Affirmed in part, reversed in part, and remanded for resentencing by published opinion. Judge WILKINSON wrote the opinion, in which Judge GREGORY and Judge STAMP joined.
OPINION
In this case, we must decide whether defendants are criminally hable for a scheme that raised the prices the Department of Defense (“DOD”) pays to transport its personnel’s belongings overseas. Defendants have admitted to orchestrating this scheme and have agreed to accept liability under the Sherman Act, 15 U.S.C. § 1 (2000), and the federal anti-fraud statute, 18 U.S.C. § 371 (2000), if we determine that their behavior is not immune from such liability under the Shipping Act, 46 U.S.C. app. §§ 1701-1719 (2000). We hold that the Shipping Act’s immunity provisions afford defendants no relief from liability for the antitrust violation and conspiracy to defraud they have admitted. We therefore affirm in part, reverse in part, and remand for resentencing.
I.
A.
When personnel of the DOD are posted to foreign countries, the International Through Government Bill of Lading program (“ITGBL”) covers their moving expenses. The DOD contracts with private companies to provide this service. Under the Military Traffic Management Command (“MTMC”), bids are solicited for “through rates” from U.S. freight forwarding companies. A through rate is a payment encompassing all the costs involved in a door-to-door move of DOD personnel’s household effects. Bidding for through rates occurs biannually and involves a two step process.
In the first step, or “initial filing,” the freight forwarders file a bid for a through rate associated with a particular route, or channel. The low bid that emerges is referred to as the “prime through rate.” MTMC publishes this bid and the next four lowest bids. The company that bids the prime is entitled to a set percentage of DOD freight business for the associated channel.
In the second step, other freight forwarders resubmit bids in light of the published prime. The remaining companies may match, or “me-too,” the prime for each channel, or they may bid a higher rate. When the channel at issue operates *506in a competitive market, a forwarder must typically me-too the prime to receive any DOD business. Forwarders that me-too the prime are also entitled to a set portion of DOD business for the cycle and channel for which they have bid.
Because through rates are unitary, they encompass many costs, all of which the U.S. forwarders become responsible for when the DOD accepts their bids. Some of these costs relate to moving services undertaken by other firms along the channel. Costs of this sort cover five general categories of service: the carriage of goods between inland U.S. cities and U.S. ports, services performed at U.S. ports, ocean transportation between U.S. and foreign ports, foreign port services, and carriage of goods between foreign ports and foreign inland points. U.S. freight forwarders must naturally consider these costs in setting their bids.
B.
Defendant Gosselin World Wide Moving N.V. (“Gosselin”), a Belgian corporation, and defendant The Pasha Group (“Pasha”), a U.S. corporation, operate in the channels between the United States and Germany. Both companies provide a package covering local German moving agent services, European port services, and ocean transport services in this market. Defendants thus deal with goods shipments between German points of origin (the households of DOD personnel abroad) and U.S. ports of destination. Gosselin and Pasha offer a “landed rate,” which is a fee that covers all the moving costs involved in the portion of the channels they service.
Defendants also act as the exclusive agents of the International Shippers’ Association (“ISA”), a conference of freight forwarders organized to negotiate collectively with shippers operating in the through transportation market. Many of the U.S. freight forwarders who place bids in the MTMC are also ISA members. In their capacity as ISA agents, Gosselin and Pasha negotiate service contracts with the Trans Atlantic American Flag Line Operators (“TAAFLO”), a group of U.S. ocean carriers. TAAFLO’s service contract with the ISA entitles all ISA members to ocean transportation with TAAFLO member-carriers at a predetermined rate.
In late 2001, initial filings for the summer bidding cycle of 2002 occurred. A U.S. freight forwarder (“FF1”) filed prime through rates with the MTMC for twenty-six of the channels between Germany and the U.S. FF1 did not use the landed rate offered by either defendant. Instead, by negotiating separately with each service provider at every step of the transportation chain, FF1 was able to undercut its competitors by three dollars per hundredweight in twelve of the twenty-six channels. In December 2001, DOD published FFl’s prime bid along with the next four lowest. The remaining forwarders then had until January 12, 2002 to file their second round bids.
