OPINION OF THE COURT

Defendants West Indies Transport, Inc., WIT Equipment Co., and W. James Oelsner appeal their convictions and sentences for visa fraud, environmental crimes, conspiracy, and racketeering. The district court had jurisdiction under 48 U.S.C. § 16121 and 18 *584U.S.C. §§ 3231 and 3241.2 We have jurisdiction under 28 U.S.C. § 1291.3 We will affirm.4

I. FACTS AND PROCEDURAL HISTORY

West Indies Transport, Inc. and WIT Equipment Co. (collectively "West Indies Transport") operated several businesses in Krum Bay, St. Thomas, including a dry dock, ship repair facility, and barge towing company. West Indies Transport's chief operating officer was W. James Oelsner. In 1987, West Indies Transport obtained permits to use five barges as fixed docks for its other vessels. In 1989, Hurricane Hugo seriously damaged some of these barges, shifting them from their permitted positions. West Indies Transport did not attempt to repair, reposition, or salvage these barges after the storm. Instead, it used these barges as docks, repair facilities, and housing for employees in their new unauthorized locations. In the process, West Indies Transport attached the barges permanently to shore, constructed walkways and ramps between the barges for use by vehicles and employees, and wired them for electricity.

To staff its facilities, West Indies Transport hired an overseas agent to recruit Filipino workers. The Filipino workers were instructed to apply for D-l visas intended for non-immigrant foreign maritime crewmen, not the H-2 visas required by law. The "West Indies Transport crewmen" never put to sea. Instead, West Indies Transport housed them in a converted shipping container *585on a barge and used them as dock workers. The Filipino workers were paid approximately $400 per month for a 56-hour work week. By using underpaid illegal foreign employees, West Indies Transport was able to reduce significantly its expenses for wages and wage taxes.

In the course of its repair operations, West Indies Transport discharged several different pollutants into the navigable waters of the United States. Witconcrete II, a ferro-concrete barge, was heavily damaged in Hurricane Hugo. The stern was partially severed from the remainder of the barge, attached only by metal reinforcing bars, known as rebar. West Indies Transport did not attempt to repair, break up, or salvage the damaged stern. Instead, it cut the rebar by which the stern was attached and dumped the stern into the bay. Later, when West Indies Transport decided to move the barge, it cut additional protruding pieces of rebar from the structure and dumped them in the water. West Indies Transport also sand-blasted the hull of a vessel moored in its facility, causing paint chips and sand to fall into Krum Bay near the main water intake for the St. Thomas desalinization plant. The toilet system on the Witrollon, the barge on which illegal Filipino workers were housed, discharged raw sewage directly into the bay. West Indies Transport also collected steel scrap from its repair operations and dumped it twelve miles out at sea undercover of darkness. West Indies Transport never obtained a permit for any of these pollution discharges.

Defendants were charged in a twenty-one count indictment for visa fraud, environmental crimes, conspiracy, and racketeering. Five counts were dismissed on motion of the government. A jury found defendants guilty on the remaining sixteen counts. Defendants moved for post-verdict judgment of acquittal, which the district court denied. This appeal followed.

II. VISA FRAUD

A.

Defendants were convicted of aiding and abetting visa fraud in *586violation of 18 U.S.C. § 2 and 18 U.S.C. § 1546.5 At trial, the district court instructed the jury that defendants' representations to U.S. immigration and State Department officials verifying that Filipino workers hired by West Indies Transport would be working as crewmen aboard foreign flagged vessels were material as a matter of law. These instructions were consistent with our decision in United States v. Greber, 760 F.2d 68 (3d Cir.), cert. denied, 474 U.S. 988 (1985), which held that when a defendant is tried for perjury the issue of materiality is decided by the court.

Between verdict and sentencing, the United States Supreme Court held that on a perjury charge under 18 U.S.C. § 1001, materiality must be submitted to the jury. United States v. Gaudin, 515 U.S. 506 (1995). "The Constitution gives a criminal defendant the right to have a jury determine, beyond a reasonable doubt, his guilt of every element of the crime with which he is charged. The trial court's refusal to allow the jury to pass on the materiality of Gaudin's false statements infringed that right." Id. at 2320.

The rule announced in Gaudin applies retroactively to this direct appeal. Johnson v. United States, _ U.S. _, 117 S. Ct. 1544, 1549 (1997) (Gaudin applies retroactively on direct review; citing Griffith v. Kentucky, 479 U.S. 314,328 (1987)). Defendants contend that Gaudin requires a new trial.

Defendants submitted to the district court proposed jury instructions which took the issue of materiality away from the jury, but now object to those same instructions. For this reason, the government asks us to treat the district court's instructions as non-reviewable invited error, under United States v. Console, 13 F.3d *587641 (3d Cir. 1993), cert. denied, 513 U.S. 812 (1994) and Herman v. Hess Oil Virgin Islands Corp., 524 F.2d 767 (3d Cir. 1975). We decline to do so. Where a defendant submits proposed jury instructions in reliance on current law, and on direct appeal that law is declared constitutionally infirm, we will not apply the invited error doctrine. Instead, we will review for plain error under Fed. R. Crim. P. 52. See Johnson, 117 S. Ct. at 1548-49 (reviewing Gaudin error under plain error standard where defendant, relying on current law later declared unconstitutional, insisted at trial that materiality was an issue for the court, not jury, to decide). Under Rule 52, "before an appellate court can correct an error not raised at trial, there must be (1) error, (2) that is plain, and (3) that affects substantial rights. If all three conditions are met, an appellate court may then exercise its discretion to notice a forfeited error, but only if (4) the error seriously affects the fairness, integrity or public reputation of the judicial proceedings." Johnson, 117 S. Ct. at 1549 (internal quotations and brackets omitted; citing United States v. Olano, 507 U.S. 725, 732 (1993)). As the Supreme Court explained in Johnson, "in a case such as this — where the law at the time of trial was settled and clearly contrary to the law at the time of appeal — it is enough that an error be 'plain' at the time of appellate consideration." Id. See also United States v. Retos, 25 F.3d 1220 (3d Cir. 1994)(question is not whether error was plain at time of trial, but whether it is plain based on current law at time of direct appeal).

