OPINION AND ORDER

MUKASEY, District Judge.

This diversity suit concerns’liability insurance coverage for personal injury claims arising from exposure to asbestos. Defendant and third-party plaintiff Tread-well Corporation (“Treadwell”) installed and otherwise handled products containing asbestos between the 1940s and the 1980s, during some of which time Treadwell was covered by primary and excess liability insurance. In 1994, Treadwell and several of its liability insurers sought declaratory relief clarifying the extent to which Tread-well was entitled to indemnification for claims arising out of its asbestos-related activities (the “Asbestos Claims”). In 1997, however, Treadwell and all parties other than the United States Fire Insurance Company (“U.S.Fire”) and the Home *82 Insurance Company (“Home Insurance”) settled their disputes. Treadwell’s third-party claims against U.S. Fire and its cross-claims against Home Insurance are the only disputes remaining.

Both Treadwell and U.S. Fire now move for summary judgment pursuant to Fed. R.Civ.P. 56. By stipulation, the parties agree for the purposes of these motions that to the extent a person asserting a claim against Treadwell was injured by exposure to asbestos, he was injured at all points in time from initial exposure through the date his claim was filed or he died. (StipJ 3) 1 Thus, the parties agree that some of those making claims against Treadwell (the “Asbestos Claimants”) might have suffered injury continuously from the 1940s, when Treadwell’s asbestos-related activities began, through the 1990s, when the most recent Asbestos Claimants filed suit — a span that includes a period of more than 20 years when Treadwell did not have insurance as well as a period of 20 years in which it was insured under both primary and excess policies.

U.S. Fire provided Treadwell excess insurance from 1970 through 1972. By the terms of its policies, U.S. Fire agreed to assume coverage responsibility upon exhaustion of Treadwell’s primary insurance policies for-these years, which were issued by the American Mutual Liability Insurance Company (“AMLIC”). AMLIC is now insolvent, however, so Treadwell assumed in the 1997 settlement some of the liability that might otherwise have been borne by AMLIC. As discussed below, the principal question before the court, therefore, is whether this liability assumed by Treadwell can be allocated entirely to the AMLIC policy years, which would exhaust the AMLIC policies and trigger U.S. Fire’s coverage. Resolving this question, however, requires consideration of several subsidiary questions, including: (1) whether this court has authority to order allocation of Treadwell’s liability for the Asbestos Claims among all potentially liable parties; (2) whether Treadwell itself must assume some share of the liability for the years in which it was uninsured; and (3) what effects, if any, Treadwell’s settlements with its other insurers have on U.S. Fire’s liability. Whether, and to what extent, U.S. Fire is obligated to defend or indemnify Treadwell for any of the Asbestos Claims turns on the answers to these questions.

For the reasons stated below, I conclude that the primary insurance polices underlying U.S. Fire’s policies likely are not yet exhausted and, therefore, that U.S. Fire has no present obligation to defend or indemnify Treadwell. Accordingly, U.S. Fire’s motion for summary judgment will be granted, and Treadwell’s denied, subject to confirmation of that likelihood through examination of the individual Asbestos Claims in conformity with the rulings below.

The following relevant facts are undisputed, unless otherwise noted. Treadwell, a privately held corporation organized under Delaware law with its principal place of business in Connecticut, manufactures, repairs and maintains oxygen generators used on nuclear submarines. (Compl. ¶ 4; 9/16/98 Johnson Aff. ¶ 4) 2 From sometime in the 1940s to sometime in the 1980s, however, Treadwell served also as a contractor or subcontractor, primarily at utility powerhouse sites in the New York metropolitan area. (9/16/98 Johnson Aff. ¶ 4) As part of this work, Treadwell installed and otherwise handled material containing asbestos. (Id; see Stip. ¶ 1) At no point did Treadwell manufacture, sell or distrib *83 ute asbestos or asbestos-containing products. (Stip^ 1)

In the late 1980s, Treadwell began to be named as a defendant in lawsuits alleging bodily injury arising from exposure to asbestos. (Id.) A large number of these Asbestos Claims have been settled, dismissed or otherwise disposed of, but as of August 31, 1998, there were more than 6000 such cases still pending against Treadwell, predominantly in New York state court. (9/16/98 Johnson Aff. ¶ 15;. see Antonucci Aff. ¶ 2; Stip. ¶ 1) 3 Nearly all the plaintiffs in these cases allege exposure to asbestos prior to January 1, 1970, the effective date of U.S. Fire’s excess insurance policies. (Antonucci Aff. ¶ 4. But see U.S. Fire Local Rule 56.1 Statement ¶ 9 (noting that there “were at least 39 Powerhouse Claimants who did not begin working at the powerhouses until 1970 or later and so could not have been first exposed to asbestos at the powerhouses prior to 1970”))

A. Treadwell’s Insurance Coverage

Treadwell was uninsured prior to 1967. 4 (Reilly Aff. ¶ 46) However, from January 1, 1967 until July 1, 1986, a period Treadwell refers to as “the Coverage Block,” the company was insured under several primary comprehensive general liability (“CGL”) policies: From 1967 through 1969, and again from 1973 through June 20, 1983, Treadwell was' insured under policies issued by CIGNA Property and Casualty Insurance Company, its subsidiaries and affiliates (“CIGNA”); from 1970 through 1972, the company was insured by AMLIC; and from June 20, 1983 through July 1, 1986, Treadwell was insured by the Travelers Insurance Companies (“Travelers”). (Treadwell Local Rule 56.1 Statement ¶ 33) For all of this period, Treadwell was insured also under excess CGL policies, triggered by exhaustion of the underlying primary insurance: From 1967 through 1969, and again from 1973 through June 20, 1985, Treadwell was insured under excess CGL policies issued by CIGNA; and from 1970 through 1972, Treadwell was insured under excess CGL policies issued by U.S. Fire. 5 (Id. ¶33) Thus, Treadwell’s insurance coverage for the years relevant to these motions was as follows:

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In addition to these insurance policies, which were purchased directly by Tread-well and which provided comprehensive coverage within their respective periods, Treadwell was a named insured on several policies purchased by utilities covering work done at their sites. The United States Fidelity & Guaranty Co. (“USF & G”) and the Commercial Union Insurance Company (“CU”) each issued primary insurance policies naming Treadwell as an insured. (9/16/98 Johnson Aff. ¶ 8(b)) Exhaustion of the USF & G policy triggered an excess policy issued by Home Insurance, which named Treadwell also as an insured. (Id.)

