
608 F.3d 139 (2010)
In re DELTA AIR LINES, INC., Debtor.
The Northwestern Mutual Life Insurance Company, Appellant,
v.
Delta Air Lines, Inc., Bank of New York, as Indenture Trustee and Pass Through Trustee, and Bank of America, N.A.,[1] Appellees.
DFO Partnership, Appellant,
v.
Delta Air Lines, Inc., and Strategic Value Partners, LLC, Appellees,
Wilmington Trust Company, as Owner Trustee, and Cargill Financial Services International, Inc., Interested-Parties Appellees.
AT & T Credit Holdings, Inc., Appellant,
v.
Delta Air Lines, Inc., and Bank of America, N.A., Appellees, *140 
Bank of New York, as Indenture Trustee, Interested-Party Appellee.
Docket Nos. 08-5002-bk, 08-5230-bk, 08-5236-bk.[2]
United States Court of Appeals, Second Circuit.
Argued: September 21, 2009.
Decided: June 22, 2010.
*141 Lisa Hill Fenning, Arnold & Porter LLP, Los Angeles, CA, for Appellant The Northwestern Mutual Life Insurance Company.
Richard G. Smolev, Kaye Scholer LLP, New York, N.Y. (Piper A. Brock, on the brief), for Appellants DFO Partnership and AT & T Credit Holdings, Inc.
Stephen Sanders, Mayer Brown LLP, Chicago, IL, and Andrew H. Schapiro, David F. Abbott, and John M. Conlon, Mayer Brown LLP, New York, NY, for Amicus Curiae General Foods Credit Corporation in Support of Reversal.
Lawrence M. Handelsman, Stroock & Stroock & Lavan LLP, New York, N.Y. (Kristopher M. Hansen and Jayme T. Goldstein, Stroock & Stroock & Lavan LLP, New York, NY, and Michael E. Wiles and Jessica R. Simonoff, Debevoise & Plimpton, LLP, New York, NY, on the brief), for Appellee Delta Air Lines, Inc.
Leo T. Crowley, Pillsbury Winthrop Shaw Pittman LLP, New York, N.Y. (Eric Fishman and Margot P. Erlich, on the brief), for Appellee the Bank of New York Mellon, f/k/a the Bank of New York, as Indenture Trustee and Pass Through Trustee.
Michael J. Edelman, Vedder Price, P.C., New York, N.Y. (Douglas J. Lipke, on the brief), for Appellees Bank of America, N.A., and Strategic Value Partners, LLC.
Mark M. Elliott, Bingham McCutchen LLP, New York, N.Y. (Michael J. Reilly and Joshua Dorchak, on the brief), for Interested-Party Appellees Wilmington Trust Company, as Owner Trustee, Cargill Financial Services International, Inc., Bank of New York, as Indenture Trustee, and The Bank of New York Mellon.
Before LEVAL, RAGGI, and LIVINGSTON, Circuit Judges.
LEVAL, Circuit Judge.
Northwestern Mutual Life Insurance Company, Inc. ("Northwestern"), DFO Partnership ("DFO"), and AT & T Credit Holdings ("AT & T") (collectively, the "Appellants" or "Claimants"), who are claimants in the bankruptcy proceedings of Delta Air Lines, Inc. ("Delta"), appeal from a ruling of the United States District Court for the Southern District of New York (Berman, J.) affirming final orders of the United States Bankruptcy Court for the Southern District of New York (Hardin, J.) (the "Bankruptcy Court Orders"). The bankruptcy court upheld Delta's objections to Appellants' claims for approximately $1 billion under tax indemnity agreements. For the reasons discussed herein, the judgment is VACATED, and the cases are REMANDED with instructions to reject Delta's objections.