Gosselin was evidently alarmed that FF1 had been able to low-bid for the twelve channels without using Gosselin’s landed rate. Later in December, Gosse-lin’s managing director sent an email to another landed rate provider, inviting the provider to collude with Gosselin to prevent the me-too rates for the twelve routes at issue from converging to the prime. Such convergence was likely, as we have noted, because of the competitiveness of the US-Germany through transportation market. The Gosselin managing director observed that by “not taking [FFl’s bid] into consideration we would increase the rate level with an average of [$3.63].” The director opined that “[t]his is the only thing that in my mind can happen.” In a reply email sent the same day, an execu*507tive at the competitor concurred, noting that “if we do not react and give [the] industry a clear message which rate to base the [me-too bids] on, then everyone will use the low rate and later expect us to reduce our rates so those carriers can work under their [me-too] rates.”
Shortly after this exchange, Gosselin’s managing director forwarded the emails to the president of Pasha. The Gosselin executive identified the twelve channels, which had “quite some money on the table,” and inquired “what rate levels would you be able to support if those [channels] would go to second level?” The director stressed that “it is important we [ ] move rather quickly.now.” Pasha later indicated its willingness to cooperate.
Defendants faced a difficult task in preventing the imminent me-too bids from converging to the prime. FF1 had already demonstrated that defendants’ landed rates could be undercut by contracting separately for each transportation segment along the twelve channels. Defendants therefore had to take preemptive action to prevent the remaining U.S. forwarders from following FFl’s lead. In early January 2002, the managing director of Gosse-lin agreed in writing to pay twelve of the largest German moving agents a specified fee. The German agents, for théir part, agreed not to handle business from freight forwarders in those channels unless the forwarders submitted me-too bids at the second lowest level (the “second low”) or above. Gosselin thereafter arranged a te-lefax to U.S. freight forwarders who were finalizing their second-step bids advising them of the German agents’ undertaking.
Not content with securing their share of the DOD business designated for the second-round bids, defendants set about eliminating FFl’s prime rate in the twelve channels at issue. First, they persuaded FF1 to cancel its'bid with the MTMC if the remaining freight forwarders would file second-step bids at or above the sec'ond-low level. Defendants then secured such an agreement from the remaining forwarders. The forwarders overwhelmingly honored this agreement, and those who strayed below the second-low level were persuaded to withdraw their competitive bids.
As a result of defendants’ scheme, a good deal of household goods shipments during the 2002 summer cycle in the twelve channels occurred at or above the second-low rate. The net financial effect of the conspiracy was to cause the DOD to pay substantially more than if FFl’s original prime rate had prevailed.
C.
The Department of Justice (“DOJ”) charged defendants by information with two counts. The first count alleged a con•spiracy to restrain trade in violation of the Sherman Act. 15 U.S.C. §. 1 (2000). The second count alleged a conspiracy to defraud the United States under 18 U.S.C. § 371 (2000).
Defendants agreed to conditional pleas. They stipulated to a statement of facts on the basis of which they would move the district court to dismiss both counts. Gosselin and Pasha agreed in their pleas to make only one argument in support of their motion to dismiss: that the conduct set forth1 in the statement of facts “is immune from prosecution under the [Shipping Act.]” If the district court found such immunity with respect to “both counts,” and this finding was affirmed on appeal, defendants would not enter a guilty plea. If the district court , denied the motion “as to either or both counts,” however, the defendant would plead guilty on the “remaining counts” subject to withdrawal if a higher court overturned the district court’s *508finding. The plea agreements also indicated that the parties would recommend to the district court specified sentences in the form of financial penalties depending on which count or counts survived the motion to dismiss.
Pursuant to the plea agreement, defendants filed a motion to dismiss on the basis of immunity under the Shipping Act, 46 U.S.C. app. §§ 1701-1719 (2000). The district court granted the motion with respect to the antitrust count, but denied it with respect to the conspiracy to defraud count. Following the arrangement set out in the plea agreements, Gosselin and Pasha pled guilty to the conspiracy to defraud count. Again pursuant to the pleas, the district court imposed on each defendant a criminal fine of $4.6 million. After the final sentencing order, the DOJ appealed the dismissal on immunity grounds of the antitrust count and defendants cross-appealed their convictions on the conspiracy to defraud count. We now address these appeals, beginning with the issue of immunity under the Shipping Act.
II.