Failure to submit the issue of materiality to the jury was error. Gaudin, 115 S. Ct. at 2320; Johnson, 117 S. Ct. at 1549. That Gaudin involved perjury under 18 U.S.C. § 1001 rather than 18 U.S.C. § 1546, the relevant statute here, is not significant given the identical character of the materiality element in both perjury statutes. See Johnson, 117 S. Ct. 1544 (1997) (applying Gaudin to case involving perjury under 18 U.S.C. § 1623); United States v. DiRico, 78 F.3d 732 (1st Cir. 1996) (applying Gaudin to perjury under 26 U.S.C. § 7206(1)).

A "plain" error is an error which is "clear" or "obvious." Johnson, 117 S. Ct. at 1549; Olano, 507 U.S. at 734. Failure to send the issue of materiality to the jury is, in light of Gaudin, obvious or clear and therefore "plain" error. Johnson, 117 S. Ct. at 1549.

*588To satisfy the "substantial rights" prong of the plain error test, defendants usually must show that the error was "prejudicial" — "It must have affected the outcome of the District court proceedings." Olano, 507 U.S. at 734; United States v. Turcks, 41 F.3d 893 (3d Cir.) (same), cert. denied, 514 U.S. 1074 (1994).6 Defendants bear this burden of proof. Id. Defendants here have not brought to our attention any facts suggesting that a jury might have reached a conclusion different from the district court on materiality. Defendants presented no evidence at trial that their statements were not material. More importantly, the government introduced substantial evidence proving the defendants' representations were material. Indeed, had immigration officials known the true facts behind the Filipino workers' applications for visas — defendants' intention to employ as dock workers illegally underpaid foreign workers housed permanently on derelict barges — the visas never would have been granted. For these reasons, defendants have not met their burden of proving that the failure to submit the issue of materiality to the jury affected the outcome of the trial. See United States v. Kramer, 73 F.3d 1067 (11th Cir.) (Gandin error not reversible plain error; defendant failed to show that error affected outcome of trial), cert. denied, 117 S. Ct. 516(1996); United States v. Ross, 77 F.3d 1525 (7th Cir. 1996)(Gaudin error not reversible plain error; issue of materiality not seriously disputed at trial).

"When the first three parts of Olano are satisfied, an appellate court must then determine whether the forfeited error seriously affects the fairness, integrity, or public reputation of judicial proceedings before it may exercise its discretion to correct the error." Johnson, 117 S. Ct. at 1550(internal quotations and brackets omitted). Whether or not their substantial rights were affected, *589defendants have not satisfied the fourth prong of the Olano test. In Johnson, a case involving similar facts, the Supreme Court observed that the evidence of materiality was "overwhelming," materiality was "essentially uncontroverted at trial," and the defendant had presented "no plausible argument" that her false statements were "somehow not material." Id. The Supreme Court concluded: "On this record there is no basis for concluding that the error seriously affected the fairness, integrity or public reputation of the judicial proceedings. Indeed, it would be the reversal of a conviction such as this which would have that effect. . . . No miscarriage of justice will result here if we do not notice the error, and we decline to do so." Id. (internal quotations omitted).

In the same manner, the evidence at trial that West Indies Transport's representations were material was overwhelming and uncontroverted. On appeal, defendants have not presented a plausible argument that their statements were not material. The failure to submit materiality to the jury did not seriously affect the fairness, integrity, or public reputation of the judicial proceedings. For these reasons, we will affirm the convictions on visa fraud.

B.

Defendants contend their convictions for aiding and abetting visa fraud must be reversed because the district court did not instruct the jury that it must find "knowing subscription" or "knowing presentation" of false material. Not only did defendants fail to request such an instruction, their proposed instruction was remarkably similar to that actually delivered by the district court.7 "Thus, if there was any error at all, it was 'invited error' and cannot now be a basis for reversal." United States v. Console, 13 F.3d 641, 661 (3d Cir. 1993) (quoting Herman v. Hess Oil Virgin Islands Corp., 524 F.2d 767, 772 (3d Cir. 1975)), cert. denied, 513 U.S. 812 (1994).

C.

Defendants contend as a matter of law they could not be *590convicted of aiding and abetting visa fraud because the government conceded that immigrant workers who presented false information to the INS at West Indies Transport's instigation lacked criminal intent. We review de novo where the question is one of statutory interpretation. United States v. Schneider, 14 F.3d 876 (3d Cir. 1994).

The aiding and abetting statute provides, inter alia, that a defendant is liable if he willfully causes an act to be done by another which would be illegal if he did it himself.18 U.S.C. § 2(b). For this reason, whether the immigrant workers lacked criminal intent is irrelevant so long as West Indies Transport intentionally caused them to submit false information. As the Court of Appeals for the Eleventh Circuit explained, "it is well established that § 2(b) was designed to impose criminal liability on one who causes an intermediary to commit a criminal act, even though the intermediary who performed the act has no criminal intent and hence is innocent of the substantive crime charged." United States v. Tobon-Builes, 706 F.2d 1092, 1099 (11th Cir.), reh'g denied, 716 F.2d 914 (1983). See also Springs v. First Nat. Bank of Cut Bank, 835 F.2d 1293 (9th Cir. 1988)("A person who causes the commission of an offense is punishable as a principal even though the person who commits the wrongful act violates no criminal statute because of lack of criminal intent or capacity.").

In United States v. Catena, 500 F.2d 1319 (3d Cir.), cert. denied, 419 U.S. 1047 (1974), a physician was convicted for presenting false Medicare claims to the United States. On appeal, the physician argued that his conviction must be overturned because he did not present the claims to the United States in person. Rather, he submitted the false claims to two insurance companies, which forwarded them to the United States government. We affirmed his conviction, observing that under "§ 2(b) a person may be convicted of causing a false claim to be presented to the United States even though he uses an innocent intermediary (in this case the insurance carriers) to actually pass on the claims to the United States." Id. at 1323.

