FLAUM, Circuit Judge.
This case arose out of an investigation initiated by the Royal Canadian Mounted Police into suspicious activity at Grimsby Airpark, a small, rural airstrip located approximately one hour southwest of Toronto, Ontario, just north of the Canada-United States international border. Several individuals reported seeing a small Piper Cherokee plane landing on numerous occasions when the airpark was closed, taking on passengers, and departing after being on the ground a short time. Once it was determined that the [389]*389plane was based at the DuPage County Airport in West Chicago, Illinois, agents of the United States Immigration and Naturalization Service arranged for dual surveillance of the plane’s activities at Grimsby Airpark and DuPage Airport. Largely as a result of this surveillance, the investigation revealed eight instances between February 12, and April 21, 1991, in which illegal Polish aliens were smuggled into this country. On each occasion, the aliens, who were carrying luggage, were driven by car in prearranged rides to Grimsby Airpark. There, the aliens were met by pilot Allan Parmelee, who flew them to DuPage Airport where they arrived late at night. From the airport, Parmelee drove the aliens to a prearranged rendezvous point in Chicago, usually a gas station, where Parme-lee delivered the aliens to Tadeusz Sobiecki. After taking delivery of the aliens, Sobiecki drove them by car either to their final destinations in Chicago or to other locations where he transferred the aliens to Ewa Bro-zek-Lukaszuk, her husband Lester Lu-kaszuk, and Alojzy Sandrzyk, among others, for further transport.
A grand jury returned a seventeen-count superseding indictment against Parmelee, Sobiecki, Brozek-Lukaszuk, Lukaszuk, and Sandrzyk. Count One charged all five defendants with conspiring to transport illegal aliens within the United States in violation of 18 U.S.C. § 371 and 8 U.S.C. § 1324(a)(1)(B).1 Counts Two, Four, Six, Eight, Ten, Twelve, Fourteen, and Sixteen charged Parmelee with knowingly bringing aliens into the United States at a place other than a designated port of entry in violation of 8 U.S.C. § 1324(a)(1)(A).2 The remaining counts charged the various defendants with substantive violations of 8 U.S.C. § 1324(a)(1)(B).
The defendants pleaded not guilty, and the case went to trial before a jury. In the midst of trial, Parmelee withdrew his plea of not guilty and entered a plea of guilty to all seventeen counts of the indictment. The trial continued against the remaining defendants whom the jury found guilty as charged in the indictment. The district court sentenced the defendants to the following terms of imprisonment: Parmelee, twenty-one months; Sobiecki, thirty-six months; Bro-zek-Lukaszuk, six months; and Sandrzyk, twelve months. Lukaszuk was sentenced to three years of probation, with the special condition that he serve the first sixty days in custody.
On appeal, the defendants raise a number of issues but only two require consideration: (1) the sufficiency of the instructions given to the jury for the section 1324(a)(1)(B) offense, and (2) the three-level enhancement of Par-melee’s base sentencing level under U.S.S.G. § 3Bl.l(b) for his managerial or supervisory role in the offense. For the reasons set forth below, we affirm the convictions and sentences of Sobiecki, Brozek-Lukaszuk, Lu-kaszuk, and Sandrzyk, but remand the case to the district court for resentencing of Par-melee.
I.
Sobiecki, Brozek-Lukaszuk, Lukaszuk, and Sandrzyk3 contend that their [390]*390convictions for transporting illegal aliens in violation of section 1324(a)(1)(B) should be reversed because the district court erroneously failed to instruct the jury on an essential element of the offense — the defendants’ willfulness in furthering the aliens’ continued illegal presence in the United States. The district court instructed the jury as follows:
Counts 3, 5, 7, 9, 11, 13, 15, and 17 of the indictment charge one or more of the defendants with unlawfully transporting aliens within the United States in violation of Title 8, United States Code, Section 1324(a)(1)(B). That statute provides in relevant part:
‘Any person who knowing or in reckless disregard of the fact that an alien has come to, entered or remains in the United States in violation of law, transports or moves or attempts to transport or move such alien within the United States by means of transportation or otherwise in furtherance of such violation of law shall be guilty of an offense against the United States.’
You should refer to the indictment to determine which defendant is charged in each count.
In order to sustain a charge of unlawful transportation of an alien within the United States the government must prove each of the following propositions beyond a reasonable doubt:
First, that the alien had entered or remained in the United States in violation of law;
Second, that the defendant knew or recklessly disregarded the fact that the alien had entered or remained in the United States in violation of law; and
Third, that the defendant transported the alien in furtherance of the alien’s unlawful entry to or presence in the United States.