BACKGROUND

I. Underlying Agreements
Each of these three appeals requires that we construe a set of agreements governing a leveraged lease, a financing structure commonly employed by airlines to fund the acquisition of aircraft. Because of its chronic unprofitability, Delta was unable to benefit from the right to take accelerated depreciation deductions accorded by the Internal Revenue Code to *142 the owner of equipment used in business. See 26 U.S.C. §§ 167(a), 168. The purpose of the leveraged lease was to place ownership of the aircraft in a profitable entitythe Owner Participantwhich would put up a portion of the acquisition cost and take accelerated depreciation against its own profits; the aircraft would be leased to Delta. The Owner Participant's bearing of a portion of the purchase price of the aircraft as an equity investor (in order to obtain the benefits of accelerated depreciation) reduced the percentage of acquisition cost that needed to be financed by debt, thus reducing the interest cost of the acquisition.

A. The Leveraged Leases
In each of these leveraged lease transactions, the parties entered into a master agreement (the "Participation Agreement"), which specified the roles of the parties and identified the various constituent agreements. An "Owner Trust" was established to purchase aircraft with funds provided by (i) an equity contribution (of approximately 20%) from the Owner Trust's beneficiary (the "Owner Participant") and (ii) non-recourse borrowings (of approximately 80%) from lenders (the "Lenders"). Each Claimant was the Owner Participant and beneficiary of such an Owner Trust.
In each transaction, the Owner Trust leased the aircraft to Delta pursuant to a "net" lease (the "Lease") that required Delta to pay all operating expenses. Basic rent payments were calculated to amortize the debt due to the Lenders and in some cases to provide a cash return to the Owner Participant. In each case, in order to provide security for the borrowed funds, the Owner Trust granted a security interest in the aircraft and assigned its interest in the Lease (subject to certain exceptions) to an "Indenture Trustee" acting for the Lenders, pursuant to an indenture agreement (the "Indenture"). The Indenture Trustee was charged with making debt payments from the Lease rentals and distributing the excess, if any, to the Owner Trust. As assignee of the lessor's interest, the Indenture Trustee was entitled to control the exercise of remedies if Delta defaulted under the Lease.

B. Tax Indemnity Agreements and Stipulated Loss Value
The primary incentive of the Owner Participant in advancing 20% of the purchase price of the aircraft was to obtain the benefits of accelerated depreciation. That interest, or in any event its economic value to the Owner Participant, was protected by two mechanisms against events that would prevent the Owner Participant from taking full advantage of the deductions, including Delta's default under the Lease (which might result in the Indenture Trustees' foreclosing on the aircraft). The first form of protection for the Owner Participant was a Tax Indemnity Agreement ("TIA"), which required Delta to compensate the Owner Participant in the event that, upon a foreclosure on the aircraft, the Internal Revenue Service required the Owner Participant to "recapture" deductions it had taken for accelerated depreciation. The second was a provision of each Lease that permitted the lessor (or the Indenture Trustee, as assignee) to demand that Delta pay "stipulated loss value" ("SLV") if Delta defaulted under the Lease. SLV (the precise amount of which was fixed by an appendix to the Lease and was tied to the date of the default) was calculated to provide for (i) the payment of the remaining debt with all interest due and (ii) the agreed-upon return to the Owner Participant through the date of termination, taking into account all adverse tax consequences that would result from the default.
*143 In each case, the rights assigned to the Indenture Trustee as security for the loan to the Owner Trust included the right to demand payment of SLV. The terms of the Indenture provided that, upon the Indenture Trustee's collection of SLV, the funds would first be applied to the parties' expenses, and then to any outstanding balance on the loan. Remaining funds would be paid over to the Owner Trust, and ultimately to the Owner Participant. This sequence of payments was known as the "Indenture waterfall."
Because SLV was calculated to be sufficient to compensate the Owner Participant for all adverse tax consequences of a Lease default, if Delta were to make a full payment of SLV and a full payment under the TIA, the Owner Participant would receive double compensation, at least to the extent of the tax losses indemnified by the TIA. Accordingly, each TIA contained an exclusionary provision, which stipulated in some form that, in the event that Delta paid SLV under the Lease, the Owner Participant was not entitled to collect under the TIA. (For the same reasoni.e., to protect against the Owner Participant's receipt of double paymentthe Participation Agreements contained provisions requiring reduction of the SLV to account for any amount paid by Delta to the Owner Participant under a TIA.)
The precise language employed in the exclusionary provisions of the TIAs is not standardized, but varies slightly as among the three sets of leveraged lease transactions involved in these appeals. DFO's TIAs provide that no amount is due under the TIAs where Delta is "required to pay" SLV. AT & T's agreements provide that it is not entitled to anything under the TIAs where Delta "pays an amount equal to" SLV. Northwestern's TIAs provide that it is not entitled to "any payment ... in respect of any Loss ... arising as a result of ... [a]ny event whereby [Delta] pays Stipulated Loss Value ... or an amount determined by reference thereto." DFO TIA § 7c; AT & T TIA § 6c; Northwestern TIA § 6c.