The Court of Appeals for the Ninth Circuit reached the same conclusion in United States v. Causey, 835 F.2d 1289(9th Cir. 1987). In *591Causey, a tax protester was convicted for aiding and abetting tax evasion by helping persons file false tax returns. On appeal, he argued the government failed to prove that the persons actually submitting the false returns possessed criminal intent. The court rejected this argument "because it is immaterial to Causey's conviction whether or not the taxpayers were shown to have intended to file, false tax returns." Id. at 1291. "Under § 2(b) . . . the government need not prove that someone other than the defendant was guilty of the substantive crime. A person who causes the commission of an offense is punishable as a principal even though the person who completes the wrongful act violates no criminal statute because of lack of intent or capacity . . . . Whether the taxpayers had guilty knowledge in submitting the claims becomes irrelevant under § 2(b)." Id. at 1291.

West Indies Transport's arguments are indistinguishable from those rejected in Catena and Causey. When a defendant uses an innocent intermediary to present false claims or make false statements to the government, the criminal intent of the intermediary is not an element of the offense. 18 U.S.C. § 2(b). For this reason, the district court's charge was not erroneous.

III. ENVIRONMENTAL CRIMES

A.

Defendants were convicted of violating the Clean Water Act, 33 U.S.C. § 1251 et seq., by (1) severing a 250-ton concrete and rebar block from the stern of Witconcrete II, a ferrous concrete barge, and dumping it into Krum Bay, St. Thomas; (2) severing approximately one hundred pieces of rebar and attached concrete from the stern of Witconcrete II and dropping it into Krause Lagoon; and (3) conducting sandblasting operations on a floating barge that projected sand and paint chip residue into Krum Bay. The Clear Water Act generally prohibits discharging pollutants into the navigable waters of the United States without a permit. But it only regulates "discharges" of pollutants from a "point source." See 33 U.S.C. *592§§ 1311(a) and 1362(12).8 Defendants contend as a matter of law their conduct did not constitute discharge of a pollutant from a point source. We review questions of statutory interpretation de' novo. United States v. Schneider, 14 F.3d 876 (3d Cir. 1994).

Barges are “floating craft," expressly included within the definition of “point source." 33 U.S.C. 1362(14).9

“Discharges" include “any addition of any pollutant to navigable waters from any point source." Defendants concede that Krum Bay and Krause Lagoon are navigable waters of the United States. Rebar, concrete, sand and paint chips fall within the Clean Water Act's broad definition of “pollutant." 33 U.S.C. § 1362(6).10 Therefore, cutting off pieces of a ferro-concrete barge and dumping them in Krum Bay and Krause Lagoon, or conducting sandblasting on a floating craft and allowing the residue to fall into Krum Bay, constitutes making an addition of a pollutant to navigable waters of the United States from a point source. Defendants' conduct fell within the applicable statutory definitions.

Appellants' reliance on United States v. Plaza Health Labs., Inc., 3 F.3d 643 (2d Cir. 1993), cert. denied, 512 U.S. 1245 (1994), does not alter our conclusion. There, defendant removed containers loaded with blood vials from his office, transported them in his car, and carried them to the Hudson River, where he deposited them during low tide in a bulkhead separating his home from the river. *593The United States Court of Appeals for the Second Circuit refused to consider defendant a "point source." But Plaza offers no guidance here because it focused almost exclusively on the application of the Clean Water Act to human beings:

As the parties have presented the issue to us in their briefs and at oral argument, the question is 'whether a human being can be a point source.'

* * if

Human beings are not among the enumerated items that may be a 'point source' .... if every discharge involving humans were to be considered a 'discharge from a point source.' the statute's lengthy definition of 'point source' would have been unnecessary.

* * sfr

The Clean Water Act generally targets industrial and municipal sources of pollutants, as is evident from a perusal of its many sections .... The legislative history of the CWA . . . confirms the act's focus on industrial polluters.

* * *

We find no suggestion either in the act itself or in the history of its passage that congress intended the CWA to impose criminal liability on an individual for the myriad, random acts of human waste disposal, for example, a passerby who flings a candy wrapper into the Hudson River, or a urinating swimmer. Discussions during the passage of the 1972 amendments indicate that congress had bigger fish to fry.

Id. at 647 (citations omitted). Congress intended a broad definition of "point source:" "[t]he concept of a point source was designed to further this [regulatory] scheme by embracing the broadest possible definition of any identifiable conveyance from which pollutants might enter the waters of the United States." United States v. Earth *594Sciences, Inc., 599 F.2d 368, 373 (10th Cir. 1979). Plaza properly circumscribed the breadth of the "point source" definition that the rebar was actually part of the Witconcrete II and does not alter the analysis. Before and after the severance of the rebar, the Witconcrete II qualified as a "vessel or other floating craft" within the parameters of 33 U.S.C. § 1362(14). The deliberate amputation of a portion of the vessel did not destroy the Witconcrete II's suitability as a "point source." Cf. Hudson Riverkeeper Fund, Inc. v. Harbor at Hastings Assocs., 917 F. Supp. 251, 257 (S.D.N.Y. 1996) ("[i]t would seem unlikely that Building 15 would fit into this interpretation of point source as any discharge of material would not be deliberate or systematic"). We see no error here.

B.

Defendants were also convicted for discharging untreated sewage into Krum Bay from a barge used to house their workers, in violation of 33 U.S.C. §§ 1311(a) and 1319(c)(2)(A).11 Defendants correctly argue and the government concedes that "sewage from vessels" is regulated under 33 U.S.C. § 1322, not §§ 1311 and 1319.Thus, if defendants' barge falls within the statutory definition of "vessel," the conduct in question does not violate § 1311(a) and § 1319(c)(2)(A) and their convictions must be reversed. Defendants maintain their barge on which they housed Filipino workers is a vessel. We disagree.