Defendants’ collusion with each other and with other firms operating in the twelve transportation channels clearly violated the Sherman Act’s injunction on combinations “in restraint of trade.” 15 U.S.C. § 1 (2000). “It has been held too often to require elaboration [] that price fixing is contrary to the policy of competition underlying the Sherman Act....” United States v. McKesson & Robbins, Inc., 351 U.S. 305, 309, 76 S.Ct. 937, 100 L.Ed. 1209 (1956). Defendants’ scheme, which prevented second round bids from converging to the prime and even erased FFl’s first round prime bid, amounted to naked bid rigging. And “bid rigging agreement is price-fixing agreement of the simplest kind.” United States v. Portsmouth Paving Corp, 694 F.2d 312, 318 (4th Cir.1982) (quoting United States v. Bensinger Co., 430 F.2d 584, 589 (8th Cir. 1970)); see also United States v. W.F. Brinkley & Son Const. Co., Inc., 783 F.2d 1157, 1160 (4th Cir.1986). Criminal antitrust liability is therefore appropriate unless defendants enjoy immunity under another federal law.
The Supreme Court has consistently construed the reach of exemptions from antitrust laws narrowly, even when Congress confers these exemptions in terms. See, e.g., Union Labor Life Ins. Co. v. Pireno, 458 U.S. 119, 126, 102 S.Ct. 3002, 73 L.Ed.2d 647 (1982). This narrow construction of antitrust immunity is appropriate because the robust marketplace competition that antitrust laws protect is a “fundamental national economic policy.” Carnation Co. v. Pac. Westbound Conference, 383 U.S. 213, 218, 86 S.Ct. 781, 15 L.Ed.2d 709 (1966); see also Otter Tail Power Co. v. United States, 410 U.S. 366, 374, 93 S.Ct. 1022, 35 L.Ed.2d 359 (1973). This canon of construction has been employed by the Supreme Court to defeat antitrust exemptions claimed under provisions of the McCarran-Ferguson Act, see Group Life & Health Ins. Co. v. Royal Drug Co., 440 U.S. 205, 231-32, 99 S.Ct. 1067, 59 L.Ed.2d 261 (1979), the Miller-Tydings and McGuire Acts, see McKesson, 351 U.S. at 316, 76 S.Ct. 937, and the Agricultural Marketing Agreement Act, see United States v. Borden Co., 308 U.S. 188, 198-200, 60 S.Ct. 182, 84 L.Ed. 181 (1939).
Defendants here claim exemption from antitrust law under a federal maritime statute, the Shipping Act of 1984. 46 U.S.C. app. §§ 1701-1719 (2000). The Act modified an earlier law enacted in 1916. See 46 U.S.C.app. §§ 801-842 (1982). The earlier enactment grew out of the difficulties faced by the U.S. shipping industry in *509the early part of the last century. See generally Puerto Rico Ports Auth. v. FMC, 919 F.2d 799, 806-807 (1st Cir.1990); Plaquemines Port, Harbor and Terminal Dist. v. FMC, 838 F.2d 536, 542-43 (D.C.Cir.1988). To set Ü.S. shippers on an equal footing with foreign competitors, who operated outside of U.S. antitrust strictures, Congress granted them limited antitrust immunity. See 46 U.S.C.app. § 814 (1982).
This immunity, however, came with regulatory strings attached. See id. § 804. The regulatory requirements of the 1916 Act were designed to prevent the maritime transportation industry from monopolis-tically abusing its newly conferred grant of immunity. See Puerto Rico Ports, 919 F.2d at 807. Regulation under the 1916 Act thus preserved some anti-competitive prohibitions. See id.; A & E Pacific Const. Co. v. Saipan Stevedore Co., Inc., 888 F.2d 68, 71 (9th Cir.1989); Plaquemines, 838 F.2d at 542-43. Nonetheless, regulated firms did enjoy the real benefit of operating outside the full strictures of federal antitrust laws. Mindful of this benefit, the Supreme Court concluded that the traditional canon of narrow Construction, applicable to antitrust exemptions generally, applied with full force to the coverage provisions of the 1916 Act. See FMC v. Seatrain Lines, Inc., 411 U.S. 726, 732-33, 93 S.Ct. 1773, 36 L.Ed.2d 620 (1973); Carnation, 383 U.S. at 217-218, 86 S.Ct. 781.