II. Procedural History

A. Bankruptcy Filing and Exercise of Remedies by Indenture Trustees
On September 14, 2005, Delta filed a voluntary Chapter 11 petition. On September 28, 2005, the Office of the United States Trustee appointed an Official Committee of Unsecured Creditors. On April 25, 2007, the bankruptcy court confirmed Delta's Joint Plan of Reorganization, which became effective on April 30, 2007. Delta's bankruptcy filing was an event of default under all of the Leases and Indentures, and entitled the Indenture Trustees to exercise the remedies provided under the Leases.
Many of the aircraft at issue were disposed of pursuant to a term sheet (the "Bingham Term Sheet") negotiated among Delta and an ad-hoc committee of debtholders and approved by the bankruptcy court on February 15, 2006. The Bingham Term Sheet authorized and directed a series of transactions, consisting of (1) foreclosure upon the collateral, including the aircraft, by the Indenture Trustees, (2) rejection of the applicable Leases, and (3) execution of new, post-petition leases. The Owner Participants did not participate in the new leases. The Bingham Term Sheet set forth a formula to determine the amount of the Indenture Trustees' claims for rejection damages, roughly: SLV (calculated as of the date of Delta's filing), less the aggregate rent payments to be received under the restructured leases, less the expected residual value of the aircraft at the end of the restructured lease terms.
*144 Northwestern was the Owner Participant in leveraged leases of three aircraft (tail numbers N182DN, N803DE, and N804DE). Early in the bankruptcy, Delta rejected its leases with respect to airplanes N803DE and N804DE, whereupon the Indenture Trustee repossessed and sold the aircraft. The Indenture Trustee foreclosed on Northwestern's remaining plane and re-leased it to Delta pursuant to the Bingham Term Sheet. The Indenture Trustee filed three proofs of claim arising from Delta's default under the Northwestern Leases. The claims for N803DE and N804DE were for SLV less sale proceeds, and the claim for N182DN was for the lease rejection damages stipulated in the Bingham Term Sheet.
DFO was the Owner Participant in leveraged leases of eight aircraft (tail numbers N914DL, N915DL, N916DL, N954DL, N955DL, N956DL, N957DL, and N958DL). The Indenture Trustee foreclosed on three of DFO's aircraft and re-leased them to Delta pursuant to the Bingham Term Sheet (N914DL, N915DL, and N916DL). With respect to the other five aircraft, Delta and the Indenture Trustee entered into restructuring agreements under which DFO's interest in the aircraft was foreclosed out. The restructuring agreements (as under the Bingham Term Sheet) provided for new leases and stipulated lease rejection damages (calculated by reducing SLV by the present value of the restructured lease and the residual value of the aircraft).
AT & T was the Owner Participant in leveraged leases involving seven aircraft (tail numbers N131DN, N178DN, N660DL, N962DL, N963DL, N964DL, and N965DL). The Indenture Trustee foreclosed on all of AT & T's aircraft and re-leased them to Delta pursuant to the Bingham Term Sheet.