33 U.S.C. § 1322(a)(1) defines "new vessel" and "existing vessel" to include "every description of watercraft or other artificial contrivance used, or capable of being used, as a means of transportation on water." This definition contrasts vessels with "other floating craft," a term which the Clear Water Act does not define, but which suggests by its terms and in the context of the statute an artificial water-borne contrivance that, in contrast to a vessel, is not used or capable of being used for transportation purposes. See 33 U.S.C. § 1362(12). At all relevant times, the barge in question was moored permanently to shore. It was used to house foreign *595workers, not as a means of transport. Nor could the barge have been used for transport. According to testimony at trial, defendants' barge was half submerged in the water of Krum Bay, with part of the hull resting on the bottom and with water visible below decks. The barge could not be moved from its mooring. There was sufficient evidence therefore for the trier of fact to conclude that the barge was not a vessel within the meaning of the Clear Water Act.

Though we are not aware of any authority interpreting the meaning of "vessel" under § 1322, our view is in accord with long-standing interpretation of the term "vessel" in other contexts. See Cope v. Valette Dry-Dock Co., 119 U.S. 625 (1887) (dry dock attached to shore by large chains, with no means of propulsion, and incapable of being used for navigation, not a vessel; "The fact that it floats on the water does not make it a ship or vessel."); Kathriner v. UNISEA, Inc., 975 F.2d 657 (9th Cir. 1992) ("[Floating structures are not classified as vessels in navigation if they are incapable of independent movement over water, are permanently moored to land, have no transportation function of any kind, and have no ability to navigate.").

C.

33 U.S.C. § 1319(c)(2)(A) establishes criminal penalties for anyone who "knowingly" violates 33 U.S.C. § 1311.Defendants contend the district court erred when it failed to instruct jurors on the definition of "knowingly," arguing that jurors might have been unaware that an accidental discharge of pollutants was insufficient to convict. Defendants did not raise this objection at trial, so we review for plain error.

Despite defendants' contention, the court instructed jurors on the meaning of the term "knowingly." It stated: "An act is done knowingly if done voluntarily and intentionally, and not because of mistake or accident or other innocent reason. The purpose of adding the word 'knowingly' is to insure that no one will be convicted for an act done because of mistake, accident, or other innocent reason." There was no error here.

D.

Defendants were convicted for violating the Rivers and Harbors Act, 33 U.S.C. § 403, which provides, in part:

*596it shall not be lawful to build or commence the building of any wharf, pier, dolphin, boom, weir, breakwater, bulkhead, jetty, or other structures in . . . any water of the United States, outside established harbor lines, or where no harbor lines have been established, except on plans recommended by the Chief of Engineers and authorized by the Secretary of the Army.

Defendants contend the district court should have dismissed this count because the government "did not prove that the Defendants had knowingly built a pier, wharf, or any other structure."

Under longstanding precedent, the prohibition on "build[ing] or commencing the building of any wharf, pier. . . or other structures" contained in § 403 contemplates "the purposeful creation of something formulated or designed, construction work in the conventional sense." United States v. Bigan, 274 F.2d 729, 732 (3d Cir. 1960).Thus, we have held that negligent creation of an obstruction to navigation does not violate § 403. See id. (negligently caused land slide resulting in blocked river channel not a violation of § 403).

At trial, the government presented evidence that defendants intentionally strung together numerous derelict barges to form a permanent dock for loading activities, repairs, and the housing of employees. West Indies Transport permanently attached these barges together and to land with rope and wire cable. The barges and shore were connected by walkways defendants constructed out of metal and wood. The resulting wharfs were wired for electricity and were substantial enough to support significant loading and repair operations, including the use of forklifts. This evidence provided sufficient basis that defendants purposefully built an unauthorized structure. This was not a case where an act of nature or negligence resulted in an obstruction to navigation. It was clear that defendants here intentionally built a large dock to conduct their business activities.12

*597E.

Defendants raise a second objection to their convictions under 33 U.S.C. § 403, the Rivers and Harbors Act. 33 U.S.C. § 403 sanctions the construction of structures in water of the United States only when those structures are built "outside established harbor lines, or where no harbor lines have been established." 33 U.S.C. § 403. The district court did not instruct the jury that it must find defendants built a structure outside harbor lines, or where no lines have been established. Although defendants now contend on appeal the jury instruction was fatally deficient, their proposed jury instruction made no mention of the "harbor lines" element. "Thus, if there was any error at all, it was 'invited error' and cannot now be a basis for reversal." United States v. Console, 13 F.3d 641, 661 (3d Cir. 1993)(quoting Herman v. Hess Oil Virgin Islands Corp., 524 F.2d 767, 771 (3d Cir. 1975)).

If not invited error, we would review for plain error because defendants did not object at trial. A plain error must be "prejudicial" — "It must have affected the outcome of the district court proceedings." Olano, 507 U.S. at 734; United States v. Turcks, 41 F.3d 893 (3d Cir. 1994) (same).Defendants bear this burden of proof. Id.

Defendants have not brought to our attention any evidence suggesting that the district court's instruction affected the outcome of the trial. West Indies Transport has not argued, at trial or on appeal, that its docks were in fact constructed within established harbor lines, or where no lines have been established. On the *598contrary, defendants appear to concede this issue. Nor do defendants contend that a reasonable jury might have acquitted them on this charge had it been instructed on the harbor lines requirement. We see no indication that the district court's jury instruction had any impact on the outcome of the trial. For these reasons and because the district court followed the defendants' proposed instruction, the court's instruction did not seriously affect the fairness, integrity, or public reputation of the judicial proceedings. Therefore we see no plain error.

IV. ALLEGED PREJUDICIAL TESTIMONY

Randolph Allen, a local labor official, testified for the government regarding the costs defendants would have incurred had they employed workers through legal means. Defendants objected to his testimony on the ground that it was unduly prejudicial and irrelevant. The district court allowed Allen's testimony as probative of defendants' motive and intent to commit visa fraud.