The 1916 Act was supplemented by the Shipping Act of 1984, 46 U.S.C. app. §§ 1701-1719 (2000). Although the 1984 Act contained several new grants of antitrust immunity, see id. § 1706(a), nowhere in the 1984 Act did Congress indicate an intention to override the principle of narrow construction for antitrust exemptions that the Supreme Court had long applied to the 1916 Act. Moreover, this- interpretive maxim-has informed the construction of every other grant of antitrust immunity in federal legislation. We therefore see no reason to depart from ordinary practice in construing the 1984 Act.
III.
With the foregoing interpretive framework in mind, we turn to defendants’ particular contentions. The district court found antitrust imipunity for Gosselin and Pasha in three distinct statutory provisions of tbe Shipping Act. We address immunity under each statutory provision separately.1
A.
Defendants first claim immunity under 46 U.S.C. app. § 1706(a)(4) (2000), which exempts from antitrust liability “any agreement or activity concerning the foreign inland segment of through transportation that is part of transportation provided in a United States import or export trade.”
Defendants argue that this provision covers all aspects of their scheme to rig bids. The first step in this scheme, defendants emphasize, was the agreement with twelve large German local agents to handle no business from forwarders who filed bids below the second low level. This agreement, defendants claim, is covered by § 1706(a)(4) because the German agents *510provide only services between German ports and destinations in the interior — a “foreign inland segment.” Gosselin and Pasha had market leverage only in this segment; in the other segment they service, ocean transportation, they were constrained by their status as ISA agents and the strict terms of the TAAFLO service contract. Thus the success of the remainder of their scheme depended entirely on the continued viability of the arrangement defendants had reached with the local German firms. For this reason, defendants conclude, the scheme in its entirety should be covered by the immunity provision of § 1706(a)(4).
We do not believe that the statutory exemption extends as far as Gosselin and Pasha would have it. To begin with, the statutory language does not support defendants’ position. For an agreement or activity to “[concern] the foreign inland segment,” § 1706(a)(4) (emphasis added), as the statute requires, the parties undertaking the agreement or participating in the activity must have in mind some consequence for the foreign inland segment that they intend their behavior to have. Accord Hileman v. Pittsburgh & Lake Erie Props., Inc., 290 F.3d 516, 519 (3d Cir.2002) (“ ‘[Concerning’ ... is essentially a connecting term, the scope and meaning of which is defined in part by the terms it modifies.”); Commerford v. Thompson, 1 F. 417, 420 (C.C.D.Ky.1880) (observing that the “broadest sense” of the term “ ‘concerning’ ” is “ ‘pertaining to or relative to’ ”). Because defendants’ collusive effort was aimed at the entire through transportation market, rather than just the foreign inland segment, we do not think that they can claim exemption from antitrust liability under § 1706(a)(4). Indeed, defendants fixed bids for through transportation rates, i.e. door-to-door rates, not just rates for the “foreign inland segment” of the routes. § 1706(a)(4).
It is true that defendants’ original agreement with the German local agents may have had the relationship to a “foreign inland segment” that the statute requires. Id. Indeed, United States v. Tucor Int’l, Inc., 35 F.Supp.2d 1172 (N.D.Cal. 1998), aff'd, 189 F.3d 834 (9th Cir.1999), the case upon which Gosselin and Pasha chiefly rely, awarded immunity under the Shipping Act. In Tucor, several Philippine firms, operating in a through transportation market “packed, picked up, and trucked household shipments [of U.S. military personnel] from Subic Naval Base and Clark Air Force Base ... to a Philippine seaport.” 189 F.3d at 836. The firms were indicted under the Sherman Act for conspiring amongst each other “to suppress competition by fixing prices.” Tu-cor, 35 F.Supp.2d at 1175. Defendants pled guilty, but the district court later dismissed the indictments on the basis of immunity under § 1706(a)(4). The Ninth Circuit affirmed, finding that § 1706(a)(4)’s reference to a “foreign inland segment,” “unambiguously exempts the activities of [defendants],” Tucor, 189 F.3d at 836, occurring as they did between points “entirely within a foreign country.” Id. at 835.
There is an argument to be made that the. agreement defendants made with the local German firms fits under the immunity announced in Tucor. And if defendants’ scheme had ended there, we would have to decide whether the agreement did so qualify and whether Tucor should be adopted in this circuit. But the scheme did not stop there. Rather, Gosselin and Pasha took additional steps to perfect their bid-rigging plan. And we are not persuaded that these additional steps “[concerned] the foreign inland segment,” in the manner the statute requires. § 1706(a)(4).