B. The U.S. Fire Policies

As noted, Treadwell purchased primary liability insurance from AMLIC for the years 1970, 1971 and 1972. For each of these three years, AMLIC’s coverage was limited to $100,000 per person, $300,000 per occurrence and $300,000 in “products aggregate” for bodily injuries. (Stip. ¶ 7 & Ex. C) To insure against liability above these limits, Treadwell purchased two excess umbrella policies from U.S. Fire, which together covered the same period. (Id. ¶¶ 4-6)

The U.S. Fire policies, like Treadwell’s other insurance policies, are CGL policies, standard-form industry contracts dating to the 1960s. See American Home Prods. Corp. v. Liberty Mut. Ins. Co., 565 F.Supp. 1485, 1500-03 (S.D.N.Y.1983) (discussing the history and purpose of the CGL policies), aff 'd as modified by 748 F.2d 760 (2d Cir.1984). To the extent relevant here, those policies provide that U.S. Fire will indemnify Treadwell for “ultimate net loss” arising from personal injury or property damage in excess of the policy limits of the AMLIC policies, up to $10 million in the aggregate for each policy year and excluding “liability for contamination or pollution ... or any injuries or damages resulting therefrom.” (E.g., Stip. Ex. A at 1, 4-5) Additionally, the policies provide that U.S. Fire will “defend any suit” against Treadwell alleging a loss covered by the policies but “not covered” by the AMLIC policies or by “any other underlying insurance.” (Id. at 1)

The policies define “ultimate net loss” as the total of the following sums “with respect to each occurrence”:

(1) All sums which the insured, or any company as his insurer, or both, become legally obligated to pay as damages, whether by reason of adjudication or settlement, because of personal injury ... to which this policy applies, and

(2) All expenses incurred by the insured in the investigation, negotiation, settlement and defense of any claim or suit seeking such damages....

(Id. at 2) In turn, the policies define “occurrence” as “a continuous or repeated exposure to conditions which unexpectedly and unintentionally causes injury to persons or tangible property during the policy period. Ml damages arising out of such exposure to substantially the same general *85 conditions shall be considered as arising out of one occurrence.” (Id. at 5)

Finally, to the extent relevant here, the U.S. Fire policies both contain “other insurance” clauses. Those clauses read in relevant part: “If other collectible insurance with any other insurer is available to the insured covering a loss also covered hereunder ... the insurance hereunder shall be in excess of, and not contribute with, such other insurance.” (Id. at 3)

C. Early Negotiations, the Interim Agreement and the Commencement of Litigation

Soon after the Asbestos Claims were initiated, Treadwell provided notice and sought reimbursement for defense and indemnity against its principal primary insurers — CIGNA, Travelers and AMLIC. (9/16/98 Johnson Aff. ¶ 6) After initially disclaiming coverage, AMLIC declared insolvency and went into liquidation. (Id.) As a result, New York State Superintendent of Insurance Edward Muhl (the “Superintendent”) was appointed ancillary receiver for AMLIC. (Id.)

With AMLIC in receivership, Treadwell, CIGNA and Travelers negotiated over defense and indemnification for the Asbestos Claims. (Id. ¶¶ 6-7) In December 1991, the three companies reached an agreement (the “Interim Agreement”) dividing the relevant costs. (Id. ¶7 & Ex. 2) First, CIGNA and Travelers agreed to assume two-thirds and one-third, respectively, of defense costs retroactive to May 7, 1991. (Id.) Second, with Treadwell substituting for AMLIC — presumably due to the latter’s insolvency — the three companies agreed to assume the following proportions of responsibility for indemnification: CIG-NA, 71.4%; Treadwell, 17.2%; and Travelers, 11.4%. (Id.) According to Treadwell, this allocation of indemnification responsibility was based on the proportion of years CIGNA, AMLIC and Travelers, respectively, were each “on the risk” during the so-called Coverage Block — that is, between January 1, 1967 and July 1, 1986, or the period of time in which Treadwell had insurance coverage. (Treadwell Local Rule 56.1 Statement ¶ 30) The letter memorializing the Interim Agreement, however, does not specify the basis for the parties’ allocation. 6 (9/16/98 Johnson Aff. Ex. 2)

Notwithstanding the Interim Agreement, Treadwell pressed to obtain coverage for its losses as the number of Asbestos Claims against it multiplied. (Id. ¶ 8) First, the company asserted claims in the AMLIC liquidation proceedings. (Id. ¶ 8(a)) Second, it provided notice and asserted claims for defense and indemnity against USF & G, CU and Home Insurance. (Id. ¶ 8(b)) Finally, by letter dated February 7, 1992 from its insurance broker, Treadwell notified U.S. Fire about its “potential asbestos liability” and requested the carrier’s “immediate attention” to the matter. (Reilly Aff. Ex. D; see 9/16/98 Johnson Aff. ¶ 9)

U.S. Fire responded with a letter of its own, dated August 12, 1992. (Reilly Aff. Ex. E) In that letter, U.S. Fire rejected “any present duties” to indemnify or defend Treadwell, citing several grounds. (Id. at 4) First, noting its duty to indemnify only upon exhaustion of the underlying primary insurance, U.S. Fire contended that “there is no indication that underlying limits are at or near exhaustion.” (Id.) Second, acknowledging a duty to defend any suit alleging a covered loss not covered by other insurance, the carrier argued that “there is no indication that the alleged injury is not covered by underlying insurance.” (Id.) Finally, citing the “other insurance” provision in each of its policies, *86 U.S. Fire asserted that, “until all underlying insurance is paid, no duties can arise under the U.S. Fire policies.” (Id.)

In addition to providing these three reasons for rejecting “any present duties” under its policies, U.S. Fire raised several “additional serious questions of coverage” in its letter as follows:

To the extent “personal injury” as defined by the policy did not take place there would be no coverage for the claims. Further, to the extent “personal injury” as defined by the policy took place but was not within our policy period, there would be no coverage for the claim. We reserve the right to deny coverage on this basis.

.... Further, to the extent an “occurrence” as defined by the policies took place but was not within our policy period, there would be no coverage for the claims. We reserve the right to deny coverage on this basis.

In addition, both policies contain a contamination and pollution exclusion .... To the extent the damage alleged falls within the purview of this exclusion there would be no coverage for the claim. We reserve the right to deny coverage on this basis.

(Id. at 4-5) Further, U.S. Fire explicitly reserved “the right to assert any and all policy defenses including those discussed above and any not mentioned herein.” (Id.) In addition, the carrier asked Tread-well to keep it informed “if underlying limits are approaching exhaustion.” (Id.)

USF & G, CU and Home Insurance declined coverage of Treadwell’s claims also. (9/16/98 Johnson Aff. ¶ 10) Thereafter, USF & G commenced this action, naming Treadwell, CU and Home Insurance as defendants and seeking a declaratory judgment as to the nature and extent of its obligations to Treadwell. Treadwell filed an answer, counterclaims and cross-claims, in essence seeking a declaratory judgment regarding the carriers’ obligations to defend and indemnify and seeking also damages for breach of contract.