After the conclusion of Allen's testimony defendants asked for a mistrial, citing possible prejudice among union workers on the jury against someone who employed alien labor. Defendants also asked the court to question the jury for possible prejudice. Denying the motion for mistrial, the Court noted that defendants failed to raise this question with potential jurors during pre-trial voir dire. Nevertheless, the district court halted the trial and asked the jurors whether any of them had "such strong feelings for or against alien workers" that they would not be able "to decide this case fairly and impartially." No juror responded affirmatively.

We review denial of mistrial for abuse of discretion. United States v. Wright-Barker, 784 F.2d 161, 175 (3d Cir.1986). Allen's testimony was relevant to and probative on the intent element of the charged visa fraud counts because it tended to establish the defendants' motive. We see no sign of undue prejudice. Though the defendants did not raise this issue during voir dire, the district court carefully questioned the jury to ensure there was no prejudice that might affect the jury's impartiality. We see no abuse of discretion here.

*599V. ENTRAPMENT BY ESTOPPEL

Defendants contend they were denied a fair trial when the district court prevented them from presenting evidence relevant to, and failed to instruct the jury on, two "entrapment by estoppel" defenses.

A.

The affirmative defense of entrapment by estoppel has its roots in two Supreme Court decisions, Raley v. State of Ohio, 360 U.S. 423 (1959) and Cox v. State of Louisiana, 379 U.S. 559 (1965), reh'g denied, 380 U.S. 926 (1965), finding violations of due process. In Raley, defendants refused to answer questions of the Ohio Un-American Activities Commission after a state official erroneously informed them that they were protected under the state constitution's privilege against self-incrimination. The defendants were subsequently held in contempt. The Supreme Court reversed, holding that the state may not "convict[ ] a citizen for exercising a privilege which the state clearly had told him was available to him," for to do so "would be to sanction the most indefensible sort of entrapment." Id. at 438. The Court applied the doctrine again in Cox, where it reversed state law convictions for picketing because a state official had granted defendants permission to picket.

We have applied the entrapment by estoppel defense in only one prior decision, United States v. Pennsylvania Industrial Chemical Corp., 461 F.2d 468 (3d Cir. 1972), modified and remanded, 411 U.S. 655 (1973). In Pennsylvania Industrial, the defendant was charged with discharging pollution into the Monongahela River, in violation of the Rivers and Harbors Act, 33 U.S.C. § 407. At trial, the defendant sought to present evidence that its allegedly criminal acts had been authorized by Army regulations and the federal government's long-term interpretation of the statute. The district court prohibited the defendant from introducing the evidence and refused to instruct a jury that the defendant should be acquitted if his actions resulted from affirmative government representations that its acts were lawful.

Citing due process grounds, we reversed on appeal. "The concept of fair play is implicit in our basic notions of what is meant by due process of law In this regard, an individual or corporation *600should not be held criminally responsible for activities which could not reasonably have been anticipated to be illegal based on 70 years of consistent government interpretation and subsequent behavior." Id. at 479. Because the defendant had not been allowed to present the evidence nor had the jury been instructed on the entrapment by estoppel defense, we granted a new trial. Id.

The Supreme Court agreed with our statement of the law, holding "it was error for the District Court to refuse to permit PICCO to present evidence in support of its claim that it had been affirmatively misled into believing that the discharges in question were not a violation of the statute." United States v. Pennsylvania Indus. Chem. Corp., 411 U.S. 655, 775 (1973). The Court also held that the defense applied only where there is reliance in fact and that reliance was reasonable under the circumstances. Id.

Since Pennsylvania Chemical was decided, other courts of appeals, citing the due process clause, have applied the entrapment by estoppel defense, although employing slightly different tests. See, e.g., United States v. Rector, 111 F.3d 503, 506-07 (7th Cir. 1997) (entrapment by estoppel defense applies where "the one misleading the defendant bean official of the state; that he actively mislead the defendant; and that the defendant's reliance be actual and reasonable in light of the identity of the agent, the point of law represented, and the substance of the misrepresentation"; additionally, defendant's reliance must be in good faith); United States v. Aquino-Chacon, 109 F.3d 936, 938 (4th Cir. 1997) ("A criminal defendant may assert an entrapment-by-estoppel defense when the government affirmatively assures him that certain conduct is lawful, the defendant thereafter engages in the conduct in reasonable reliance on those assurances, and a criminal prosecution based upon the conduct ensues."); United States v. Trevino-Martinez, 86 F.3d 65, 69 (5th Cir. 1996) ("criminal defendant may be entitled to raise a defense of entrapment by estoppel only when a government official or agent actively assures a defendant that certain conduct is legal and the defendant reasonably relies on that advice and continues or initiates the conduct") (internal quotations omitted), cert. denied, 117 S. Ct. 1109 (1997); United States v. Brebner, 951 F.2d 1017, 1024 (9th Cir. 1991) ("The entrapment by estoppel defense applies when an authorized government official tells the defendant *601that certain conduct is legal and the defendant believes the official."); United States v. Smith, 940 F.2d 710, 714 (1st Cir. 1991) ("Entrapment by estoppel has been held to apply when an official assures a defendant that certain conduct is legal, and the defendant reasonably relies on that advice and continues or initiates the conduct."). These courts agree that reasonable reliance means a defendant must establish that "a person truly desirous of obeying the law would have accepted the information as true, and would not have been put on notice to make further inquiries." Trevino-Martinez, 86 F.3d at 69; Brebner, 951 F.2d at 1024.

We hold the entrapment by estoppel defense applies where the defendant establishes by a preponderance of the evidence that (1) a government official (2) told the defendant that certain criminal conduct was legal, (3) the defendant actually relied on the government official's statements, (4)and the defendant's reliance was in good faith and reasonable in light of the identity of the government official, the point of law represented, and the substance of the official's statement.13

B.