*511Gosselin and Pasha’s contacts with FF1, for instance, related not to foreign inland services, but to defendants’ desire that FF1 withdraw the prime through rate bid it had filed with MTMC. Similarly, the agreement defendants secured from other U.S. freight forwarders to file bids at or above the second low level had little to do with the German inland segment of the through services these forwarders offered. Rather, the agreement was a precommitment mechanism to ensure that none of the freight forwarders defected from the anticompetitive cartel that defendants were assembling. When some of these forwarders later broke ranks, defendants instituted measures to reign them in. But these measures were designed only to secure withdrawal of the competitive through rate bids the forwarders had filed in the second round, not to have consequences for the foreign inland segment.
In short, none of the additional steps Gosselin and Pasha took beyond their agreement with the German local agents had intended effects for any aspect of the German inland part of the through transportation market. It is unclear, therefore, how these steps “[concerned]” this foreign inland segment, as they must for immunity to attach under § 1706(a)(4).
Moreover, a broad immunity of the sort that Gosselin and Pasha seek would threaten to excise antitrust liability from the through transportation market completely. If § 1706(a)(4) exempted from anti-trust all stages of a conspiracy that involves in some manner a foreign inland segment, then any firm operating in any segment of any through transportation channel need only execute an agreement with a local moving agent to shield itself from the antitrust laws entirely. It does not take much to imagine how sophisticated transportation firms, intent on reaping larger gains, might abuse the immunity of such a rule. The incentives for opportunistic associations with companies operating in foreign inland segments would simply be too great. And without the constraint of anticipated antitrust liability, the prices charged by companies in the through transportation market would escalate. Further, the agreements and activity for which defendants seek immunity here were not regulated by the FMC. Lack of regulatory oversight might only exacerbate the upward pressure on prices for through transportation engendered by the absence of antitrust liability.
The upshot of defendants’ interpretation of § 1706(a)(4) would therefore be a through transportation market beset with collusive and artificially inflated bids, detrimental to consumers- and non-cooperating competitors alike. The government, as a repeat purchaser, would stand to lose much, and the extra money it would have to pay would come from the fisc and thus taxpayers.
It is unlikely that Congress intended such dismaying effects, but if there is any doubt over whether § 1706(a)(4) affords defendants relief, it is settled by the maxim that exceptions to the antitrust laws should be construed narrowly. See Seatrain, 411 U.S. at 732-33, 93 S.Ct. 1773- The Supreme Court has relied on this principle to render agreements subject to the antitrust laws rather than the lesser anticompetitive protections of FMC regulation. See id. Here defendants seek exemption from legal enforcement by the DOJ for agreements that have not been regulated by the FMC. We hold for reasons earlier expressed that § 1706(a)(4) does not immunize defendants’ scheme to raise through rate bids in the twelve channels at issue.
B.
Defendants next claim immunity under § 1706(a)(2). That section exempts from antitrust laws
*512any activity or agreement within the scope of this chapter ... undertaken or entered into with a reasonable basis to conclude that (A) it is pursuant to an agreement on file with the [FMC] and in effect when the activity took place, or (B) it is exempted by the FMC under § 1715] from any filing or publication requirement of this chapter.
Defendants do not claim that their “activity or agreement[s]” were undertaken “pursuant to an agreement on file with the” FMC. Rather, they point to a tariff filing exemption that the FMC granted to non-vessel operating common carriers, like defendants, for the “[transportation of used military household goods and personal effects by ocean transportation intermediaries.” 46 C.F.R. § 520.13(c) (2004). Gosse-lin and Pasha argue that they reasonably believed their collusive “activities] and agreements]” to be exempt from the filing requirements of the Shipping Act under this regulation, and thus beyond the antitrust laws under § 1706(a)(2)(B).
The touchstone of § 1706(a)(2)(B) is reasonableness. Yet the terms of the exemption on which defendants rely, and other features of the regulatory framework in which defendants operate, demonstrate that their reliance was, if anything, unreasonable.