B. Objections to TIA Claims of Owner Participants
Appellants filed claims under their TIAs for tax losses that arose when the Indenture Trustees foreclosed on the aircraft, forcing Appellants to recapture prior accelerated depreciation deductions. See 26 U.S.C. § 1245(a). Delta decided to object to such tax indemnification claims brought by leveraged lease Owner Participants. Because Delta faced hundreds of such claims, totaling over $1.5 billion in aggregate, the bankruptcy court approved procedures permitting Delta to designate objections to selected sets of TIA claims, which would serve as "test cases" governing the disposition of similar claims. The bankruptcy court upheld the objections of Delta and the official committee to the claims of DFO, Northwestern, and AT & T.
The objection to DFO's claims, designated "TIA/SLV Objection 1," addressed TIAs providing that no payment would be due if a loss arose as a result of "any event whereby a party to any of the Operative Documents is required to pay" SLV. The objection to Northwestern's claims, designated "TIA/SLV Objection 2," addressed TIAs providing that no payment would be due if a loss arose as a result of "any event whereby the Lessee pays [SLV] or an amount determined by reference [to SLV]." The objection to AT & T's claims, designated "TIA/SLV Objection 5I," addressed TIAs providing that no payment would be due if a loss arose as a result of "[a]ny event whereby the Lessee pays an amount equal to Stipulated Loss Value."

C. The Bankruptcy Court's Ruling
The bankruptcy court upheld each of the three categories of objections on the following reasoning. First, the court reasoned that discharge of a debt in bankruptcy is effectively payment of the debt. *145 The court reviewed dictionary definitions of "pay" and "paid," which provided that a payment is an event that "discharge[s]" a debt. In re Delta Air Lines, Inc., 381 B.R. 57, 68-69 (Bankr. S.D.N.Y.2008). The court reasoned that "[t]he only meaning of pay/paid/pays which can rationally be ascribed to such terminology in the context of an insolvent and bankrupt airline/lessee is the common dictionary meaning of payment in the sense of discharge of the indebtedness." Id. at 82. (The court rejected Claimants' argument that, in light of the purpose of the exclusionary provisions, "pays SLV" could only refer to payment of the full amount of SLV, as depending on a "narrow and eccentric meaning of `pay.'" Id. at 69.) Because each Indenture Trustee's claim for SLV would be discharged in Delta's bankruptcy, each SLV had been "paid" within the meaning of the TIA, with the consequence that a TIA claim could not be asserted. Id. at 71.
The court found additional basis for rejecting DFO's claims in the specification of DFO's exclusionary language that Delta would not be obligated to make a payment under the TIA as a result of "any event whereby [Delta was] required to pay" SLV. The court reasoned that, in each case, it was undisputed that such an "`event' has happenedby reason of Delta's [default], the indenture trustee has demanded that Delta pay, and Delta `is required to pay,' SLV under ... the Lease." In re Delta Air Lines, Inc., 370 B.R. 552, 559 (Bankr. S.D.N.Y. 2007). The court thus found that in any case where the Indenture Trustee had demanded payment of SLV, Delta had been "required to pay" SLV, with the consequence that the Owner Participant was barred from asserting a claim under a TIA containing such a carveout.
Finally, the court focused on the language in Northwestern's agreements that Delta would not be obligated to make a payment under a TIA if it paid the Indenture Trustee "an amount determined by reference [to SLV]." It concluded that the distribution to an Indenture Trustee of a pro rata share of its SLV claim was such an amount, as the amount of the distribution would be determined as a percentage of the full SLV claim. Id. at 562. The court also concluded that payments to the Indenture Trustee for stipulated lease rejection damages (as described in the Bingham Term Sheet and similar agreements) were "amount[s] determined by reference" to SLV, because the damages were calculated using SLV as a starting point. The court thus held that in any case where Delta had paid a percentage of (1) SLV or (2) the lease rejection damages specified in the Bingham Term Sheet and similar agreements, Delta had paid "an amount determined by reference [to SLV]," and the Owner Participant would not be permitted to recover under a TIA containing such a carveout.