******
In order for transportation to be in furtherance of an alien’s unlawful entry or presence, there must be a direct or substantial relationship between the defendant’s act of transportation and the alien’s unlawful entry to or presence in the United States. In other words, the act of transportation must not be merely indicental [sic] to a furtherance of the alien’s violation of the law.
An act of transportation is in furtherance of the alien’s unlawful entry of [sic] presence if such transportation brings the alien to his or her destination or place of refuge, or helps the alien remain in the country unlawfully, undetected by those responsible for enforcing the immigration laws.
A surreptitious or furtive transportation of an alien which inhibits the enforcement of immigration laws may be in furtherance of the alien’s unlawful entry of [sic] presence.
(Tr. 2954-56). The defendants argue that these instructions allowed the jury to find them guilty simply for transporting illegal aliens even if they did not know they were furthering the aliens’ violation of the law.
We have no question that section 1324(a)(1)(B) implicitly requires the government to prove beyond a reasonable doubt not only that the defendant knew the alien he transported had entered this country in violation of immigration law, but also that the defendant knowingly transported the alien to further that violation, that is, acted willfully. See, e.g., United States v. Chavez-Palacios, 30 F.3d 1290, 1294 (10th Cir.1994); United States v. Diaz, 936 F.2d 786, 788 (5th Cir.1991); United States v. Medina-Garcia, 918 F.2d 4, 7 (1st Cir.1990); United States v. Hernandez, 913 F.2d 568, 569 (8th Cir.1990) (per curiam); United States v. Morales-Rosales, 838 F.2d 1359, 1360 (5th Cir.1988); United States v. Merkt, 764 F.2d 266, 270 (5th Cir.1985) (per curiam); United States v. Moreno, 561 F.2d 1321, 1322 (9th Cir.1977). Without a mens rea requirement, section 1324(a)(1)(B) could penalize purely innocent conduct. Staples v. United States, — U.S. -, -, 114 S.Ct. 1793, 1799, 128 L.Ed.2d 608 (1994); Liparota v. United States, 471 U.S. 419, 426, 105 S.Ct. 2084, 2088, 85 [391]*391L.Ed.2d 434 (1985). For example, it could conceivably criminalize the actions of a cab driver who transports in a routine commercial transaction an individual who announces his illegal alien status during the course of the ride. We do not read section 1324(a)(1)(B) as enacting such sweeping liability. See United States v. Turkette, 452 U.S. 576, 580, 101 S.Ct. 2524, 2527, 69 L.Ed.2d 246 (1981) (absurd results are to be avoided); United States v. Wilson, — U.S. -, -, 112 S.Ct. 1351, 1354, 117 L.Ed.2d 593 (1992) (same); Matter of Udell, 18 F.3d 403, 410-12 (7th Cir.1994) (Flaum, J., concurring) (same). Rather, we hold that a defendant’s guilty knowledge that his transportation activity furthers an alien’s illegal presence in the United States is an essential element of the crime stated in section 1324(a)(1)(B). In so holding, we decline to adopt a special test for determining guilty knowledge. See United States v. 1982 Ford Pick-Up, 873 F.2d 947, 950-51 (6th Cir.1989) (comparing “direct or substantial relationship” and “intent-based” approaches). As in other criminal prosecutions that require mens rea, the government may prove the defendant’s knowledge by reference to the facts and the circumstances surrounding the case. Liparota, 471 U.S. at 434,105 S.Ct. at 2093. Relevant considerations bearing on this issue include whether the defendant received compensation for his transportation activity, whether the defendant took precautionary efforts to conceal the illegal aliens, and whether the illegal aliens were the defendant’s Mends or co-workers or merely human cargo. 1982 Ford Pick-Up, 873 F.2d at 951; United States v. Perez-Gomez, 638 F.2d 215, 218-19 (10th Cir.1981); United States v. Salinas-Calderon, 585 F.Supp. 599, 602 (D.Kan.1984).