To begin with, the exemption facially covers only “tariffs,” see 46 C.F.R. § 520.1(a) (2004), not the kind of agreements and activities involved in defendants’ bid rigging scheme. Yet a distinction between tariffs on the one hand and operating agreements on the other pervades the Shipping Act. Compare § 1703(a) (cataloguing the “agreements by or among ocean common carriers” to which the “chapter applies,” including agreements to “discuss, fix, or regulate transportation rates”), with § 1707 (describing “tariffs” that “each common carrier and conference shall keep open to public inspection”). This statutory distinction makes implausible defendants’ claim that they understood the reference to tariffs in the exemption to cover the collusive agreements they secured during the course of their scheme.2
The terms of § 1715, the Shipping Act provision mentioned in § 1706(a)(2)(B) which governs the FMC’s exemption procedures, further erodes Gosselin and Pasha’s claim of immunity under § 1706(a)(2)(B). Section 1715 conditions exemption from the disclosure requirements of the Act on a finding by the FMC “that the exemption will not result in substantial reduction in competition or be detrimental to commerce.” The FMC was thus required to make such a finding before passing the tariff filing dispensation on which defendants claim to have relied.
Section 1715 is quite clear in laying out the criteria for the granting of filing ex*513emptions: no “substantial reduction in competition” nor a “[detriment] to commerce” may result from the exemption. The agreements that defendants secured during their bid rigging scheme, however, accomplished just those ends: indeed, it was precisely by a “reduction in competition” that Gosselin and Pasha succeeded in inflating bids above the prime level, and this result was clearly “[detrimental] to commerce.” The incongruence between the conditions that § 1715 sets forth and the effects of defendants’ bid-rigging scheme erodes defendants’ claim that they reasonably understood the tariff filing exemption to permit such activity.
Pasha and Gosselin complain that the ex ante judgment of the FMC under § 1715 should not apply ex post to our interpretation of the reasonableness standard under § 1706(a)(2)(B). But the statutory phrase “with a reasonable basis to conclude,” § 1706(a)(2), clearly contemplates an inquiry into the propriety of a party’s belief in light of the circumstances. And one of those circumstances is surely the terms of the statute governing the exemption. As sophisticated businesses operating in a regulatory regime, defendants are properly charged with knowledge of the statute that applies to their behavior. Accord Hal Roach Studios, Inc. v. Richard Feiner & Co., Inc., 896 F.2d 1542, 1548 (9th Cir.1989) (citing Kansas Power & Light Co. v. Burlington Northern R.Co., 544 F.Supp. 1336, 1347 (D.Kan. 1982)) (indicating that “specialized knowledge” including of “statutory ... law” may properly be presumed of parties according to their “experience”). Thus aware of the criteria set forth in § 1715, Gosselin and Pasha can hardly claim a “reasonable basis to conclude that” their behavior was covered by the tariff filing exemption. § 1706(a)(2). An exemption conditioned upon no “substantial reduction in competition” simply should not be read to sanction, in any manner, behavior intended to accomplish just such a reduction. § 1715.
Moreover, defendants’ position flies once again in the face of the maxim that exceptions to antitrust liability should be narrowly construed. Gosselin and Pasha’s claim that the scope of the tariff filing exemption somehow applies to the stark anticompetitive agreements here is simply not persuasive. Section 1706(a)(2)(B) may well extend to behavior taken pursuant to an FMC filing or exemption whose anti-competitive effects are inadvertent, tangential, or debatable. But when, as here, the anticompetitive effects are intentional, direct, and palpable, reading § 1706(a)(2)(B) to insulate these effects from liability would encourage gross violations of the antitrust laws and vitiate the canon of construction that aims to protect the operation of these laws.
For the foregoing reasons, we do not believe that Congress intended § 1706(a)(2)(B) to confer immunity on the kind of conduct for which defendants are being prosecuted. We therefore find that defendants’ scheme to rig'bids is not exempt from antitrust under § 1706(a)(2)(B).
C.
The final part of the Shipping Act under which defendants claim immunity is § 1706(c)(1). This . provision states that “[a]ny determination by an agency or court that results in the denial or removal of the immunity to the antitrust laws set forth in [§ 1706(a) ] shall not remove or alter the antitrust immunity- for the period before the determination.” Defendants contend that an adverse decision on one of the two other statutory immunities they seek— § 1706(a)(4) and § 1706(a)(2)(B) — constitutes a “denial or removal,” and that § 1706(c)(1) thus requires that any penalty be imposed only prospectively.