D. District Court Decision and Appeals to this Court
Each of the Claimants appealed to the United States District Court for the Southern District of New York from the bankruptcy court order disallowing its claims. On September 29, 2008, the district court issued a decision on all appeals affirming the rulings below, and generally adopting verbatim the reasoning of the Bankruptcy Court Orders. In re Delta Air Lines, Inc., No. 07-cv-7745, 07-cv-11437, 08-cv-2411, 08-cv-2449, 08-cv-6879, 2008 WL 4444001 (S.D.N.Y. Sept. 29, 2008). These related appeals followed.

DISCUSSION
All issues on appeal involve contract interpretation, and are thus subject to de novo review. Fin. One Pub. Co. v. *146 Lehman Bros. Special Fin., Inc., 414 F.3d 325, 339 (2d Cir.2005). Under the doctrine of Butner v. United States, 440 U.S. 48, 99 S.Ct. 914, 59 L.Ed.2d 136 (1979), principles of state law govern the interpretation of contractual provisions in bankruptcy. Under New York law, which governs by reason of the choice of law clauses in the TIAs, "[t]he fundamental, neutral precept of contract interpretation is that agreements are construed in accord with the parties' intent." Greenfield v. Philles Records, Inc., 98 N.Y.2d 562, 750 N.Y.S.2d 565, 780 N.E.2d 166, 170 (2002). While "[t]he best evidence of what parties to a written agreement intend is what they say in their writing," id. (internal quotation marks omitted), "[e]ach word must be considered along with not only all the other words that surround it, but also the history and education of the parties, the nature of the contract, the purposes of the parties, and all other relevant circumstances." 5 Corbin on Contracts § 24.21 (Joseph M. Perillo ed., 2009); accord Aron v. Gillman, 309 N.Y. 157, 128 N.E.2d 284, 288 (1955).

I. Purpose of Tax Indemnification Agreements and Their Exclusionary Provisions
To understand the Tax Indemnification Agreements at issue, it is necessary to take into account their purpose in the leveraged leases and the purpose of their exclusionary provisions. The purpose of each TIA was to compensate the Owner Participant in the event it was required to recapture accelerated depreciation it had taken. The Owner Participant's primary motivation in putting up 20% of the purchase price of the aircraft was to obtain the benefits of accelerated depreciation. The circumstance most likely to deprive the Owner Participant of that benefit was Delta's falling into insolvency. If Delta were forced by insolvency to declare bankruptcy or to default on its rent payments under a leveraged lease, in all likelihood the Indenture Trustee would foreclose on the aircraft, and the Owner Participant would be required to recapture accelerated depreciation it had taken. The TIA was designed to remedy that loss by obligating Delta to compensate the Owner Participant for it.
The purpose of the exclusionary provisions was simply to ensure that an Owner Participant not receive double compensation for depreciation recapture. Delta's default might give rise to two obligationsone to pay the Owner Participant as provided in the TIA, and a second to pay SLV to the Indenture Trustee. SLV was calculated to include an amount to compensate the Owner Participant for loss of accelerated depreciation. It was therefore theoretically possible, although as a practical matter highly improbable, that an Owner Participant might recover twice for the loss occasioned by its depreciation recapture. The improbability of such double recovery resulted from the terms of the Indenture waterfall, which provided that no portion of SLV collected by the Indenture Trustee would go to the Owner Participant until the Lenders had been paid in full. Thus, only in the unlikely event that Delta, after its default, paid virtually the entirety of SLV would the Owner Participant receive any portion of it. The purpose of the exclusionary provision was to eliminate any such double compensation, leaving the Owner Participant with a one-time compensation (a protection further provided in the terms of the Lease, which required that SLV be diminished to reflect any amounts paid by Delta under the TIA).

II. The Bankruptcy Court's Interpretation of the Agreements
Upon recognition of the purpose of the TIA and the function of its exclusionary *147 provision, it becomes apparent that the bankruptcy court's interpretation, far from reflecting the intentions of the contracting parties, was virtually certain to defeat those intentions.

