The issue on this interlocutory appeal from an order denying a motion to dismiss an antitrust price-fixing claim is whether *147the plaintiff had sufficient notice of the availability of the claim against a Chapter 11 debtor to satisfy due process requirements and render the claim discharged. This issue arises on an appeal by Defendants-Appellants United Air Lines, Inc., DBA United Airlines, and United Continental Holdings, Inc., FKA UAL Corp. (collectively “United”), from the May 18, 20l2, order of the United States District Court for the Eastern District of New York (John Gleeson, District Judge), denying United’s motion to dismiss an antitrust complaint brought against it by Plaintiff-Appellee DPWN Holdings (“DHL”). See DPWN Holdings (USA), Inc. v. United Air Lines, Inc. (“Dist.Ct.Op.”), 871 F.Supp.2d 143 (E.D.N.Y.2012).
We conclude that, in the circumstances of this case, the District Court applied an incorrect standard in accepting as true DHL’s allegation that it was not aware of, or with due diligence could not have become aware of, sufficient facts to plead an antitrust claim that would survive a motion to dismiss in the context of a bankruptcy proceeding. We therefore remand for further development of the facts concerning (a) what DHL knew or reasonably should have known in time to present an antitrust claim in the bankruptcy proceeding, or to file a late proof of claim or move to amend the reorganization plan and (b) what United knew or reasonably should have known concerning DHL’s claim.
Background
Facts concerning the alleged price-fixing conspiracy. Because this appeal is from the denial of a motion to dismiss, the facts regarding United’s alleged involvement in the price-fixing conspiracy are taken from DHL’s complaint and are assumed to be true. See Bryant v. N.Y. State Education Department, 692 F.3d 202, 210 (2d Cir.2012). United was a member of the International Air Transport Association (“IATA”) at all times relevant to this appeal. IATA enjoyed limited antitrust immunity in the European Union through a “block exemption.” In 1993, the European Union’s Directorate General for Competition (“DGC”) sent a letter to an official at IATA specifying that the block exemption did not cover the coordinated implementation of surcharges. This letter was shared with IATA members. The United States Department of Transportation (“DOT”) communicated a similar conclusion to IATA. Nevertheless, in 1993 IATA adopted a surcharge “upon the pretext of recouping increased costs.” As a result, the DGC withdrew IATA’s block exemption and subsequently denied an application for an individual exemption for the surcharge.
On August 9,1996, United and two other airlines, Lufthansa and Scandinavian Airlines (“SAS”) entered into an agreement to provide “globally integrated air transportation services in competition with other carriers and carrier alliances while remaining independent companies.” On November 1, 1996, DOT issued an order permitting the alliance and providing it limited antitrust immunity. However, the agreement prohibited the airlines from “ex-chang[ing] information, discussing], agree [ing] upon, or coordinating] ... on any subject or in any manner that would cause any Party to contravene (i) any law....”
In early 1997, members of IATA considered joint strategies to manage increases in the price of aviation fuel, including implementing fuel surcharges. At that time, members of IATA considered the antitrust risks of coordinated surcharging. Minutes from an IATA conference on the topic, quoting Andrew Charlton, director of the IATA legal department, stated:
Antitrust laws prohibit competitors reaching any form of agreement, under*148standing or arrangement which is likely to have an impact on price.... [A] relevant exception is where immunity has been granted by the relevant authority for rates reached pursuant to a particular procedure and within the strict confines of the terms of the approval itself.
Without any immunity, authorities regard with great suspicion any situation where competitors charge the same rate. In the event that there is any evidence whatsoever that competitors have had an opportunity to communicate in any way, and charge the same rate, there is a very strong assumption that they do so having colluded.
Until the particular approval is granted for any rate agreed at this conference, that situation would apply. In other words, in my opinion, any airline which moves to charge the rate which is agreed at this conference before government approval, and therefore antitrust immunity, is obtained, would face a very strong evidential presumption that the rate being charged had been agreed between competitors and without antitrust immunity.
On August 7, 1997, IATA approved Resolution 116ss, under which member airlines would introduce a' fuel surcharge tied to changes in the spot price of aviation fuel as tracked by the IATA Fuel Price Index (“FPI”). IATA officials were later advised that DOT refused to give approval to the resolution, which would confer antitrust immunity, “unless accompanied by economic justification based on current prices,” which the airlines were unable to provide. As a result, IATA’s Board, of Governors declined to make the resolution effective.
In late 1999 to early 2000, for the first time since approval of Resolution 116ss, fuel spot prices increased enough to trigger a fuel surcharge. On January 28, 2000, IATA submitted Resolution 116ss for approval by DOT, hoping to secure antitrust immunity and put the resolution into effect. United informed its competitors that it planned to impose a fuel surcharge effective February 1, 2000. Then, before receiving a response from DOT, United and a number of other airlines started charging DHL and other customers a fuel surcharge “pursuant to the terms of Resolution 116ss.”