*514Section 1706(c)(1) was designed for those instances in which a firm has been operating under a clearly established statutory immunity, whose validity or scope is subsequently called into doubt — for instance because of a changed circumstance or because of some discrete action on the part of the firm that the statute prohibits. See, e.g., § 1709 (listing a variety of prohibited actions for firms operating under filed tariffs or agreements). When such an event occurs and immunity is abrogated, § 1706(c)(1) ensures that subsequent legal or administrative proceedings will not impose liability for the period between the event and the proceedings. The provision thus affords the regulated firm some time to re-engage the administrative process or otherwise render itself compliant. Under this interpretation, § 1706(c)(1) promotes beneficial reliance by the regulated industry on the regulatory process, particularly when the event that abrogates immunity is the invalidation of a filed tariff or operating agreement. Congress was evidently mindful of this end in passing this provision. See, e.g., H.R.Rep. No. 98-53, pt. 1, at 33 (1983) (“[Section 1706(c)] is needed to provide a degree of stability and certainty to an agreement filed in good faith and valid on its face.”)
To qualify for relief under § 1706(c)(1), defendants must therefore identify a discrete event that triggers the provision’s grace period. Obviously, that event cannot be our present denial of immunity under another statutory provision of the Shipping Act, as defendants would have it. Were we to countenance such an argument, a maritime firm wishing to avoid full antitrust liability would simply invent a series of spurious immunity arguments and remain perpetually one step ahead of the judicial or administrative proceedings invalidating them. Such a state of affairs would be the antithesis of the antitrust protections that the maxim requiring narrow construction of exemptions therefrom contemplates. See Seatrain, 411 U.S. at 732-33, 93 S.Ct. 1773. We therefore reject defendants’ interpretation of § 1706(c)(1).
D.
In short, we hold that defendants’ scheme to rig bids does not qualify for immunity under any of the three provisions Gosselin and Pasha rely on— § 1706(a)(4), § 1706(a)(2), and § 1706(c)(1).3 We therefore conclude that defendants enjoy no immunity from antitrust prosecution under the Shipping Act.4
*515IV.
The charging information also contained a conspiracy to defraud count. See 18 U.S.C. § 371 (2000). Defendants argued in their motion to dismiss that the immunity provisions of the Shipping Act were broad enough to insulate them from liability under a conspiracy to defraud theory. Despite the district court’s conclusion that defendants wpre indeed immunized from antitrust liability by the Shipping Act, the court found that this immunity did not extend to conspiracy to defraud. Employing the test set forth in Blockburger v. United States, 284 U.S. 299, 52 S.Ct. 180, 76 L.Ed. 306 (1932), the district court further determined that the elements of the antitrust claim did not subsume those of the conspiracy to defraud claim. The district court thus concluded that defendants could properly be prosecuted for the same behavior under both counts. See United States v. Ashley Transfer & Storage Co., Inc., 858 F.2d 221, 224-25 (4th Cir.1988) (finding that conduct may form basis for prosecution under § 371 following acquittal on Sherman Act count). As a result, the court rejected defendants’ motion to dismiss the fraud count on Shipping Act immunity grounds, and, following the terms of the plea agreements, Gosselin and Pasha pled guilty under § 371.
We have concluded that defendants enjoy no antitrust immunity under the Shipping Act. We therefore need not determine, as the district court did, whether immunity under the Shipping Act extends to anticompetitive behavior that is also actionable under a conspiracy to defraud theory. Furthermore, defendants concede on appeal that the district court’s Block-burger analysis is “certainly correct” and that “simultaneous Sherman Act and Section 371 prosecutions are not multipliei-tous.” Prosecution of defendants’ particular course of action under both statutes is therefore permissible.
In reviewing the district court’s disposition of the conspiracy to defraud counts, it remains only to address the contention, raised on appeal, that there is insufficient factual support in the plea agreements and incorporated statement of facts for an adjudication of guilt under § 371.