In May 1996, Treadwell impleaded Travelers, CIGNA, U.S. Fire and the Superintendent — the last as ancillary receiver for AMLIC — seeking a declaratory judgment as to the carriers’ obligations and, with respect to Travelers and CIGNA, seeking damages for breach of contract. To the extent relevant here, Treadwell’s initial third-party complaint acknowledged that “the limits of the underlying coverage for the excess policies” issued by U.S. Fire had “not yet been exhausted.” (1996 Compl. ¶¶ 56, 127) 7 Nevertheless, Tread-well sought “a judicial declaration that upon the exhaustion of the underlying coverage ... U.S. Fire is required to indemnify Treadwell.” (Id. ¶ 130)

D. Settlement with the Other Insurers

Following commencement of the third-party action, Treadwell entered into settlement negotiations with several of its insurance carriers. (E.g., 9/16/98 Mensch Aff. Exs. A1-A4) These negotiations led, in April and May 1997, to two settlement agreements. First, Treadwell and the Superintendent agreed to settle all of Tread-well’s claims with respect to AMLIC (the “AMLIC Agreement”). (Stip. ¶9 & Ex. E) Pursuant to this agreement, the Superintendent agreed to pay Treadwell $475,-000 from the New York Property/Casualty Insurance Security Fund (the “New York Insurance Fund”). (Stip. Ex. E ¶ 1) In exchange, Treadwell gave the Superintendent and all other relevant parties a general release “from any liability for any past, present or future claim whatsoever arising under any and all insurance policies which may have been issued by [AMLIC] to Treadwell, known or unknown” — including the policies in effect from 1970 through 1972. (Id. If 2)

*87 Second, Treadwell entered into a “Settlement and Claims Handling Agreement” (the “Settlement Agreement”) with USF & G, CU, Travelers and CIGNA. (Stip. ¶ 11 & Ex. F (“Agrmt.”)) To the extent relevant here, the Settlement Agreement allocates responsibility for payment of defense and indemnity costs arising from the Asbestos Claims among Treadwell, USF & G, CU, Travelers and CIGNA. 8 The Settlement Agreement specifies, first, that defense costs are to be allocated among the four settling insurers, with CIGNA assuming roughly three-quarters of the costs; Travelers, approximately 15%; and USF & G and CU, about 6% each. (Agrmt. at 10-14) Additionally, the Settlement Agreement designates CIGNA as the “Lead Insurer” and authorizes CIG-NA, in that capacity, to manage the defense and disposition of the Asbestos Claims on behalf of the other parties. (Id. at 29-32)

Second, and more significant for these motions, the Settlement Agreement allocates responsibility among Treadwell and the four settling insurers for indemnity payments. Specifically, the Settlement Agreement provides that CIGNA will assume 71.4% of the relevant liability; Travelers, 13.4%; and Treadwell, 15.2%, with USF & G and CU contributing toward that figure with respect to claims arising from the specific sites covered by their policies. (Id. at 16-18) The Settlement Agreement specifies also that upon exhaustion of any primary insurer’s liability, “Treadwell and/or Treadwell’s excess and/or umbrella insurers” will assume that insurer’s liability prospectively. (Id. at 20-21, 23) Finally, the Settlement Agreement notes that any funds received by Treadwell through settlement with the Superintendent or U.S. Fire are “for the sole benefit of Treadwell,” unless such funds exceed Treadwell’s obligations under the Settlement Agreement, in which case the excess is to be allocated “solely to or for the benefit of the Insurers.” (Id. at 27-28)

The Settlement Agreement specifies that the parties’ liability for both defense costs and indemnity is several. (Id. at 10, 16) However, it does not state explicitly the basis for its allocation of liability among the parties. Nevertheless, the Settlement Agreement includes as an exhibit a schedule listing the policies provided by the settling insurers to Treadwell (id. Ex. A), and from this list — along with provisions in the Settlement Agreement governing adjustments to the parties’ respective liabilities (e.g., id. at 20) — an allocation formula can be inferred: The shares of the indemnification payments assumed by CIGNA, Travelers and Treadwell under the Settlement Agreement correspond roughly to the proportion of time between January 1, 1967 and July 1, 1986 — the so-called Coverage Block — that each of CIG-NA, Travelers and AMLIC provided primary coverage to Treadwell. 9 (See also Treadwell Local Rule 56.1 Statement ¶¶ 30-31)

E. Correspondence Between Treadwell and U.S. Fire

In the months leading up to the Settlement Agreement, Treadwell notified U.S. Fire several times, directly and indirectly, about the ongoing negotiations with the other carriers, and invited U.S. Fire to join the developing agreement or to negotiate its own. (9/16/98 Mensch Aff. Exs. A1-A9) Following these invitations, representatives of U.S. Fire communicated with representatives of Treadwell — in person, by telephone and by letter — requesting details regarding the Settlement Agreement *88 and other information, including the liability limits of Treadwell’s primary insurance policies and the total payments made by Treadwell itself in connection with the Asbestos Claims. (E.g., id. Ex. A5) Tread-well provided this information, including, on March 19, 1997, “a chart reflecting Treadwell’s insurance coverage for the years 1967 — 1986, the years contained in the coverage block agreed among Tread-well, [CIGNA, Travelers, USF & G and CU].” (Id. Ex. A7; see also id. Exs. A6, A8)

On April 10, 1997, Treadwell’s counsel, Martin Mensch, Esq., wrote to U.S. Fire’s counsel, Vincent Reilly, Esq., questioning the support for “two separate positions” which Reilly had indicated in a previous conversation U.S. Fire “may take ... in attempt to avoid its obligations under the excess policies issued to Treadwell”: first, that U.S. Fire was not obligated to “drop down” and cover the Asbestos Claims until all of Treadwell’s primary insurance coverage was exhausted; and second, that the “so called [sic ] pollution exclusion applies.” (Reilly Aff. Ex. AA) By letter dated May 20, 1997, Reilly repliéd, pointing to “the ‘Other Insurance’ clause of the policies” as support for U.S. Fire’s exhaustion argument, and opining that the pollution exclusion clause “speaks for itself.” (Id Ex. BB)

F. The Parties’ Arguments for Summary Judgment

As noted, Treadwell purchased primary liability insurance from AMLIC for the years 1970,1971 and 1972, up to a limit of $300,000 in “products aggregate” for bodily injury claims. As of September 1998, Treadwell had paid or agreed to pay an aggregate of $944,984 in indemnity payments, allegedly pursuant to the Settlement Agreement. (11/17/98 Johnson Aff. ¶ 4; see also 9/16/98 Johnson Aff. ¶ 20; 11/2/98 Mensch Aff. ¶ 10) 10 Contending that this payment represents the amount it has paid in lieu of AMLIC for the three years that AMLIC provided primary coverage, Treadwell seeks a declaration that the AMLIC policies are now exhausted and, thus, that U.S. Fire must “drop down” to indemnify and defend the Asbestos Claims. 11 (Compl.lffl 34, 39)

In seeking summary judgment, U.S. Fire no longer presses the two positions taken by Reilly in his May 20, 1997 letter. 12 Instead, it cites Stonewall Insurance Co. v. Asbestos Claims Management Corp-, 73 F.3d 1178, 1202 (2d Cir.1995), modified on denial ofreh’g, 85 F.3d 49 (2d Cir.1996), and argues for application of the so-called “proration-to-the-insured approach” to allocating liability among *89 Treadwell and its insurers. According to this approach, U.S. Fire contends, Tread-well’s payments should be allocated evenly across all the years triggered by the Asbestos Claims for which the company did not have liability insurance — a period that for some of the Asbestos Claims probably stretches from sometime in the 1940s, when Treadwell’s asbestos-related activities began, through 1967 and, again, from 1970 through 1972. Allocated in this manner, U.S. Fire argues, Treadwell’s $944,984 in payments would not come close to exhausting the liability limits of the AMLIC policies, because only a small portion of those payments would count toward the years 1970, 1971 and 1972. Therefore, U.S. Fire asserts, it has no present duty to defend or indemnify Treadwell for any of the Asbestos Claims.