We also believe that the instructions as a whole did not clearly place this element before the jury. See United States v. Goines, 988 F.2d 750, 772 (7th Cir.) (in reviewing instructions to the jury, we consider the charge as a whole), cert. denied, — U.S. -, 114 S.Ct. 241, 126 L.Ed.2d 195 (1993). While the jury was instructed concerning the general definition of “knowingly” taken from our pattern instructions,4 Federal Criminal Jury Instructions of the Seventh Circuit § 6.04 (1980), the jury was not specifically informed that to be guilty the defendants had to know not only that the Polish aliens had entered this country illegally, but also that they were furthering the aliens’ illegal entry by transporting them. See Liparota, 471 U.S. at 424-25 n. 7, 105 S.Ct. at 2088 n. 7; United States v. Kerley, 838 F.2d 932, 937 (7th Cir.1988). A proper jury instruction under section 1324(a)(1)(B) could have been made either by appending the requisite mental state to the third element of the offense or by adding it as a fourth element and by deleting the remainder of the charge, which was ambiguous regarding the statute’s state of mind requirement.5 See Liparota, 471 U.S. at 433 n. 16, 105 S.Ct. 2093 n. 16.
[392]*392Hence, we are left with the question whether this error, which bears on the Fifth Amendment requirement of proof beyond a reasonable doubt and the Sixth Amendment requirement of a jury verdict, Sullivan v. Louisiana, — U.S. -, -, 113 S.Ct. 2078, 2079-80, 124 L.Ed.2d 182 (1993), automatically entitles the four defendants to a new trial, or whether it is instead subject to the harmless-error analysis originated in Chapman v. California, 386 U.S. 18, 24, 87 S.Ct. 824, 828, 17 L.Ed.2d 706 (1967) (“[B]e-fore a federal constitutional error can be held harmless, the court must be able to declare a belief that it was harmless beyond a reasonable doubt.”).6 While the Supreme Court has yet to decide the question whether instructional error of this sort can ever be harmless,7 we believe that in light of Sullivan, its most recent pronouncement on the circumstances in which per se error will be found, the Court would resolve this question in the affirmative. Thus, our application of the reasoning in Sullivan to the facts of the present case leads us to conclude that the district court’s failure to clearly instruct the jury on section 1324(a)(l)(B)’s guilty knowledge requirement is amenable to harmless-error review. In our opinion, there exists “beyond a reasonable doubt” jury findings from which we can say that the instructional error did not contribute to the jury’s verdict of guilty.
In Sullivan, the defendant argued on direct appeal from his conviction for first-degree murder that the reasonable doubt instruction given at his trial was unconstitutional. The State of Louisiana conceded that the jury instruction was erroneous, but claimed that it was harmless. Justice Scalia, writing for a unanimous Supreme Court, disagreed and held that a constitutionally deficient reasonable-doubt instruction can never be harmless error.8 The Court reasoned that the harmless-error inquiry in Chapman
is not whether, in a trial that occurred without the error, a guilty verdict would surely have been rendered, but whether the guilty verdict actually rendered in this trial was surely unattributable to the error. That must be so, because to hypothesize a guilty verdict that was never in fact rendered — no matter how inescapable the findings to support that verdict might be— would violate the jury-trial guarantee.
[393]*393— U.S. at -, 113 S.Ct. at 2081-82 (emphasis in original) (citations omitted). The Court determined that in the context of a defective reasonable-doubt instruction, the Chapman standard did not apply.9 Id.-, 113 S.Ct. at 2082. The Court stated:
There being no jury verdict of guilty-beyond-a-reasonable-doubt, the question whether the same verdict of guilty-beyond-a-reasonable-doubt would have been rendered absent the constitutional error is utterly meaningless. There is no object, so to speak, upon which harmless-error scrutiny can operate. The most an appellate court can conclude is that a jury would surely have found petitioner guilty beyond a reasonable doubt — not that the jury’s actual finding of guilty beyond a reasonable doubt would surely not have been different absent the constitutional error. That is not enough. The Sixth Amendment requires more than appellate speculation about a hypothetical jury’s action, or else directed verdicts for the State would be sustainable on appeal; it requires an actual finding of guilty.
Id. (emphasis in original) (citations omitted). The Court distinguished an instruction that erects a presumption regarding an element of the offense from one that misdescribes the burden of proof because in the latter instance the error “vitiates all the jury’s findings” and leads the appellate court to simply speculate as to what a rational jury would have done. Id. In the case of a mandatory presumption, the instructional error would be found harmless “when the [predicate] facts ‘are so closely related to the ultimate fact to be presumed that no rational jury could find those facts without also finding that ultimate fact, making those findings is functionally equivalent to finding the element required to be presumed.’ ” Id. (quoting Carella v. California, 491 U.S. 263, 271, 109 S.Ct. 2419, 2423-24, 105 L.Ed.2d 218 (1989) (per curiam) (Scalia, J., concurring)).