Challenges to the factual basis for an adjudication of guilt following a guilty plea are severely circumscribed. “A voluntary and intelligent plea of guilty is an admission of all the elements of a formal criminal charge.” United States v. Willis, 992 F.2d 489, 490 (4th Cir.1993) (quoting McCarthy v. United States, 394 U.S. 459, 466, 89 S.Ct. 1166, 22 L.Ed.2d 418 (1969)). A defendant who pleads guilty therefore “admits all of the factual allegations. made in the indictment,” O’Leary v. United States, 856 F.2d 1142, 1143 (8th Cir.1988) (per curiam), and waives “all non-jurisdictional defects, including the right to contest the factual merits of the charges.” Willis, 992 F.2d at 490 (internal citations omitted); see also United States v. Wiggins, 905 F.2d 51, 52 (4th Cir.1990). In these circumstances, courts have permitted a defendant to challenge an adjudication of guilt only with the argument that “the facts underlying the charge” are insufficient “to constitute a crime.” Stanback v. United States, 113 F.3d 651, 654 (7th Cir.1997).
The most that Gosselin and Pasha may argue, therefore, is that the allegations in the plea agreements and the *516incorporated statement of facts are so insubstantial that they could not constitute an offense under § 371. It is clear that the factual recitations in the plea documents easily surmount this low hurdle. Conspiracy to defraud under § 871 requires three elements: “(1) the existence of an agreement, (2) an overt act by one of the conspirators in furtherance of the objectives, and (3) an intent on the part of the conspirators to agree as well as to defraud the United States.” United States v. Tedder, 801 F.2d 1437, 1446 (4th Cir.1986). The statute covers “not only conspiracies intended to involve the loss of government funds but also any conspiracy for the purpose of impairing, obstructing, or defeating the lawful function of any department of government.” Id. The statement of facts laid out in some detail the course of defendants’ conspiracy, including the discrete agreements Gosselin and Pasha secured with various firms engaged in the bidding cycle. The statement of facts also unequivocally recites that the foregoing actions “[increased] the rates paid by DOD for the transportation of military goods during the [cycle] to levels higher than would have prevailed in the absence of their conspiracy.” The stipulation therefore contains an abundance of information to establish a conspiracy to “[impair] ... the lawful function of [a] department of government,” id. — namely the MTMC program.
V.
The final contention that Gosselin and Pasha raise on appeal concerns their sentence. Following the adjudication of guilt on the conspiracy to defraud count, the district court considered the sentences that the parties had agreed to recommend in the event of this outcome. The district court settled on the figure recommended in the plea agreements — a fine of $4.6 million for each defendant for its part in the conspiracy to defraud. Gosselin and Pasha now argue that this fine exceeded the maximum permissible under the relevant sentencing statute, 18 U.S.C. § 3571 (2000). They assert that the “gross loss” to the government as a result of the conspiracy to defraud was only $1 million, id. § 3571(d), less than the $2.3 million amount on which the plea agreements’ sentencing recommendations for the § 371 count were predicated.
The sentencing arrangement that the parties agreed to is carefully set out in each plea document. In the event of an adjudication of guilt, “the United States and the defendant agree that the appropriate disposition of this case is, and agree to recommend jointly, that the Court impose a sentence requiring the defendant to pay to the United States a criminal fine.... ” The agreements further provide that “Count 1 and Count 2 are [to be] grouped together” for sentencing purposes, “and thus, the total fíne paid will be the greater of’ two figures that each sentencing agreement recites. The first figure is derived by applying various listed Sentencing Guidelines factors to the penalty provisions governing Sherman Act violations. The second figure is derived by applying various listed Sentencing Guidelines factors to the penalty provisions governing § 371 violations.
Operating under the assumption that defendants were guilty only of conspiracy to defraud, the district court limited its attention during sentencing to the conspiracy to defraud part of each plea agreement’s sentencing recommendation. We have found additionally that the Shipping Act affords defendants no immunity from the antitrust count. We therefore vacate the sentence and remand for resentencing in light of our immunity holding and the entirety of *517each plea agreement’s sentencing provisions.
VI.
We have found that the three immunity-provisions of the Shipping Act under which Gosselin and Pasha claim antitrust immunity afford them no relief. We have also determined that there was no error in the district court’s adjudication of guilt on the conspiracy to defraud count. Because the district court applied the sentencing provisions of the plea agreement under the assumption that defendants were only guilty of conspiracy to defraud, a remand for resentencing in light of our disposition of the antitrust issue is in order. The judgment of the district court is therefore
AFFIRMED IN PART, REVERSED IN PART, AND REMANDED FOR RE-SENTENCING.