At trial, defendants sought to raise two entrapment by estoppel defenses. First, they wished to present testimony from certain West Indies Transport employees and INS agents. Defendants claimed the testimony would show that they had fully informed INS that they wanted to employ foreign nationals admitted to the United States on D-l crewman visas as dockworkers at their facility, and that INS had approved of the scheme.

The district court held that "[t]o establish entitlement to the defense of entrapment by estoppel. . . defendants must show (1) that after fully informing government officials with actual or apparent authority of the underlying facts, they were advised that the alleged conduct was legal; (2) that they relied on that advice; and (3) that reliance was reasonable, and given that reliance, prosecution would be unfair." After holding an in camera hearing *602to review the proffered evidence, the district court concluded defendants' evidence demonstrated only that INS extended the Filipino workers' visas based on representations by West Indies Transport that the workers would soon be employed as crewmen on ocean-going vessels. The evidence also showed that defendants never informed any United States officials at any time that the workers would be living on United States soil and that they would work as dock workers on derelict barges and on land. For these reasons, the district court held that defendants had offered no evidence tending' to prove that the INS was informed of and approved defendants' scheme to employ alien workers admitted to the United States on D-l foreign crewman visas as permanent dockhands.14

As the district court correctly observed, defendants pointed to no evidence tending to prove that the INS was informed of and approved defendants' scheme to employ alien workers admitted to the United States on D-l foreign crewman visas as permanent dockhands. Defendants have failed to establish a necessary element of the defense —that government officials told them that their conduct was lawful. For that reason, the district court correctly excluded the proffered evidence.

C.

The second entrapment by estoppel claim arises out of defendants' convictions under the Ocean Dumping Act, 33 U.S.C. §§ 1411(a) and 1415(b)(1). Defendants were convicted for dumping large quantities of scrap metal and other debris into the ocean under cover of darkness, without a permit. Coast Guard regulations implementing the Act to Prevent Pollution from Ships, 33 U.S.C. § 1901-11, require all vessels 26 feet and longer to carry placards that warn vessel owners and crews that certain discharges *603of ship-generated garbage and sewage are prohibited at various distances from shore. At trial, defendants argued that the placards led them to believe that they could legally dump scrap metal into the ocean so long as the dump site was at least twelve miles offshore. The district court allowed them to present their evidence, but did not instruct the jury on the entrapment by estoppel defense.15

Defendants contend their reasonable reliance on these signs absolved them of criminal responsibility under the doctrine of entrapment by estoppel. In the alternative, they contend the failure to instruct on the entrapment by estoppel defense violated their due process rights.

Defendants have included in the appellate record examples of placards similar to those on which they claimed they relied when they believed their dumping operations were legal. One example, apparently produced by the Coast Guard, states that certain types of "non-plastic trash" may be discharged at sea if the vessel is at least twelve nautical miles from shore. The placard makes no representations about scrap metal. It also states, in clear type: "The information contained on this device is provided as a guidance to many, but not all, of the discharge restrictions which apply under United States law. There are a number of discharge restrictions which are not set out in this device."

Defendants were not entitled to an entrapment by estoppel instruction on the strength of this placard. The placard makes no representations about the legality of defendants' conduct — dumping scrap metal off-shore. The placard expressly states that other discharge restrictions may apply, putting defendants on notice to make further inquiries to determine whether their conduct was legal. Nor would it have been reasonable for defendants to rely on this placard as an authorization to dump scrap metal off-shore. Large quantities of scrap metal generated by a ship repair facility do not fall within the plain meaning of "non-plastic trash." Moreover, there is substantial evidence that the defendants' claimed reliance was neither actual nor in good faith. Had West *604Indies Transport truly believed that its ocean dumping was legal, it would not have consistently dumped scrap metal under cover of darkness.

The second example placard submitted by the defendants was manufactured by "Seachoice Products," apparently a private ship chandler. The entrapment by estoppel defense applies only to representations made by government officials, not to asserted reliance on legal advice or representations from non-governmental actors. Representations made by Seachoice Products or any other private entity as to the legality of ocean dumping cannot remotely establish a valid entrapment by estoppel defense. Even if the placard contained representations by the government, it would not warrant the defense, for The placard contains no statements regarding the legality of dumping scrap metal at sea.

No government official ever told West Indies Transport its dumping operations were legal. Nor does it appear from the record that West Indies Transport ever asked the government for advice on this matter. Defendants we reexperienced operators in the maritime industry. It was clearly unreasonable for defendants to rely on a placard that appears on all types of vessels, including recreational boats, as legal justification for industrial ocean dumping.

VI. RACKETEERING AND CONSPIRACY

Defendants assert if we reverse their convictions on the immigration and environmental crimes counts, we must reverse their convictions for conspiracy and racketeering. Because we affirm defendants' convictions for visa fraud and environmental violations, we will affirm these convictions as well.

Defendants also contend their racketeering convictions must be overturned because none of the predicate acts was a local Virgin Islands offense. The Virgin Islands RICO statute, 14 V.I.C. § 604, requires only that at least one predicate act charged as a federal offense also "constitute" a felony under Virgin Islands law. 14 V.I.C. § 604(j)(2)(C). But, the one requisite local predicate act need not be charged as a local felony, but merely "constitute" one. Here, defendants were charged with and convicted for conspiracy *605under federal law. Conspiracy also constitutes a felony under the Virgin Islands Code. See 14 V.I.C. § 551. We see no error here.

VII. SENTENCING

Defendants raise several sentencing objections.

A.

First, defendants contend that the $500,000 fine imposed by the district court under the Corrupt Organizations Act, 14 V.I.C. § 605, was excessive. We review the district court's determination of the amount of a fine for clear error. United States v. Seale, 20 F.3d 1279, 1284 (3d Cir. 1994).The defendants concede the fine falls within the range permitted by law. Nor have defendants pointed to any legal or factual error underlying the assessment of a fine in this amount. We see no error here.