On March 14, 2000, DOT rejected the airlines’ application for approval, stating, “The uniform, industry-wide index mechanism proposed here appears fundamentally flawed and unfair to shippers and other users of cargo air transportation.” On March 21, 2000, IATA members circulated a statement advising its airlines that implementing surcharges pursuant to the resolution might be illegal price-fixing. The statement advised:
If [members] were to coordinate pricing by reference to the Index, whether pursuant to this disapproved Resolution or simply through de facto parallel pricing actions, that could be regarded as an illegal conspiracy in violation of applicable Competition laws.... Because any further pricing actions linked to the now tainted Index could expose the carriers engaging in such pricing actions to serious antitrust liability, we must advise that carriers not engage in any pricing actions tied to the Index.
IATA also announced that it would stop publishing the FPI, because “The Index has now become tainted by the DOT order finding Resolution 116ss, to which the Index was linked, to be adverse to the public interest and in violation of law.”
DHL alleges that after the DOT’S rejection of Resolution 116ss, United and other airlines continued charging fuel surcharges “as if Resolution 116ss had been ap*149proved.” For example, DHL alleges that in late 2000, United “and other cartel members — in a coordinated, largely parallel fashion — increased the Fuel Surcharge to DHL ... in accordance with Resolution 116ss.”
Over the next few years, the airlines strayed from the methodology set forth in Resolution 116ss. Despite these deviations, United and the other airlines continued to fix fuel charges in the same anticompetitive and illegal manner. For example, in late 2001, the airlines recalib-rated the fuel surcharge formula in a coordinated manner. DHL’s complaint alleges that the airlines did so “to preserve the supracompetitive profits generated by the Fuel Surcharge” despite lower fuel prices. Then, in July 2002, United began using its own “Jet Fuel Index.” DHL’s complaint alleges that this index was “a fagade to help [United] maintain the appearance of acting unilaterally.” DHL alleges many other actions in furtherance of a conspiracy to fix fuel surcharges until at least mid-October 2006.
The Chapter 11 proceeding. On December 9, 2002, United filed a petition for relief under Chapter 11 of the Bankruptcy Code. As part of its claims notification procedures, United identified DHL as a potential creditor holding more than twenty disputed claims. An antitrust price-fixing claim was not mentioned. DHL received actual notice of United’s bankruptcy and all relevant deadlines.
On January 20, 2006, the bankruptcy court confirmed United’s reorganization plan, which became effective on February 1, 2006. Pursuant to 11 U.S.C. § 1141(d), the plan provided for a blanket discharge of all claims and causes of action, “known or unknown,” “of any nature whatsoever” against United “that arose before the Confirmation Date.” Also on February 1, distribution of shares of stock in the reorganized United began and was 80 percent complete by March 21, 2006.
On December 8, 2009, a final decree was entered in United’s bankruptcy. All holders of general, unsecured claims received stock in the reorganized company that was valued at between 4 and 8 cents on the dollar.
Post-confirmation developments. On February 14, 2006, law enforcement officials raided the offices of several airlines, other than United, allegedly involved in a fuel surcharge price-fixing conspiracy. Three days later, on February 17, a class action was filed against United and others, asserting price-fixing claims like those asserted in DHL’s pending lawsuit.1 See Dist. Ct. Op., 871 F.Supp.2d at 149. In June 2006, the U.S. Department of Justice (“DOJ”) served a subpoena on United “requesting information related to certain passenger pricing practices and surcharges.” DOJ did not indict United for a price-fixing conspiracy, although United was named as a defendant in over ninety class actions alleging such a conspiracy. United settled with the majority of class action plaintiffs in return for agreements to cooperate with the plaintiffs’ investigation.
On July 5, 2010, as a result of a settlement with one of the airlines involved in the alleged price-fixing conspiracy, DHL obtained access to documents disclosing United’s participation in the scheme.
DHL’s antitrust suit. On February 4, 2011, DHL filed a lawsuit in the District *150Court alleging that United was part of a conspiracy to fix the price of air cargo shipments, in violation of section one of the Sherman Act, 15 U.S.C. § 1. The alleged scheme involved fixing the base freight rate and various surcharges. Anticipating United’s defense that DHL’s antitrust claim was discharged in the bankruptcy proceeding, DHL alleged that it first learned of United’s involvement in a price-fixing conspiracy “after July 5, 2010, when DHL obtained access to confidential documents describing the scope of the cartel and providing evidence of [UnitedJ’s participation in the cartel. Complaint ¶ 18. DHL also alleged that it “did not and could not have discovered the injuries it sustained as a result of [UnitedJ’s illegal activity until after. July 5, 2010.” ¶ 161. United moved to dismiss DHL’s antitrust suit on the ground that, among other things, DHL’s cause of action was discharged by the confirmation of United’s plan of reorganization.