A. Meaning of "Pay"
The bankruptcy court's rejection of the Owner Participants' claims was based on its ruling that an exclusionary clause, which canceled Delta's obligation to pay under the TIA if it "paid" SLV, was satisfied by the discharge in bankruptcy of Delta's obligation to pay SLV. The court's reasoning was based in part on alternative dictionary definitions of "pay" to the effect that an obligation is deemed "paid" once the obligation has been discharged.
We find this reasoning erroneous. Assuming that the reference, in the exclusionary clauses, to "payment" of SLV is ambiguous, the court's interpretation depended on a strained and improbable reading, which inevitably defeated the intentions of the contracting parties. Adoption of the bankruptcy court's construction of "pay" nullified Delta's obligation to pay the Owner Participant under the TIA upon the occurrence most likely to call its provisions into playDelta's insolvency. Delta's insolvency would predictably at once bring about (1) the foreclosure of the aircraft, causing the loss to the Owner Participant for which Delta promised compensation, and (2) Delta's bankruptcy and discharge, causing (under the bankruptcy court's interpretation) nullification of Delta's obligation to compensate the Owner Participant under the TIA. This interpretation of "pay" rendered the agreement nonsensical and self-defeating, by making it inoperative in the very circumstance for which it was designed.
Delta's obligation to pay compensation under the TIA, of course, did not provide the Owner Participant with complete protection. Since the Owner Participant's loss of tax benefits would likely come about as a result of Delta's insolvency and consequent bankruptcy, the Owner Participant could not realistically expect to collect 100% of what Delta would owe it under the TIA. What the Owner Participant could reasonably expect to receive was a claim against Delta in bankruptcy for the amount due to it under the TIA, and to recover ratably for that claim along with the other creditors. This contractual expectation was defeated by the bankruptcy court's interpretation, which treated Delta's bankruptcy as simultaneously causing the Owner Participant's loss for which Delta owed compensation under the TIA and nullifying Delta's obligation to compensate the Owner Participants for that loss. This was not a reasonable interpretation of the contract.
Nor is it an answer that, notwithstanding the cancellation of Delta's obligation to pay under the TIA, the Owner Participant retained the opportunity to recover for its loss of depreciation by way of SLV. As noted, under the terms of the Indenture waterfall, the Owner Participant would receive no part of SLV until the Lenders were fully compensated. By giving the Owner Participant a right to recover directly from Delta, the TIA placed the Owner Participant in equal status with other unsecured creditors, to the extent of its claim for depreciation recapture. Relegating it to recover only indirectly through the indenture waterfall, from payment of SLV, deprived the Owner Participant of that contractual entitlement and defeated the purpose of the contract.
Notwithstanding that dictionary definitions of "pay" include this strained alternative, the bankruptcy court was not at liberty to adopt it as the meaning of the contractual term, when that was plainly *148 not the understanding of the contracting parties.[3]

B. Meaning of "Required to Pay"
The bankruptcy court's interpretation of the "required to pay" language in DFO's TIAs was no less flawed. The court found that "[t]here can be no dispute that [an excluded event] has happenedby reason of Delta's [Lease default], the indenture trustee has demanded that Delta pay, and Delta `is required to pay,' SLV under Section 15(e) of the Lease." In re Delta Air Lines, Inc., 370 B.R. at 559. Though it is not entirely clear, the court's reasoning seems to be that Delta is "required to pay" SLV whenever an Indenture Trustee makes a legally supported demand for payment of SLV, whether or not that demand is met. In other words, the bankruptcy court held that whenever an Indenture Trustee properly demands of Delta that it pay SLV, Delta is released from its obligation under the TIA to indemnify the Owner Participant for its tax losses, regardless of whether Delta ever pays any part of SLV to the Indenture Trustee. For all the reasons just discussed, that interpretation is patently at odds with the intent of the parties in contracting for the TIAs.[4]