In support of its summary judgment motion and in response to U.S. Fire’s motion, Treadwell raises the following arguments:

(1) that U.S. Fire is barred by operation of various doctrines including waiver, equitable estoppel, judicial estoppel and collateral estoppel from arguing that Treadwell’s payments should be allocated to years prior to 1967; and

(2) that assuming U.S. Fire may raise the proration-to-the-insured argument, Treadwell can nevertheless allocate all its payments to the 1970-1972 period, for any one of three reasons:

(a) that the CGL policies Treadwell purchased from its primary insurers allow it to seek indemnification from any single insurer whose policy is triggered, subject only to the liability limits of that policy;

(b) that even assuming allocation of liability among multiple insurers is warranted, allocation of liability to Treadwell for periods during which it was uninsured is improper; or

(c) that U.S. Fire is bound by the terms of the Settlement Agreement and/or the AMLIC Agreement to accept allocation of some or all of Tread-well’s payments to the AMLIC policy periods.

One way or another, in short, Treadwell argues that U.S. Fire is bound by Tread-well’s agreement with its primary insurers to allocate liability based on the number of years each insurer was on the risk during the Coverage Block. Allocated in this manner, Treadwell argues, its $944,984 in payments exhausts the three AMLIC policies underlying U.S. Fire’s excess insurance policies, thus triggering U.S. Fire’s obligations to defend and indemnify.

II.

Summary judgment is mandated when “there is no genuine issue as to any material fact and ... the moving party is entitled to a judgment as a matter of law.” Fed.R.Civ.P. 56(c); see Anderson v. Liberty Lobby, Inc., 477 U.S. 242, 247-48, 106 S.Ct. 2505, 91 L.Ed.2d 202 (1986); Celotex Corp. v. Catrett, 477 U.S. 317, 322, 106 S.Ct. 2548, 91 L.Ed.2d 265 (1986); Matsushita Elec. Indus. Co. v. Zenith Radio Corp., 475 U.S. 574, 586, 106 S.Ct. 1348, 89 L.Ed.2d 538 (1986). In the present case, as the parties agree, no genuine issues of fact remain. (See U.S. Fire Mem. at’8; Treadwell Mem. at 51) There is no material issue of credibility, and all relevant facts are either stipulated or based on documents. Under these circumstances, either summary judgment or a decision on a stipulated record is appropriate. See, e.g., Uniroyal, Inc. v. Home Ins. Co., 707 F.Supp. 1368, 1372 (E.D.N.Y.1988). Indeed, final decision is especially appropriate where, as here, the dispositive issue involves construction of an insurance contract under New York law. See id. at 1372-78.

III.

Preliminarily, it is necessary to determine whether U.S. Fire is barred from arguing that the proration-to-the-insured approach applies. As noted, Treadwell argues that U.S. Fire is so barred by operation of various doctrines, including waiver, *90 equitable estoppel, judicial estoppel and collateral estoppel. I disagree.

A. Waiver

Treadwell’s contention that U.S. Fire waived its proration-to-the-insured argument is premised on Reilly’s failure to mention the argument in his May 20, 1997 letter to Mensch, or to challenge in any way the use of the Coverage Block as the alleged basis for allocating liability among Treadwell and its primary insurers. (See Treadwell Mem. at 22-24) To support its contention, Treadwell quotes New York v. AMRO Realty Corp., 936 F.2d 1420 (2d Cir.1991), in which the Second Circuit stated that, under New York law, “an insurer is deemed, as a matter of law, to have intended to waive a defense to coverage where other defenses are asserted, and where the insurer possesses sufficient knowledge (actual or constructive) of the circumstances regarding the unasserted defense.” Id. at 1431; see also Luria Bros. & Co. v. Alliance Assurance Co., 780 F.2d 1082, 1090-91 (2d Cir.1986); General Accident Ins. Group v. Cirucci, 46 N.Y.2d 862, 864, 414 N.Y.S.2d 512, 514, 387 N.E.2d 223 (1979) (per curiam). Because Reilly raised only two arguments in his letter, Treadwell reasons, U.S. Fire should be deemed as a matter of law to have waived all other defenses.

Reilly’s letter, however, did not constitute a notice of disclaimer within the meaning of New York law. Specifically, it was not an “unequivocal, unambiguous written notice, properly served.” Norfolk & Dedham Mut. Fire Ins. Co. v. Petrizzi, 121 A.D.2d 276, 277, 503 N.Y.S.2d 51, 53 (1st Dep’t 1986). To the contrary, Reilly’s letter merely responded to Mensch’s own April 10, 1997 letter, in which Treadwell’s counsel challenged two defenses to coverage that U.S. Fire had indicated it might raise. (See Reilly Aff. Ex. A) Thus, Tread-well itself determined the scope of Reilly’s letter, and the letter’s silence with respect to the issue of allocation cannot be considered “a voluntary and intentional relinquishment of a known right.” Albert J. Schiff Assoc., Inc. v. Flack, 51 N.Y.2d 692, 698, 435 N.Y.S.2d 972, 975, 417 N.E.2d 84 (1980); see also AMRO Realty, 936 F.2d at 1431 (“An ‘implied waiver ... exists when there is an intention to waive unexpressed, but clearly to be inferred from circumstances ....’” (quoting Kiernan v. Dutchess County Mut. Ins. Co., 150 N.Y. 190, 195, 44 N.E. 698 (1896)) (emphasis added) (omissions in original)); Gilbert Frank Corp. v. Federal Ins. Co., 70 N.Y.2d 966, 968, 525 N.Y.S.2d 793, 795, 520 N.E.2d 512 (1988) (“Waiver is an intentional relinquishment of a known right and should not be lightly presumed.” (citation omitted)). Accordingly, there was no waiver.

B. Equitable Estoppel

Treadwell invokes also the doctrine of equitable estoppel, which “has been applied where the insured has been prejudiced as a result of unreasonable delay in failing to disclaim.” Greater N.Y. Sav. Bank v. Travelers Ins. Co., 173 A.D.2d 521, 522, 570 N.Y.S.2d 122, 123 (2d Dep’t 1991); see also Appell v. Liberty Mut. Ins. Co., 22 A.D.2d 906, 906, 255 N.Y.S.2d 545, 547 (2d Dep’t 1964), aff'd, 17 N.Y.2d 519, 267 N.Y.S.2d 516, 214 N.E.2d 792 (1966); cf. Albert J. Schiff, 51 N.Y.2d at 679-99, 435 N.Y.S.2d at 974-75, 417 N.E.2d 84 (distinguishing the doctrines of waiver and equitable estoppel). Treadwell argues that U.S. Fire delayed unreasonably before raising its challenge to the Coverage Block, and that this delay caused Tread-well prejudice insofar as it might not have entered into the Settlement Agreement knowing of U.S. Fire’s objections. (See Treadwell Mem. at 24-26; see also 9/16/98 Mensch Aff. ¶¶ 5-6)

Equitable estoppel is inapplicable, however, for several reasons. First, despite the exchange of correspondence between the parties with respect to the Asbestos Claims going back as far as 1992, it does not appear that Treadwell formally asserted a claim for indemnity against U.S. Fire until at least May 1996, when the company *91 filed its initial third-party complaint. Even then, Treadwell did not allege that it was actually entitled to coverage from U.S. Fire; instead, Treadwell acknowledged that the AMLIC polices had “not yet been exhausted” and sought a judicial declaration that “upon the exhaustion” of those policies, U.S. Fire would be obligated to provide coverage. (1996 Compl. ¶¶ 56, 127,130) In these circumstances, U.S. Fire arguably had no duty to disclaim. See U.S. Underwriters Ins. Co. v. Congregar tion B’Nai Israel, 900 F.Supp. 641, 646 (E.D.N.Y.1995) (“Under New York Law, compliance with a notice-of-occurrence or notice-of-claim provision in an insurance contract is a condition precedent to an insurer’s liability under the policy.”), aff'd without opinion, 101 F.3d 685, 1996 WL 280089 (2d Cir.1996); of. Kamyr, Inc. v. St. Paul Surplus Lines Ins. Co., 152 A.D.2d 62, 66-67, 547 N.Y.S.2d 964, 967 (3d Dep’t 1989) (holding that an excess insurer’s duty to disclaim is triggered only when there is “a reasonable possibility that [its] excess coverage may be reached” (internal quotation marks and citation omitted)).