On May 18, 2012, the District Court denied United’s motion to dismiss. Dist. Ct. Op., 871 F.Supp.2d at 164. Accepting for purposes of United’s motion to dismiss DHL’s allegation concerning its lack of knowledge, the Court stated, “[IJt is undisputed for purposes of this motion that DHL could not have discovered United’s alleged antitrust violations until after confirmation of the plan.” Id. at 153. The Court held that DHL’s claim was not barred by confirmation of United’s reorganization plan because DHL was denied due process for lack of notice of its potential claim. Id. at 153-60. In view of the time and expense that a potentially needless antitrust trial would take, the Court sensibly certified its ruling for interlocutory appeal, and this Court granted United’s petition for an interlocutory appeal. See 28 U.S.C. § 1292(b).
Discussion
The basic legal principles relevant to this appeal are not in dispute. Under the Bankruptcy Code, confirmation of a Chapter 11 reorganization plan “discharges the debtor from any debt that arose before the date of [ ] confirmation.” 11 U.S.C. § 1141(d)(1)(A). In this context, a debt is defined to mean liability on a claim, and the term “claim” means “right to payment, whether or not such right is reduced to judgment, liquidated, unliqui-dated, fixed, contingent, matured, unma-tured, disputed, undisputed, legal, equitable, secured, or unsecured.” 11 U.S.C. § 101(5)(A). The discharge of preconfir-mation claims “operates as an injunction against the commencement or continuation of an action.” 11 U.S.C. § 524(a)(2). The discharge of such claims serves the bankruptcy policy of providing debtors with a “fresh start” to permit their continued operation free of pre-bankruptcy debts. See Central Virginia Community College v. Katz, 546 U.S. 356, 364-65, 126 S.Ct. 990, 163 L.Ed.2d 945 (2006). However, a claim cannot be discharged if the claimant is denied due process because of lack of adequate notice. See Wright v. Owens Corning, 679 F.3d 101, 107-08 (3d Cir.2012). And whether notice comports with due process requirements turns on the reasonableness of the notice, see Mullane v. Central Hanover Bank & Trust Co., 339 U.S. 306, 314, 70 S.Ct. 652, 94 L.Ed. 865 (1950), a flexible standard that often turns on what the debtor or the claimant knew about the claim or, with reasonable diligence, should have known, see Chemetron Corp. v. Jones, 72 F.3d 341, 345-46 (3d Cir.1995).
In ordinary cases in which a claim for money is asserted, it will often be entirely reasonable to expect that the debtor knows to whom it owes money, although many claimants will also know, or with reason*151able diligence could ascertain, that they are owed money. However, in the context of a claim for damages based on the debt- or’s alleged violation of law, two competing policies will be in tension. On the one hand is the policy sought to be vindicated by the statute alleged to be violated, here the Sherman Antitrust Act. That policy— promoting competition — is enhanced by limiting the circumstances in which the claim is discharged. On the other hand is the policy sought to be vindicated by the Bankruptcy Code. That policy — providing a debtor emerging from bankruptcy with a “fresh start” — is enhanced by expanding the circumstances in which a claim is discharged.2 Moreover, a debtor will normally be less likely to be charged with knowledge that it has violated the law than that it owes money unrelated to a law violation.
We recognized the tension between these policies in In re Chateaugay Corp., 944 F.2d 997 (2d Cir.1991), which pitted the policy of environmental protection under the Comprehensive Environmental Response, Compensation and Liability Act (“CERCLA”), 42 U.S.C. § 9601 et. seq. (1988), against the “fresh start” policy of the Bankruptcy Code. “The Code aims to provide reorganized debtors with a fresh start, an objective made more feasible by maximizing the scope of a discharge. CERCLA aims to clean up environmental damage, an objective that the enforcement agencies in this litigation contend will be better served if their entitlement to be reimbursed for CERCLA response costs based on pre-petition pollution is not considered to be a ‘claim’ and instead may be asserted at full value against the reorganized corporation.” Id. at 1002. We also recognized that it will sometimes be appropriate to permit the “fresh start” policy to override the policy of the statute alleged to be violated. “Here, we encounter a bankruptcy statute that is intended to override many provisions of law that would apply in the absence of bankruptcy — especially laws otherwise providing creditors suing promptly with full payment of their claims.” Id.