Under the above-quoted harmless-error analysis formulated by Justice Scalia in Car-ella and followed in Sullivan, the instructional error here is harmless if, given the facts of this case, no rational jury could have found the defendants guilty of violating section 1324(a)(1)(B) without also making the proper factual finding as to the missing element of willfulness. See id.; Carella, 491 U.S. at 271, (Scalia, J., concurring); see also Green v. Peters, 36 F.3d 602, 608-11 (7th Cir.1994) (Ripple, J., concurring) (advancing Justice Scalia’s harmless-error test on collateral review of instructional error under Falconer v. Lane, 905 F.2d 1129 (7th Cir.1990)).
In this ease, the jury was not asked to find that the defendants acted knowingly in transporting the illegal aliens. Rather, the instruction referred only to the defendants’ knowledge of the aliens’ violation of immigration law. In theory, under such an instruction, a jury could convict our aforementioned hypothetical cab driver for transporting a known illegal alien without also finding that the cab driver did so knowingly in furtherance of the alien’s violation of the law. However, under the factual circumstances of this case, we believe that a rational jury, which found that the defendants knew the aliens were illegal, also would have necessarily found that the defendants knew their activity furthered the aliens’ violation of the law. We base this determination on the unrebutted evidence that the defendants furtively transported the aliens late at night; drove evasively to elude police surveillance, at times at high rates of speed; and received compensation by the carload for the delivery of luggage-laden and foreign-speaking aliens who were strangers to the defendants. In view of this significant amount of mens rea evidence, we conclude that no rational jury could have found that the defendants did not act knowingly in furthering the transport of the illegal aliens. We accordingly hold that the error was harmless beyond a reasonable doubt. Chapman, 386 U.S. at 24, 87 S.Ct. at 828; Sullivan, — U.S. at -, 113 S.Ct. at 2081-82; see also, e.g., United States v. Whitmore, 24 F.3d 32, 36 (9th Cir.1994) (instruction that omitted knowledge element of the crime of using a communication facility to [394]*394engage in drug trafficking); Ianniello v. United States, 10 F.3d 59, 65 (2d Cir.1993) (instruction that failed to inform the jury in a RICO action that predicate acts must be related).
Our prior decisions on instructional error involving a missing element of an offense, United States v. Dunkel, 927 F.2d 955 (7th Cir.1991) (per curiam), and United States v. Kerley, 838 F.2d 932 (7th Cir.1988), are not inconsistent with this approach. Dunkel, a per curiam opinion, held that withdrawal of the defense of good faith misinterpretation of the law in a criminal tax prosecution was not harmless error. 928 F.2d at 956. In so holding, we relied on Justice Scalia’s concurrence in Carella v. California, which became the genesis for his harmless-error test in Sullivan. See id. By implicitly adopting Justice Scalia’s test, this court merely reached a contrary conclusion concerning the applicability of Chapman based on the particular facts before it.
In Kerley, an opinion that predated both Carella and Sullivan, the defendant was charged with refusing to register for the draft in violation of 50 U.S.C.App. § 462(a). The district court’s instruction to the jury omitted the element of the offense that the defendant know he had a duty to register. This court reviewed the instruction under the plain-error rule and concluded that “[n]o reasonable jury could have concluded that [the defendant] did not know he had a legal duty to register.” 838 F.2d at 937. Although we noted that “among the errors to which the harmless-error rule does not apply is an error that has the practical effect of withdrawing the issue of guilt from the jury,” the situation of the defendant in Kerley was distinguished on the ground that it involved “merely [a] fail[ure] to instruct clearly on an element of the crime.”10 Id. at 938.
For support, we cited the Supreme Court’s decision in Pope v. Illinois, 481 U.S. 497, 107 S.Ct. 1918, 95 L.Ed.2d 439 (1987), which rejected the proposition that “a conviction can never stand if the instructions provided the jury do not require it to find each element of the crime under the proper standard of proof.” Id. We also noted this circuit’s “narrow” interpretation of the category of fatal errors, id., as well as its “reluctance to reverse a conviction because of defective instructions even if the defects concern the elements of the crime, unless the defects might have made a difference to a rational jury.” Id. at 939. After describing the results in other circuits as “mixed,” we concluded:
We prefer the statement by the Second Circuit that, ‘in general, failure to instruct the jury on an essential element of the offense constitutes plain error.’ United States v. Golomb, 811 F.2d 787, 793 (2d Cir.1987) (emphasis added); see also Government of Virgin Islands v. Brown, 685 F.2d 834, 839 (3d Cir.1982); cf. United States v. Polowichak, 783 F.2d 410, 417 (4th Cir.1986). That formulation allows for the exceptional case, and this is one. The district judge did not fail to instruct the jury on knowledge. He failed to give an instruction that distinguished between knowledge of fact and knowledge of legal duty; and although this was a serious failure, it was not so egregious as to justify a retrial in a case where the issue of guilty knowledge was not contestable and was barely if at all contested. We are worlds away from the paradigmatic case of plain error per se; the case where the judge directs a verdict of guilty.