Moreover, notwithstanding Treadwell’s claim that the Coverage Block was established in the December 1991 Interim Agreement (see Treadwell Local Rule 56.1 Statement ¶ 29), it does not appear that Treadwell notified U.S. Fire about any “coverage block” until March 1997, when Treadwell provided to U.S. Fire “a chart reflecting Treadwell’s insurance coverage for the years 1967—1986, the years contained in the coverage block agreed among Treadwell, [CIGNA, Travelers, USF & G and CU].” (9/16/98 Mensch Aff. Ex. A7) Before that date, there is no mention in the record of any coverage block—or, more to the point, any indication that U.S. Fire was made aware of such a concept— nor any evidence that Treadwell itself had definitively settled upon 1967 to 1986 as the relevant period. Indeed, in its initial third-party complaint, Treadwell identified at least two insurance policies which it believed were in effect prior to 1967. (See 1996 Compl. ¶ 27) Additionally, the Superintendent produced evidence in July 1996 that Treadwell had filed claims for coverage based on AMLIC policies going back as far as 1947. (See Reilly Aff. Ex. B:I)

At the same time, Treadwell was on notice prior to executing the Settlement Agreement that U.S. Fire believed Tread-well’s insurance coverage between the 1940s and 1967—or the lack thereof—was relevant to the allocation question. In a meeting on March 12, 1997, for instance, U.S. Fire’s counsel, Reilly, asked Treadwell’s counsel, Mensch, about Treadwell’s liability policies before 1968, because “these policies potentially were applicable to the asbestos claims.” (Reilly Aff. ¶ 46) Further, from additional conversations with Reilly prior to May 20,1997, “Mensch knew ... that U.S. Fire was taking the position that Treadwell could not unilaterally decide to select an AMLIC policy year and allocate all amounts paid into that year because under New York law, the loss should be spread over the period of exposure to claim or death.” {Id. ¶48)

In fact, Treadwell arguably should have known as far back as 1992 that U.S. Fire might assert a defense relating to the method of allocating liability to different policy periods. In U.S. Fire’s August 12, 1992 letter rejecting “any present duties” to provide coverage'—a letter to which U.S. Fire referred repeatedly in subsequent correspondence {see, e.g., id. Exs. G-M, O-P)—the insurer reserved the right to make the type of argument it makes now. {See id. Ex. E) To be sure, U.S. Fire did not refer explicitly to “allocation” or “pro-ration-to-the-insured,” but it did state unequivocally that there would be no coverage for personal injuries or occurrences that took place outside the periods its policies were in effect. {See id. at 5)

Even assuming arguendo that U.S. Fire unreasonably delayed raising the allocation argument, equitable estoppel is unwarranted because Treadwell was not *92 prejudiced by this delay. Treadwell claims that it entered the Settlement Agreement in reliance upon its assumption that “the Coverage Block there provided was acceptable to all insurers—including U.S. Fire.” (9/16/98 Mensch Aff. ¶ 5) Had Treadwell been advised by U.S. Fire otherwise, counsel alleges, “Treadwell’s stance would have been different—the matter would certainly have been the subject of negotiation and a different outcome may well have resulted.” (Id.)

Treadwell cannot have it both ways. Notwithstanding its claims of reliance, in contending that U.S. Fire unreasonably delayed raising the allocation argument, Treadwell asserted that the Coverage Block was established as early as December 1991, in the Interim Agreement—and that the Interim Agreement was, in turn, incorporated into the 1997 Settlement Agreement. (See Treadwell Local Rule 56.1 Statement ¶ 31) Thus, Treadwell appears to have been committed to the Coverage Block even before it notified U.S. Fire about the Asbestos Claims, in February 1992, and even longer before it first mentioned to U.S. Fire the idea of a “coverage block,” in March 1997. Accordingly, Treadwell’s claims of reliance on U.S. Fire’s alleged silence with respect to the Coverage Block ring hollow. Cf. Gilbert Frank, 70 N.Y.2d at 968, 525 N.Y.S.2d at 795, 520 N.E.2d 512 (rejecting the plaintiffs equitable estoppel argument in part on the ground that the plaintiff could not have relied on allegedly improper conduct by the defendant on a later date).

C. Judicial Estoppel

Next, Treadwell invokes judicial estoppel. Judicial estoppel “forbids a party from advancing contradictory factual positions in separate proceedings.” AXA Marine & Aviation Ins. (UK) Ltd. v. Seajet Indus. Inc., 84 F.3d 622, 628 (2d Cir. 1996). The doctrine “attempts to insure The sanctity of the oath and the integrity of the judicial process.’ ” Id. (quoting Bates v. Long Island R.R., 997 F.2d 1028, 1037 (2d Cir.1993)). Thus, a party invoking judicial estoppel must show that “(1) the party against whom judicial estoppel is being asserted advanced an inconsistent factual position in a prior proceeding, and (2) the prior inconsistent position was adopted by the first court in some manner.” Id.; accord Simon v. Safelite Glass Corp., 128 F.3d 68, 71-72 (2d Cir.1997).

Here, Treadwell contends that judicial estoppel applies by virtue of a position advanced in 1986 by North River Insurance Company (“North River”), a U.S. Fire “affiliate,” in a case before the Superior Court of New Jersey styled Madsen & Howell, Inc. v. Sentry Insurance Company, No. L-021632-55 (Law Div., Middlesex County). (See 9/17/98 Warshauer Aff. ¶ 14 & Ex. K) In that case, which also involved insurance for personal injuries arising from exposure to asbestos, North River argued, inter alia, in favor of the approach to allocating liability taken by the U.S. Court of Appeals for the D.C. Circuit in Keene Corp. v. Insurance Co. of North America, 667 F.2d 1034 (D.C.Cir.1981). In North River’s words, the Keene approach—which is discussed in further detail below—renders “each of the carriers on the risk from initial exposure to manifestation of injury jointly and severally liable to the insured.” (9/17/98 Warshauer Aff. Ex. K at 15 (emphasis added)) Endorsing this approach, Treadwell argues, is inconsistent with the position advanced by U.S. Fire here, namely that each insurer is liable for only its pro rata share of the total liability.