In the pending case, the District Court accepted, for purposes of United’s motion to dismiss, DHL’s allegation that it “could not have discovered United’s alleged antitrust violations until after confirmation of the plan.” Dist. Ct. Op., 871 F.Supp.2d at 153.3 Athough factual allegations of a complaint are normally accepted as true on a motion to dismiss, see, e.g., Goldstein v. Pataki, 516 F.3d 50, 56 (2d Cir.2008), that principle does not apply to *152general allegations that are contradicted “by more specific allegations in the Complaint.” See, e.g., Hirsch v. Arthur Andersen & Co., 72 F.3d 1085, 1095 (2d Cir.1995); Barberan v. Nationpoint, 706 F.Supp.2d 408, 424 (S.D.N.Y.2010); In re Livent, Inc. Noteholders Securities Litigation, 151 F.Supp.2d 371, 405 (S.D.N.Y.2001). In Ashcroft v. Iqbal, 556 U.S. 662, 129 S.Ct. 1937, 173 L.Ed.2d 868 (2009), the Supreme Court deemed “conclusory” and “not entitled to be assumed true” on a motion to dismiss an allegation that a defendant “ ‘knew of ... harsh conditions of confinement.” Id. at 680, 681, 129 S.Ct. 1937 (quoting complaint). It is not clear, and has not since been clarified, whether the Court’s unwillingness to accept this allegation of knowledge was intended to apply generally to allegations of mental states or was a more limited pronouncement influenced by the fact that the defendants were senior officials of the Government, less likely to have knowledge of the alleged conditions of harsh confinement than lower ranking officials, like the defendant prison warden, with more immediate responsibilities for the alleged conditions.
Whatever the scope of the Supreme Court’s statement in Iqbal, DHL’s claim of lack of knowledge in this case is contradicted by several allegations in its complaint. For example, paragraph 40 alleges that members of IATA, including United, adopted Resolution 116ss to set fuel surcharges, paragraph 44 alleges that the carriers, including United, implemented the resolution, paragraphs 54 and 58 allege that the airlines raised fuel surcharges in parallel in conformity with the Resolution, paragraph 20 alleges that the surcharges increased at a greater rate than the increase in prices of aviation fuel, and paragraphs 70 and 74 allege that many of the increases occurred in a coordinated fashion.
We recognize that parallel conduct alone is generally insufficient to show an antitrust violation, see Bell Atlantic Corp. v. Twombly, 550 U.S. 544, 553-57, 127 S.Ct. 1955, 167 L.Ed.2d 929 (2007), but the facts of United’s conduct that appear to have been known or reasonably knowable by DHL prior to confirmation of the plan may well supply the “plus” factors, see In re Text Messaging Antitrust Litigation, 630 F.3d 622, 624 (7th Cir.2010), that would have permitted assertion of an antitrust claim. At a minimum, these facts contradict and may well undermine DHL’s claim of lack of sufficient knowledge of an antitrust violation. The issue here is not whether the known facts would have permitted pleading a sufficient antitrust claim outside of bankruptcy, but only whether such a claim could have been filed within a bankruptcy proceeding where the “fresh start” principle operates to channel all “claims,” broadly defined by the Bankruptcy Code, into a forum well suited to determine whether such claims deserve exploration and adjudication. And these facts bear importantly on the ultimate issue whether DHL was denied due process by lack of specific notice from United of an antitrust claim.
Furthermore, the fact that a class antitrust action was filed against United on February 17, 2006, after plan confirmation, bears importantly on the issue whether DHL could have filed a late claim or moved to amend the reorganization plan. DHL was a member of the putative class and has relied on the pendency of the class complaint to toll the statute of limitations in this litigation.
We are skeptical of DHL’s contention that it was not aware of, or with reasonable diligence could not have become aware of, its antitrust claim in time to assert it in the bankruptcy proceeding. But whether that contention is supportable *153and the related issue of whether due process required United to give DHL explicit notice of an antitrust claim should not be decided at the appellate level before the District Court has considered these matters under proper standards. Because the District Court erred in accepting as true DHL’s allegation of lack of sufficient knowledge to file an antitrust claim in bankruptcy, the matter must be remanded for reconsideration.
On such reconsideration the District Court must determine what aspects of United’s alleged price-fixing conduct were known by DHL, or reasonably ascertainable, prior to plan confirmation, whether the allegations of the class action complaint were sufficient to alert DHL to its antitrust claim, and whether a post-confirmation claim would have been entertained. If DHL lacked such knowledge, the inquiry will then shift to whether United knew or should have known of its potential antitrust liability such that due process required it to notify DHL of the potential claim. At least these matters must be considered before a determination can be made whether DHL would be denied due process if its potential antitrust claim was discharged.
Accordingly, we remand for further consideration, either on the face of the pleadings, or after discovery, of United’s contention that DHL’s antitrust claim was discharged. Any subsequent appeal will be referred to this panel. See United States v. Jacobson, 15 F.3d 19, 22 (2d Cir.1994).
Remanded.