B.

Defendants also contend the six level enhancement for ongoing, continuous, or repetitive discharge of a pollutant assessed by the district court under U.S.S.G. § 2Q1.3(b)(l)(A) should be reduced because the raw human sewage defendants dumped into navigable waters was "fully biodegradable." Our review is plenary. United States v. James, 78 F.3d 851 (3d Cir.), cert. denied, 117 S. Ct. 128(1996).

Defendants cite no authority for the proposition that untreated human sewage or fully biodegradable pollution warrants different treatment under the guidelines than other pollutants, nor any reasons why we should adopt such a rule. Because untreated human sewage falls within the clear meaning of "pollutant" under § 2Q1.3(b)(l)(A), we will affirm the enhancement.

C.

The district court ordered defendants to pay restitution to offset the costs of cleaning up their environmental damage. Restitution is authorized only for violations of Title 18 and some Title 49 provisions. See 18 U.S.C. § 3663. Defendants contend the trial court erred by ordering restitution for title 33 offenses. Our review is plenary. United States v. Maurello, 76 F.3d 1304 (3d Cir. 1996).

*606Defendants' argument is meritless. Each Title 33 offense also charged a violation of 18 U.S.C. § 2. Restitution is authorized for violation of 18 U.S.C. § 2.

D.

Defendants also imply, though they do not clearly argue, that the amount of restitution was excessive given the amount of environmental damage caused by their criminal conduct. We review the appropriateness of a particular restitution award for abuse of discretion. United States v. Maurello, 76 F.3d 1304 (3d Cir. 1996). The district court calculated restitution based on Coast Guard estimates of the costs required to clean defendants' environmental damage. The district court also ordered that if the ultimate cost of the clean-up is lower than the Coast Guard estimate, any amount over the actual costs shall be returned to the defendants. This sensible approach appears appropriate and does not constitute an abuse of discretion.

VIII.

For these reasons, the judgments of conviction and sentence will be affirmed.

concurring and dissenting

I agree with most of the government's argument. Regarding the Clean Water Act charges, I cannot. It is true, of course, that "wrecked or discarded equipment" is a listed "pollutant" under 33 U.S.C. § 1362(6). Webster's, however, defines "equipment" as "the set of articles or physical resources serving to equip a person or thing ... ." Webster's Ninth New Collegiate Dictionary 421 (1988). I do not think these parts of the Witconcrete II — which in better times were an integral part of its hull — can properly bethought of as part of the ship's equipment. They were not mere appurtenances, like a loading crane or radar antenna dumped over the side. I believe they were a part of the ship itself.

That aside, however, there still was no "point source" within the meaning of the Act. The Clean Water Act prohibits discharging pollutants into the navigable waters of the United States without a permit; however, it regulates discharges only from "point sources." *607See 33 U.S.C. §§ 1311(a), 1362(12). Appellants argue that they cannot be criminally culpable because as a matter of law the discharges above did not emanate from point sources. Under 33 U.S.C. § 1362(14), "point source" is defined as follows:

"any discernable, confined and discrete conveyance, including but not limited to any pipe, ditch, channel, tunnel, conduit, well, discrete fissure, container, rolling stock, concentrated animal feeding operation, or vessel or other floating craft, from which pollutants are or may be discharged."

Appellants rely on United States v. Plaza Health Laboratories, Inc., 3 F.3d 643 (2d Cir. 1993). There, the defendant owned a medical testing laboratory. Fie loaded vials of blood into his car and dumped them into the Hudson River. He was indicted under the Clean Water Act. The Court of Appeals, however, ruled that defendant, as an individual dumping waste directly into a body of water, was not a "point source" within the meaning of the Act and reversed his conviction.

After first observing that "this statute was never designed to address the random, individual polluter," id. at 646, the Plaza Health Court looked to the language and structure of the Act and concluded that the listed items in the statute "evoke[d] images of physical structures and instrumentalities that systematically act as a means of conveying pollutants from an industrial source to navigable waterways." Id. It then reasoned that an interpretation of the statutory text that brought every act of "discharge involving humans" within the ambit of the term "pointsource" would make that text redundant, id. at 646-47, and thus contrary to long-established principles of statutory construction.

The Court next turned to the legislative history of the Act and found no congressional intent "to impose criminal liability on an individual for the myriad, random acts of human waste disposal, for example, a passerby who flings a candy wrapper into the Hudson River, or a urinating swimmer." Id. at 647. Moreover, it found no such expansive interpretation of .the Act in the criminal case law, although it noted that courts dealing with this issue in the context of civil penalties have construed the statute more broadly. *608Id. at 648. Finally, the Plaza Health Court found no evidence of any administrative interpretation by the EPA that would bring the defendant's conduct within the statute. Id. at 649.

Based on these observations, the Court then concluded "that the term 'point source' as applied to a human beings at best ambiguous." Id. Applying the rule of lenity, it held that the prosecution must be dismissed. Id.

The government relies, however, on United States v. M.C.C., Inc., 772 F.2d 1501 (11th Cir. 1985), in which a contractor building a bridge in the Florida Keys departed from the approved plan and brought construction assemblies in by barge. Unfortunately, the tug's screws stirred up sand from the bottom of a shallow body of water and redeposited it on nearby grass beds, damaging them. The M.C.C. court held that material already in the water, when redeposited, could constitute a discharge under the Clean Water Act. Id. at 1506. Without dwelling on the issue, the court concluded that because "vessel" was included in the statutory list of possible point sources, the tug's screws were a point source under the facts of that case. Id. at 1505-06.

It is evident to me that when Congress used the term "point source," it had in mind something other than the propulsion system of every ship that happens to operate in navigable waters. I would thus conclude that a point source is the conduit, conveyance or vector by which pollutants are discharged, and not the screws of a vessel stirring up old pollutants without discharging anything at all.