C. Meaning of "Pay SLV or an Amount Determined by Reference Thereto"
Northwestern's agreements, which provide that Delta is excused from paying anything under the TIA where it "pays [SLV] ... or an amount determined by reference thereto," present a closer questionbut only marginally soas such language arguably contemplates circumstances in which payment of an amount other than SLV will satisfy Delta's obligation to the Owner Participant. Delta argues that, pursuant to this language, it owes nothing to Northwestern, because in each case it paid the Indenture Trustee either (1) a percentage of SLV net of the proceeds of the sale of the aircraft, or (2) a percentage of the stipulated lease rejection damages calculated under the Bingham Term Sheet using a formula that started from SLV. Delta argues that in each case it thus literally paid "an amount determined by reference [to SLV]."
In context and in light of the purpose of the agreements, we think it likely that the phrase "an amount determined by reference thereto" was intended to indicate that Delta could discharge its obligation under the TIAs by payment of the amount of SLV, reduced in accordance with certain *149 Lease-sanctioned offsets, such as those for fair market value, sale proceeds, insurance revenues, and government receipts, in a manner that would result in realization of the full value of SLV. However, we need not definitively resolve the meaning of the phrase; we need only decide, as above, that, as among the various possible meanings of an ambiguous contract term, the parties could not have intended that payment of any percentage of SLV would discharge Delta's obligations under the TIAs. By ruling that partial payment of the Lease claims, in however small an amount, satisfied the exclusion, the bankruptcy court effectively nullified the TIAs by stripping them of their ability to protect the Owner Participant in the event of Delta's default.
The problem with the interpretation urged by Delta is even clearer if one considers its consequences in a non-bankruptcy context. The tax benefits secured by the TIAs were crucial to the Owner Participants' agreement to enter into the leveraged leases. It cannot possibly be that the parties understood that those benefits could be eliminated as the result of any Delta payment to the Indenture Trustee, so long as it was determined by reference to SLV, notwithstanding that such payment would in no way benefit the Owner Participant. Delta and the Indenture Trustee could not, consistent with the parties' contractual intent, discharge Delta's obligations to the Owner Participants under the TIAs by agreeing to cancel its SLV liabilities for ten cents on the dollar, of which no portion would go to the Owner Participants. Absent an understanding that the agreements would operate differently in bankruptcy, or a specific statute authorizing different treatment in bankruptcy, see Travelers Cas. & Sur. Co. of Am. v. Pac. Gas & Elec. Co., 549 U.S. 443, 448, 127 S.Ct. 1199, 167 L.Ed.2d 178 (2007), they cannot do so here.