Treadwell’s argument is without merit, however, for three reasons. 13 First, and most significant, it is not apparent that the position taken by North River in Madsen & Howell is inconsistent with the position advanced by U.S. Fire here. To be sure, North River endorsed a precedent that *93 would appear, in most respects, to support Treadwell’s present position. Nevertheless, at the same time, North River argued explicitly for proration of the defendant insurers’ obligations based on the number of years each insurer was on the risk. (See, e.g., id. at 15-16, 19-20) Indeed, the very title of the section of North River’s brief from which Treadwell quotes states as much explicitly: “POINT II: THE COVERAGE AND DEFENSE OBLIGATIONS TO BE AFFORDED BY EACH INSURER SHOULD BE ALLOCATED BASED UPON THE YEARS OF COVERAGE EXTENDED BY EACH INSURER DURING THE PERIOD BETWEEN INITIAL EXPOSURE AND MANIFESTATION.” (Id. at 15) Thus, the two positions are not irreconcilable. Cf. Simon, 128 F.3d at 72-73 (“[T]here must be a true inconsistency between the statements in the two proceedings. If the statements can be reconciled there is no occasion to apply an estoppel.”). 14

Second, whatever inconsistency there is between the positions advanced by North River and U.S. Fire pertains to the construction of insurance policies. To the extent relevant here, however, such an issue is one of law, not fact. See, e.g., K. Bell & Assocs., Inc. v. Lloyd’s Underwriters, 97 F.3d 632, 637 (2d Cir.1996). Thus, it cannot be said that U.S. Fire has advanced an “inconsistent factual position,” making judicial estoppel inapplicable. AXA Marine, 84 F.3d at 628 (emphasis added); see TLC Beatrice Int’l Holdings, Inc. v. CIGNA Ins. Co., No. 97 Civ. 8589(MBM), 1999 WL 33454, at *7 (S.D.N.Y. Jan. 27, 1999) (holding that judicial estoppel applies only to inconsistent factual positions, not inconsistent legal positions); Seneca Nation of Indians v. New York, 26 F.Supp.2d 555, 565 (W.D.N.Y.1998) (same), aff'd, 178 F.3d 95 (2d Cir. 1999) (per curiam).

Finally, it is Treadwell’s burden to show that the New Jersey Court adopted North River’s argument “in some manner.” AXA Marine, 84 F.3d at 628. Indeed, judicial estoppel “only applies when a tribunal in a prior proceeding has accepted the claim at issue by rendering a favorable decision,” because only then is “the risk of inconsistent results with its impact on judicial integrity ... certain.” Simon, 128 F.3d at 72. Nevertheless, there is no record whatsoever of the New Jersey Court’s decision in Madsen & Howell. Thus, the risk of inconsistent results is far from certain, and judicial estoppel is inapplicable. 15

D. Collateral Estoppel

Finally, Treadwell argues that U.S. Fire is collaterally estopped by the Supreme Court of Pennsylvania’s decision in J.H. France Refractories Co. v. Allstate Insur- *94 anee Co., 534 Pa. 29, 626 A.2d 502 (1993). In that ease, to which U.S. Fire was a party defendant, J.H. France, a manufacturer and distributor of products containing asbestos, sought a declaratory judgment with respect to its insurers’ duties to defend and indemnify against asbestos-related personal injury claims. As here, it was determined that the claimants’ injuries spanned multiple policy periods as well as periods in which J.H. France did not have insurance. Thus, the Pennsylvania courts were faced with the very question presented here: how to allocate liability among multiple insurers and the insured for asbestos-related personal injuries. The trial court, holding for the defendant insurers, “prorated the obligations of all insurers whose policies were in effect throughout the development of the disease, including J.H. France as a self-insurer during periods when it did not purchase liability insurance.” Id. at 506 (describing the trial court’s holding). On appeal, however, the Supreme Court of Pennsylvania reversed. J.H. France, the Court held, could recover the full extent of its loss from any insurer or insurers on the risk, subject only to those insurers’ policy limits. See id. at 508-09.

Because J.H. France was a Pennsylvania case, Pennsylvania law applies to the question of whether U.S. Fire is collaterally estopped. See Migra v. Warren City Sch. Dist. Bd. of Educ., 465 U.S. 75, 81, 104 S.Ct. 892, 79 L.Ed.2d 56 (1984). Under Pennsylvania law, three requirements must be satisfied to bar a party from relitigating an issue previously decided: (1) the.“identical issue must have been necessary to final judgment on the merits” in the prior action; (2) “the party against whom the plea is asserted must have been a party, or in privity with a party, to the prior action”; and (3) the relevant party “must have had a full and fair opportunity to litigate the issue in question” in the prior action. Bortz v. Workmen’s Compensation Appeal Bd., 546 Pa. 77, 683 A.2d 259, 261 (1996) (citing Balent v. City of Wilkes-Barre, 542 Pa. 555, 669 A.2d 309, 313 (1995)). That the issue in question might be “based on a cause of action different from the one previously litigated” has no effect on the inquiry. Id. (internal quotation marks omitted).

Notwithstanding that several requirements for collateral estoppel are met here, to give J.H. France binding force in this case would be “unfair and inappropriate,” for two reasons. American Home Prods., 565 F.Supp. at 1490-91 n. 1; cf. D’Arata v. New York Cent. Mut. Fire Ins. Co., 76 N,Y.2d 659, 664, 563 N.Y.S.2d 24, 26, 564 N.E.2d 634 (1990) (“Collateral estoppel ... is grounded on concepts of fairness and should not be rigidly or mechanically applied.” (citation omitted)). First, as discussed further in the next section of this opinion, other courts have considered the question of whether to allocate liability for continuous injury among multiple insurers and an insured, and have reached results different from the result reached in J.H. France. See, e.g., In re Prudential Lines, Inc., 158 F.3d 65, 83-87 (2d Cir. 1998) (discussing cases); Michael G. Doherty, Comment, Allocating Progressive Injury Liability Among Successive Insurance Policies, 64 U. Chi. L.Rev. 257, 269-85 (1997) (“Doherty, Allocating Progressive Injury Liability") (discussing several different approaches and citing cases); cf. American Home Prods., 565 F.Supp. at 1490-91 n. 1 (stating that collateral estop-pel is “unfair and inappropriate” when other courts have decided the same issue in different ways); Clark v. Troutman, 509 Pa. 336, 502 A.2d 137, 139 (1985) (holding that collateral estoppel does not apply when “ ‘[t]he issue is one of law’ ” and “ ‘a new determination is warranted in order to take account of an intervening change in the applicable legal context or otherwise to avoid inequitable administration of the laws’ ” (quoting Restatement (Second) of Judgments § 28(2) (1982))). In fact, several such cases—including two decided under New York law—involved U.S. Fire *95 itself. See, e.g., Stonewall Ins. Co. v. National Gypsum Co., No. 86 Civ. 9671(JSM), 1992 WL 163180 (S.D.N.Y. June 24, 1992) (applying New York and Texas law), aff'd in part, rev’d in part sub nom. Stonewall Ins. Co. v. Asbestos Claims Management Corp., 73 F.3d 1178 (2d Cir.1995), modified on denial of reh’g, 85 F.3d 51 (2d Cir.1996); Diamond Shamrock Chems. Co. v. Aetna Cas. & Sur. Co., 258 N.J.Super. 167, 609 A.2d 440 (1992) (applying New York law); see also Missouri Pac. R.R. v. International Ins. Co., 288 Ill.App.3d 69, 223 Ill.Dec. 350, 679 N.E.2d 801 (1997) (applying Illinois law).