Id.
On rehearing, however, the defendant successfully demonstrated that he had properly preserved his objection to the erroneous jury instruction pursuant to Fed.R.Crim.P. 30. Id. at 942. Accordingly, we issued a supplemental opinion, holding that, “[t]he ground was valid, and although the error was not plain, the government does not argue that it was harmless; it was therefore a reversible error, so Kerley is entitled to a new trial.” Id. While, at first glance, this specific language may appear to suggest that an instructional error on the elements of an offense is never harmless, the opinion itself does not purport to adopt any per se approach. In any event, as discussed above, the more re[395]*395cent Supreme Court jurisprudence would appear to disfavor the creation of such a rule. To this observation, we wish to underscore that the doctrine of harmless-error “has become an integral component of our criminal justice system.” Sullivan, — U.S. at -, 113 S.Ct. at 2084 (Rehnquist, J., concurring). It “recognizes the principle that the central purpose of a criminal trial is to decide the factual question of the defendant’s guilt or innocence, and promotes public respect for the criminal process by focusing on the underlying fairness of the trial rather than on the virtually inevitable presence of immaterial error.” Delaware v. Van Arsdall, 475 U.S. 673, 681, 106 S.Ct. 1431, 1436, 89 L.Ed.2d 674 (1986).
II.
The second issue concerns the propriety of the district court’s finding that pilot Parmelee acted as a either a manager or supervisor in the smuggling ring, resulting in a three-level increase in his base sentencing level under U.S.S.G. § 3Bl.l(b).11 The three-level increase for being a manager or supervisor in an offense
is appropriate for those defendants whose “relative responsibility” for the offense is found to have been greater than that of its other participants. In determining relative responsibility, a significant factor to be considered is whether the defendant exercised authority or control over others in the criminal operation. The fact, however, that the deféndant did not exercise such control, in the sense of having power to tell the others what to do, does not necessarily disqualify the defendant for a Section 3B1.1 increase. Rather, in some cases it may be enough that the defendant “orchestrated” or simply “coordinated” the activities of others.
United States v. Vargas, 16 F.3d 155, 160 (7th Cir.1994).
Based on our review of the record, we conclude that there was insufficient evidence to support the finding that Parmelee played a supervisory or managerial role. As the pilot, Parmelee certainly was an important player in the smuggling ring, but we cannot find evidence that shows he controlled or coordinated any of his co-defendants’ activities. The government points to Parmelee’s receipt of money from Sobiecki for his services, his purchase of a beeper to inform Sobiecki of flight departures and arrivals, and his upkeep and rental of the plane. These activities, however, may be merely inherent in Parmelee’s role as pilot and do not necessarily indicate that Parmelee managed or supervised others. While it could be said that Parmelee managed the illegal aliens he flew across the border, such conduct does not warrant a section 3Bl.l(b) enhancement. See United States v. Mejia-Orosco, 867 F.2d 216, 220 (5th Cir.) (“[F]or the purpose of § 3B1.1, the aliens smuggled, transported, or harbored are not considered participants unless they actively assisted in the smuggling, transporting or harboring of others.”) (citing Commentary to U.S.S.G. § 2L1.1, which concerns the smuggling, transporting, or harboring of illegal aliens), cert. denied, 492 U.S. 924, 109 S.Ct. 3257, 106 L.Ed.2d 602 (1989). Given the record before us, the district court erred in finding that Parmelee was a manager or supervisor of the illegal alien smuggling ring. See Vargas, 16 F.3d at 160.
III.
In conclusion, we affirm the convictions and sentences of Sobiecki, Brozek-Lukaszuk, Lukaszuk, and Sandrzyk. The case is remanded for resentencing of Parmelee.
AFFIRMED IN PART AND REMANDED IN PART.