III. Delta's Other Arguments for Affirmance
As an alternative basis for affirmance, Delta argues that a single loss can only give rise to a single claim in bankruptcy, and that Appellants seek to be compensated for losses on account of which another set of claimsthe SLV claimshas already been allowed. Delta presses this argument notwithstanding that the TIA claims and SLV claims arise under agreements (1) between different parties, (2) addressing different events, and (3) providing for different remedies. In light of these facts, we agree with the bankruptcy court that:
Each agreement was freely negotiated and fully supported by fair consideration on both sides. If a component of the SLV claim under the Lease is calculated by reference to the owner participant's tax consequences which are indemnified under the TIA (the "overlap" Delta objects to), so be it. That is what Delta agreed to and what both the owner participant and the indenture trustee relied upon in negotiating the agreements. If Delta has contracted to pay duplicative claims, then it must pay bothit cannot repudiate its duty to party A under contract A by asserting that it contracted to pay the same amount to party B under contract B.
In re Delta Air Lines, Inc., 370 B.R. at 557.
Delta argues that the bankruptcy court's decision in this respect "rested on three errors of law." Delta Br. at 21. First, Delta argues that the court failed to appreciate that "[a]n agreement to pay an amount, upon default, that is not based on the other party's actual loss is contrary to public policy and void as a penalty." Id. However, as the bankruptcy court noted, *150 "the general legal principle that precludes double liability for a single injury or loss has never been applied by any court to void separate contract obligations owed to different parties under different contracts." In re Delta Air Lines, Inc., 370 B.R. at 557. Moreover, even if it were true as a general principle that "[a]n agreement to pay an amount... that is not based on the other party's actual loss is ... void as a penalty," Delta Br. at 21, that principle would be of limited applicability in the instant case (to bar Appellants' claims), where it is uncontested that Appellants have suffered an actual loss that has not been compensated.
Next, Delta argues that the bankruptcy court erred in finding that its obligations under the TIAs and Leases were owed to different parties, because the Indenture Trustees are mere assignees of the Owner Trusts' interests in the Leases, and "[f]or tax purposes, the Owner Trust[] has no separate existence; the Owner Trust[] and Owner Participant are the same entity." Delta Br. at 22 (emphasis added). As Appellants point out, this argument is unavailing because the tax regulations specify that the tax treatment of single-member entities is independent of their corporate separateness for all other purposes, including entry into and enforcement of contracts. See, e.g., Treas. Regs. §§ 301.7701-1 to -3.
Finally, Delta argues that the claims asserted against a debtor in bankruptcy are "supposed to equal the out-of-bankruptcy right of payment." Delta Br. at 23. In effect, Delta argues that allowing Appellants' claims would violate the bankruptcy policy of equality of distribution among creditors, see, e.g., Musso v. Ostashko, 468 F.3d 99, 104 (2d Cir.2006), because the collective recovery of the Appellants and Indenture Trustees would exceed their pro rata share of entitlements. To the extent that this is true, it is Delta's own fault: the problem exists because Delta (and the creditors' committee) agreed, under the Bingham Term Sheet, the other restructured lease agreements, and Delta's plan of reorganization, to pay the Indenture Trustees more than they were entitled tonamely, their share and the Owner Participants' share. While Delta is correct that the aggregate amounts claimed by the Owner Participants and the Indenture Trustees exceeded their proper aggregate share to the extent of the duplication of the Owner Participants' claims under the TIAs, the proper remedy was disallowance of the claims of the Indenture Trustees to the extent they were predicated on the Owner Participants' TIA entitlements.

CONCLUSION
For the foregoing reasons, the ruling of the district court is VACATED, and the cases are REMANDED with instructions that Delta's objections to Appellants' claims be overruled.
NOTES
[1]  Pursuant to the parties' notice of the dissipation of the Post-Effective Date Committee, The Clerk of Court is directed to amend the official captions in these cases to conform to the listing of the parties above.
[2]  On October 23, 2009, after we heard oral argument in these cases, appellants Bell Atlantic Tricon Leasing Corporation and Verizon Capital Corp. withdrew their appeal docketed at No. 08-5296-bk.
[3]  The bankruptcy court characterized "full payment" as a "narrow and eccentric" definition of the term "payment." In re Delta Air Lines, Inc., 381 B.R. at 69. In our view, however, that interpretation is consistent with common usage and understanding. By contrast, a definition of "payment" which permits the obligee to receive nothing, while the obligor is excused from the obligation by virtue of a grace conferred by law so as to enable insolvent debtors to get a fresh start, is not. If asked whether a creditor had received "payment" of a debt owed to him, in circumstances where the creditor received nothing and the debtor was discharged from the obligation by a bankruptcy court, we think that most persons would answer that it had not.
[4]  Moreover, the bankruptcy court's finding that "the [I]ndenture [T]rustee [for DFO's leveraged leases] has demanded that Delta pay ... SLV," 370 B.R. at 559, is unsupported by the record. The Indenture Trustee foreclosed on all eight of DFO's aircraft after Delta's default under the Leases, but re-leased each of them to Delta pursuant to a renegotiated lease. In each case, the Indenture Trustee filed a claim for stipulated lease rejection damagesnot SLV. Accordingly, Delta was not "required to pay" SLV in even the barest sense applied by the bankruptcy court.