Second, J.H. France was decided under Pennsylvania law, and relied exclusively for its reasoning on public policy and on the D.C. Circuit’s decision in Keene. See J.H. France, 626 A.2d at 507-09. By contrast, this case must be decided under New York law, which, as discussed below, differs in several potentially material ways from the law applied in J.H. France. The Pennsylvania Court’s “failure to apply the law of New York ... alone makes it appropriate to relitigate the issues.” American Home Prods., 565 F.Supp. at 1490-91 n. 1 (citing Restatement (Second) of Judgments § 88(7) & cmt. I (Tent. Draft No. 2, 1975)). Accordingly, collateral estoppel is inapplicable.

IV.

As noted, U.S. Fire and Treadwell have stipulated that to the extent an Asbestos Claimant was injured by exposure to asbestos, he was injured at all points in time from initial exposure through the date his claim was filed or he died. (Stip-¶ 3) Because Treadwell engaged in asbestos-related activities as early as the 1940s, the parties’ agreement means that for many of the Asbestos Claims, injury began before Treadwell first obtained insurance in 1967. In essence, therefore, the question at the heart of this case is whether this uninsured period is relevant in determining which entities are liable for the Asbestos Claims. That is, is Treadwell responsible for paying some share of the over-all liability attributable to the period before 1967? If so, some portion of the $944,984 that Treadwell has paid or promised to pay pursuant ,to the Settlement Agreement presumably would have to be allocated to the years before 1967, that portion to be determined on the basis of when each underlying claimant’s injury began. Allocated in such a manner rather than entirely to the AMLIC policy period, Treadwell’s payments would probably not yet exceed $300,000 for any of the AMLIC policy years, and U.S. Fire’s excess policies would not yet be triggered.

A. Allocation in the First Instance ?

Before considering whether any liability should be allocated to Treadwell for the period prior to 1967, however, it is necessary to consider an analytically prior issue: whether this court can allocate liability at all. Treadwell contends that under the CGL policies it purchased from its primary insurers, it is permitted to demand full coverage for continuous injury claims from any one insurer whose policy is triggered, subject only to that insurer’s liability limits. From this entitlement, Treadwell reasons, it follows that the company can allocate all its payments to the 1970-1972 period, notwithstanding the absence of insurance prior to 1967, thus exhausting the AMLIC policies and triggering U.S. Fire’s coverage. (See, e.g., Treadwell Mem. at 33-38) In response, U.S. Fire contends that each insurer is responsible for only its pro rata share of the liability for each Asbestos Claim. Thus, U.S. Fire concludes, Treadwell cannot “arbitrarily” decide what amount of liability is attributable to the AMLIC policy years; instead, Lability for each Asbestos Claim must be allocated in the first instance across all the years the Asbestos Claimant’s injury occurred, including the years prior to 1967. (See, e.g., U.S. Fire Mem. at 9-14)

Although much ink has been spilled during the last two decades on the question of whether allocation of liability *96 for continuous injury is appropriate, no consensus has emerged. See generally Doherty, Allocating Progressive Injury Liability, supra; Garrett G. Gillespie, Note, The Allocation of Coverage Responsibility Among Multiple Triggered Commercial General Liability Policies in Environmental Cases: Life After Owens-Illinois, 15 Va. Envtl. L.J. 525 (1996) (“Gillespie, Allocation of Coverage Re sponsibilityCourts are divided between the approaches urged by the parties here. Some courts have adopted the pro rata approach urged by U.S. Fire, which allocates liability for a particular claim among all triggered policies in the first instance. See, e.g., Lafarge Corp. v. National Union Fire Ins. Co., 935 F.Supp. 675, 687-88 (D.Md.1996); Stonewall, 1992 WL 163180, at *1; Uniroyal, 707 F.Supp. at 1391-93; Metropolitan Life Ins. Co. v. Aetna Cas. & Sur. Co., No. X04CV 950115305S, 1999 WL 244642, at *6-9 (Conn.Super.Ct. Apr. 16, 1999); Owens-Illinois, Inc. v. United Ins. Co., 138 N.J. 437, 650 A.2d 974, 985-94 (N.J. 1994); Northern States Power Co. v. Fidelity & Cas. Co. of New Fork, 523 N.W.2d 657, 662-64 (Minn.1994); cf Gulf Chem. & Metallurgical Corp. v. Associated Metals & Minerals Corp., 1 F.3d 365, 371-73 (5th Cir.1993) (allocating defense costs pro rata); Insurance Co. of N. Am. v. Forty-Eight Insulations, Inc., 633 F.2d 1212, 1224-25 (6th Cir.1980) (same), clarified, 657 F.2d 814, 816 (6th Cir.1981). Under this approach, the insured can recover only a share of its over-all loss from any one insurer, that share to be determined on the basis of some facially objective factor, such as the insurer’s proportion of time on the risk or proportion of total policy limits. See, e.g., Lafarge, 935 F.Supp. at 688 (allocating liability based on each insurer’s proportion of time on the risk); Northern States, 523 N.W.2d at 663 (same); Continental Ins. Co. v. Morgan, Olmstead, Kennedy & Gardner, Inc., 83 Cal.App.3d 593, 608, 148 Cal.Rptr. 57, 66 (1978) (allocating liability for defense costs based on the ratio of each insurer's policy limits to the sum of all policy limits); Owens-Illinois, 650 A.2d at 995 (allocating liability based on “both the time on the risk and the degree of risk assumed” by each insurer). See generally Armstrong World Indus., Inc. v. Aetna Cas. & Sur. Co., 45 Cal.App.4th 1, 51-53 & n. 16, 52 Cal.Rptr.2d 690, 707-08 & n. 16 (1996) (discussing different apportionment formulae and citing cases). If one of the insurers is insolvent, the insured is saddled with that insurer’s share of. the liability. See Koppers Co. v. Aetna Cas. & Sur. Co., 98 F.3d 1440, 1449-50 n. 9 (3d Cir.1996).

Other courts have concluded that each triggered policy is. jointly and severally liable for the insured’s liability and, thus, that the insured can collect under any one triggered policy the full amount of indemnity that is due, subject only to that policy’s liability limits. See, e.g., Prudential Lines, 158 F.3d at 83-86; ACandS, Inc. v. Aetna Cas. & Sur. Co., 764 F.2d 968, 974 (3d Cir.1985); Keene, 667 F.2d at 1048; Dayton Indep. Sch. Dist. v. National Gypsum Co., 682 F.Supp. 1403, 1410-11 (E.D.Tex.1988), rev’d on other grounds sub nom. W.R. Grace & Co. v. Continental Cas. Co., 896 F.2d 865 (5th Cir.1990); Lac DAmiante Du Quebec, Ltee. v. American Home Assurance Co., 613 F.Supp. 1549, 1561-63 (D.N.J.1985); Sandoz, Inc. v. Employer’s Liab. Assurance Corp., 554 F.Supp. 257, 266-67 (D.N.J.1983); J.H. France, 626 A.2d at 508-09. Under this approach, “(i) the insured selects a single policy from which to seek indemnification, (ii) that insurer pays the claim, and (iii) then the insurer seeks contribution from other liable insurers under the ‘other insurance’ provisions of the-policies or under the common law doctrine of contribution.” Prudential Lines, 158 F.3d at 84 (citing Keene, 667 F.2d at 1049-50 & n. 35; ACandS, 764 F.2d at 974; J.H. France, 626 A.2d at 509). Thus, the risk that an insurer is insolvent is transferred from the insured to one or more of the insured’s *97 other carriers. See Koppers, 98 F.3d at 1449-50 n. 9.

Notwithstanding the debate over these two approaches, the difference between them for the purposes of this ease is not as great as Treadwell and U.S. Fire appear to believe. Under either approach, an insurer is liable for only its share, however calculated, of the over-all liability. See, e.g., Koppers, 98 F.3d at 1449-50; Keene, 667 F.2d at 1050; J.H. France, 626 A.2d at 509. The only difference is when such allocation occurs: Under the pro rata approach, allocation occurs when the loss is paid in the first instance; under 'the joint and several approach, by contrast, allocation occurs in a second proceeding, when the loss becomes the subject of contribution among policies and insurers. See, e.g., Prudential Lines, 158 F.3d at 85. Thus, it does not follow, as Treadwell appears to reason, that if the joint and several approach is warranted, Treadwell will be off the hook for the years in which it lacked insurance; instead, the question of whether to prorate to Treadwell would merely be postponed to a second proceeding. 16

Although allocation occurs under both approaches, the decision to adopt one approach rather than the other can have at least two financial consequences for the parties in a case. First, as noted, the choice determines whether the insured or its insurers bears the risk of insurer insolvency. See Koppers, 98 F.3d at 1449-50 n. 9; Kenneth S. Abraham, Environmental Liability Insurance Law 122 (1991). Second, the choice may affect the number of deductibles that apply to each claim. See, e.g., Prudential Lines, 158 F.3d at 86; Koppers, 98 F.3d at 1449-50 n. 9; Lac D’Amiante, 613 F.Supp. at 1562; Abraham, supra, at 121 n. 45. But neither potential consequence is present in this case. By entering into the Settlement Agreement, Treadwell voluntarily assumed responsibility for the insolvency of AMLIC. And whatever deductibles might have applied to Treadwell’s liability were presumably (because neither party mentions them in its papers) incorporated into the Settlement Agreement with Treadwell’s primary insurers; because U.S. Fire sold Treadwell excess insurance, the only prerequisite to U.S. Fire coverage relevant here is exhaustion of the underlying primary insurance.

B. Prudential Lines

Even though Treadwell’s ultimate conclusion — that it is not liable for the years it was uninsured — does not follow from its starting premise — that joint and several liability applies — there is need nevertheless to consider its arguments against allocation, if only for formalistic reasons. That is, if the joint and several approach applies, as Treadwell argues, another court in a later proceeding could still consider the proration-to-the-insured issue and order Treadwell to contribute for the years it lacked insurance. But, under that approach, this court, in this proceeding, could not do either.

The logical starting point for this inquiry is the Second Circuit’s recent decision in Prudential Lines. 17 In that case, the *98 trustee of a shipping line in bankruptcy, Prudential Lines, Inc. (“Prudential”), sued the American Steamship Owners Mutual Protection and Indemnity Association (“American Club”), seeking indemnification for asbestos-related bodily injury claims asserted against Prudential. For the most part, American Club insured Prudential for the full period of the underlying claimants’ injuries, so the issue of allocation among multiple insurers was not presented. See Prudential Lines, 158 F.3d at 85. Nevertheless, seeking to limit the number of deductibles applicable to each claim, Prudential asserted a contract right to full indemnification from any single triggered policy for claims arising out of injury that spanned two or more policy periods. See id. at 83. In response, American Club argued that payment of each insurance claim should be allocated in the first instance among all triggered policies, with the result that “one deductible would apply per claim as well as per triggered policy. ” Id. at 86; see also id. at 83.

The Bankruptcy Court and the District Court both held in favor of Prudential on the allocation issue, basing their decisions in large part on the plain language of the policies, which provided for indemnification of “any loss” that Prudential “shall become liable to pay.” See In re Prudential Lines, Inc., 148 B.R. 730, 743-45 (Bankr. S.D.N.Y.1992); In re Prudential Lines, Inc., 170 B.R. 222, 232-36 (S.D.N.Y.1994). On appeal, the Second Circuit affirmed, but on seemingly different grounds.

The Court began its analysis with a discussion of the two different approaches to allocation. See Prudential Lines, 158 F.3d at 84-85. Noting that “[bjoth approaches allow allocation among policies at some transactional point, i.e., either when the loss is paid, or when it becomes the subject of contribution among policies and insurers,” the Court explained that courts adopting the pro rata allocation approach “have generally been motivated by considerations of equity and policy, rather than contract wording.” Id. at 85. Specifically, the Court listed three such considerations. First, the panel explained, courts have “sought to ensure that a single insurer underwriting a small proportion of the risk does not get saddled with the full loss ...., a loss that may prove uncollectible from other companies.” Id. (citing Uniroyal, 707 F.Supp. at 1392; Owens-Illinois, 650 A.2d at 992-93). Second, courts enforce allocation “to require the insured to absorb losses for periods when it was self-insured.” Id. (citing Owens-Illinois, 650 A.2d at 989). Third, courts see allocation in the first instance as more efficient, “reasoning that any contribution proceeding will involve many of the same issues that are raised in the initial liability proceeding, and that it is more efficient to deal with these issues in a single proceeding.” Id. (citing Lafarge, 935 F.Supp. at 688).

After listing these considerations, the Court turned to the facts of the case before it, noting, with a textual sigh of relief, that “Fortunately, a number of factors that *99 often complicate the inquiry are absent here.” Id. at 85. That is, Prudential had no periods of self-insurance and, for virtually the entire span of relevant years, only one insurer. See id. Thus, if joint and several liability applied, there was no danger that American Club would be saddled with more than its share of liability — or with liability that should have been assumed by Prudential itself — and no danger of additional litigation. See id. To the extent American Club wanted to allocate liability among its own policies, it could develop an “internal allocation mechanism” to do so — in other words, allocation was an issue merely of bookkeeping. Id. at 85-86.

Noting that the real “financial significance” of the allocation issue lay in its impact on the number of deductibles that would apply to each claim against Prudential, the Second Circuit then concluded:

Given: (i) the policy’s broad language covering “any loss [or] damage” which Prudential becomes liable to pay resulting — presumably even in part — -from injuries occurring during the policy period; (ii) the absence of a contractual intent to require allocation of liability among policies in the first instance; and (iii) the lack of any compelling policy or equitable considerations favoring allocation, we decline to read the policies in a way that would have the (probably unintended) effect of multiplying the deductibles applicable to each claim.

We hold that, in the circumstances presented, Prudential has the right to demand that a policy pay full coverage for each insurance claim in which the underlying Claimant suffered ... asbestos injury during the policy period.

Id. at 86 (emphasis added) (alteration in original); cf. Reichhold Chems., Inc. v. Hartford Accident & Indem. Co., 1998 WL 811592 No. X03-CV-88-0085884-S, slip op. at 21 (Conn.Super.Ct. Feb.ll, 1999) (opining that Prudential Lines “was specifically limited to its unique facts and did not change existing New York law in any way”), quoted in Metropolitan Life, 1999 WL 244642, at *7.

The circumstances of this case support a result different from the one reached in Prudential Lines. