 n. 13, 106 S.Ct. at 640 n. 13.
     
      
      . Compare Pennsylvania v. Muniz, — U.S. -, 110 S.Ct. 2638, 2644-45, 110 L.Ed.2d 528 (1990) (holding that evidence of a drunk driver’s slurred speech is admissable) with id. 110 S.Ct. at 2645-49 (holding that drunk driver’s failure to respond to question asking the year of his sixth birthday is inadmissable).
     
      
      . See South Dakota v. Neville, 459 U.S. 553, 561-62, 103 S.Ct. 916, 921-22, 74 L.Ed.2d 748 (1983).
     
      
      . See, e.g., Grancorvitz v. Franklin, 890 F.2d 34, 41-45 (7th Cir.1989) (holding that defendant’s failure to report injuries after receiving Miranda warnings is admissible to rebut his offered theory of self-defense), cert. denied, - U.S. -, 110 S.Ct. 2566, 109 L.Ed.2d 749 (1990).
     
      
      . In addition, we note that the prosecution’s comments on Vila’s demeanor were introduced in its case-in-chief and therefore may pose problems of a different dimension than the more ordinary use of silence to impeach a defendant’s testimony. See Greenfield, 474 U.S. at 292 n. 8, 106 S.Ct. at 639 n. 8; Greenfield v. Wainwright, 741 F.2d 329, 336 (11th Cir.1984), aff’d, 474 U.S. 284, 106 S.Ct. 634, 88 L.Ed.2d 623 (1986); United States v. Caro, 637 F.2d 869, 876 (2d Cir.1981) (Friendly, J.).
     
      
      . See Chapman v. California, 386 U.S. 18, 24, 87 S.Ct. 824, 828, 17 L.Ed.2d 705 (1967); United States v. Smith, 635 F.2d 411, 413 (5th Cir. Unit B 1981).
     
      
      . See United States v. Suggs, 755 F.2d 1538, 1541 (11th Cir.1985).
     
      
      . See id.; Sullivan v. Alabama, 666 F.2d 478, 484-85 (11th Cir.1982).
     
      
      . We also note that Rivera was convicted on virtually the same evidence as Vila with the exception that the prosecution did not comment on his post-Miranda silence.
     
      
      . The district court instructed the jury that:
      When knowledge of the existence of a particular fact is an essential part of an offense, such knowledge may be established if the defendant is aware of a high probability of its existence, unless he or she actually believes that it does not exist.
      So, with respect to the issue of the defendant's knowledge in this case, if you find, from all the evidence, beyond a reasonable doubt, that the defendant believed that he possessed some cocaine, a controlled substance, and deliberately and consciously tried to avoid learning that there was cocaine secreted in his suitcase, in order to be able to say, if he should be apprehended, that he did not know the contents of the suitcase, you may treat such deliberate avoidance of positive knowledge as the equivalent of knowledge.
      In other words, you may find that a defendant acted knowingly if you find, beyond a reasonable doubt, either: (1) that the defendant actually knew that he possessed cocaine, or, (2) that he deliberately closed his eyes to what he had every reason to believe was the fact.
     
      
      
        .United States v. Jewell, 532 F.2d 697, 700 (9th Cir.1976) (en banc) (citing G. Williams, Criminal Law: The General Part § 57, at 157 (2d ed. 1961)), cert. denied, 426 U.S. 951, 96 S.Ct. 3173, 49 L.Ed.2d 1188 (1976).
      As Professor Robbins, however, notes in his authoritative article on this subject, the substitution of the deliberate ignorance doctrine for the actual knowledge requirement is not a particularly well-established principle of the criminal law and was only recently revived in the 1970s by the onslaught of federal narcotics prosecutions. See Robbins, The Ostrich Instruction: Deliberate Ignorance as a Criminal Mens Rea, 81 J.Crim.L. & Criminology 191, 199-203 & n. 72 (1990).
     
      
      . Jewell, 532 F.2d at 700 (quoting Model Penal Code § 2.02(7)). For an excellent discussion of the genealogy of the relationship between the Model Penal Code’s definition of knowledge and its adoption by the federal courts as a justification for use of deliberate ignorance instructions, see Robbins, supra note 26, at 203-10.
     
      
      . United States v. Murrieta-Bejarano, 552 F.2d 1323, 1325 (9th Cir.1977).
     
      
      . United States v. Alvarado, 838 F.2d 311, 314 (9th Cir.1987), cert. denied, 487 U.S. 1222, 108 S.Ct. 2880, 101 L.Ed.2d 915 (1988).
     
      
      . Jewell, 532 F.2d at 707 (Kennedy, J., dissenting). A further consideration suggesting that courts should be guarded in their use of deliberate ignorance instructions is simply that deliberate ignorance is easier to prove than actual knowledge and that prosecutors should not be granted such a windfall advantage when the giving of such an instruction is not appropriate. See Robbins, supra note 26, at 200 & n. 55.
     
      
      . See United States v. Aleman, 728 F.2d 492 (11th Cir.1984).
     
      
      . See United States v. Restrepo-Granda, 575 F.2d 524, 528-29 (5th Cir.), cert. denied, 439 U.S. 935, 99 S.Ct. 331, 58 L.Ed.2d 332 (1978).
     
      
      . Alvarado, 838 F.2d at 314; see also United States v. Picciandra, 788 F.2d 39, 46 (1st Cir.), cert. denied, 479 U.S. 847, 107 S.Ct. 166, 93 L.Ed.2d 104 (1986).
     
      
      . See Alvarado, 838 F.2d at 314; United States v. Beckett, 724 F.2d 855, 856 (9th Cir.1984).
     
      
      . 592 F.2d 916 (5th Cir.1979).
     
      
      . Id. at 917.
     
      
      . 728 F.2d 492 (11th Cir.1984).
     
      
      . See id. at 492-94; see also United States v. Alvarez, 837 F.2d 1024 (11th Cir.) (defendant was hired by mystery man who paid for international flight so that defendant could act as cook on vessel that was transporting rotten fish to the Bahamas), cert. denied, 486 U.S. 1026, 108 S.Ct. 2003, 100 L.Ed.2d 234 (1988); United States v. Peddle, 821 F.2d 1521, 1523-25 (11th Cir.1987) (among other suspicious circumstances, defendant boat owner admitted that "something was going on with vessel and that it might be carrying contraband of some kind”).
      In holding that a deliberate ignorance instruction is incompatible in those cases in which the facts point only to actual knowledge on the part of the defendant, we recognize that we have departed from the substantive justification for such instructions—that deliberate ignorance is an alternative formulation for the requirement of “knowledge” as an element of a criminal offense. See Robbins, supra note 26, at 226-27. That is, under our view, “deliberate ignorance” is treated as an exception to the knowledge requirement, rather than a component part of its definition. See id. at 227. Although such inconsistency is clearly intolerable on theoretical grounds, we believe that this incongruity is necessary for the prudential reason of guarding against overzealous use of such instructions and the attendant prejudice to criminal defendants.
     
      
      . The district court's decision to give the jury a deliberate ignorance instruction may have been based on the defendants’ argument in their opening that Stroud would testify that the group's luggage was damaged on the trip to Barranquilla and that Stroud made arrangements to have these damaged suitcases replaced. The defendants also claimed that Stroud would testify that he received the aerosol cans from a person he met in a bar and put those cans in the suitcases without Rivera or Vila’s knowledge. If these facts had been established, the case for a deliberate ignorance instruction would have been stronger and would have come closer to the circumstances in Aleman. These facts, however, were never established because the defendants later chose not to have Stroud testify.
     
      
      . See Alvarado, 838 F.2d at 317; Beckett, 724 F.2d at 856.
     