I would not follow M.C.C. for another reason: there, the government sought only civil penalties. Here, we are reviewing a felony conviction, and must apply different maxims of statutory construction. Remedial statutes are typically construed broadly to effectuate the legislative purpose behind them. Criminal statutes are construed more narrowly to give defendants fair warning of the conduct the legislature intended to penalize. I conclude that Plaza Health fits our case particularly well, and would adopt its holding.

I would also conclude that the error here was plain. In United States v. Olano, 507 U.S. 725, 113 S. Ct. 1770(1993), the Supreme Court clarified the standard that courts of appeals must employ when deciding whether a forfeited error warrants reversal under *609Fed. R. Crim. P. 52(b). First, of course, there must be an error that has not been knowingly and intentionally waived. Id. at 732-33, 113 S. Ct. at 1777. Second, the error must be plain; that is, clear or obvious under current law. Id. at 734, 113 S. Ct. 1777. Third, the plain error must have affected substantial rights, generally by affecting the outcome of the district court proceedings. Id. at 734, 113 S. Ct. at 1777-78.Finally, once this threshold has been crossed, the reviewing court must exercise its discretion, correcting the error if it "seriously affect[ed] the fairness, integrity or public reputation of judicial proceedings," Id. at 736, 113 S. Ct. at 1779 (quoting United States v. Atkinson, 297 U.S. 157, 160,56 S. Ct. 391, 392 (1936)), as when the error caused the conviction of an "actually innocent defendant." Id. at 736, 113 S. Ct. at 1779.

Turning to this case, the Clean Water Act proscribes only "the discharge of any pollutant," 33 U.S.C. § 1311(a), which in turn is defined as "any addition of any pollutant . . .from any point source . . . ." 33 U.S.C. § 1362(12). It is evident that the requirement that the discharge emanate from a point source is an essential element of the crime.

We have held recently that "[t]he omission of an essential element of an offense from the jury instructions usually will be obvious error, and therefore ordinarily satisfies the first and second requirements of Olano." United States v. Stansfield, 101 F.3d 909, 920 (3d Cir. 1996) (citation omitted); accord United States v. Zolicoffer, 869 F.2d 771,774 (3d Cir. 1989) ("the failure to prove one of the essential elements of a crime is the type of fundamental error which may be noticed by an appellate court notwithstanding the defendant's failure to raise it in the district court"). Thus, I conclude that to the extent appellants' Clean Water Act convictions rested on the erroneous conclusion that the discharges came from point sources, the error was "plain."1

*610I likewise have no difficulty concluding that the error involved appellants' substantial rights and seriously undermined the fairness, integrity and reputation of the judicial proceedings. If the discharges did not emanate from a point source, an issue to which I shall turn shortly, then appellants could not, as a matter of law, have been convicted of Clean Water Act violations, and are "actually innocent" of the offense. Such a conviction would be classic miscarriage of justice. Accordingly, to the extent there was error, we have the power to correct it and I would exercise our discretion to do so.

I believe that neither the discharge of the Witconcrete II's stern nor its protruding rebar qualifies as a point source within the meaning of the Clean Water Act. The severing of the stern was not a discharge from a vessel, as required by 33 U.S.C. § 1362(14). Rather, a part of the vessel itself was discharged. Appellants merely severed a wrecked, useless portion of the Witconcrete II to extricate a serviceable forward portion of it. This was a salvage operation, not a discharge of concrete and rebar through the instrumentality of the barge.

Likewise, the severed rebar was not discharged through the "conveyance" of the barge, see 33 U.S.C. § 1362(14), it was part of the barge itself. Put another way, I think these two discharges are closer to the intermittent, manual blood dumping of Plaza Health than they are to the industrial paradigm of the sewage treatment plant, oil refinery or steel mill that animates most Clean Water Act cases.2 I would accordingly reverse appellants' convictions at counts one and two.

I also disagree with the government's argument concerning the Rivers and Harbors Act. I rely again on the language of the statute, 33 U.S.C. § 403,.under which it is prohibited "to build or commence the building of any wharf, pier ... or other structures." In sum, these barges were placed in their current locations by the hurricane, not by WIT. At most, WIT wired them to the local utilities- and built some walkways to connect them. That may be *611the "use" of an existing structure, but it is not the "build[ing]" of a new one.

In more detail, appellants had a permit to moor four vessels in Krum Bay as docks. When Hurricane Hugo hit the Virgin Islands in 1989, it ran some of these vessels aground and otherwise shifted their positions from those specified in the permits. After the storm, appellants did not move these vessels back to their original positions, but used them where they sat. By November 1992, the permits had expired. In count three of the superseding indictment, the government charged appellants with misdemeanor violations of the Rivers and Harbors Act, 33 U.S.C. § 403, which proscribes creating piers and wharves without a permit. Appellants did not challenge the sufficiency of the evidence to support their convictions in the district court, so again the plain error standard applies.

Under longstanding precedent, prohibiting "build [ing] or commencing] the building of any wharf, pier . . .or other structures" contained in § 403 contemplates "the purposeful creation of something formulated or designed, construction work in the conventional sense." United States v. Bigan, 274 F.2d 729, 732 (3d Cir. 1960) (emphasis added). There, we held that a negligently caused earth slide resulting in an obstruction to a river channel was not a violation of § 403. Likewise, we have held that negligently sinking a vessel in a river channel did not violate the Act. See United States v. Ohio Barge Lines, Inc., 607 F.2d 624, 629 (3d Cir. 1979); accord United States v. Wilson, 235 F.2d 251, 253 (2d Cir. 1956) (a sunken barge may be an "obstruction," but is not a "structure" in violation of § 403).

Here, appellants had every right to moor vessels in Krum Bay, but the hurricane shifted them out of position. Appellants, however, never purposely put the vessels in their current positions and hence never built any structure in violation of the Act. Because, as I have discussed supra, the government utterly failed to adduce evidence supporting an essential element of the crime, I would deem the error plain and exercise our discretion to correct it under Fed. R. Crim. P. 52(b). Accordingly, I would reverse the convictions at count three.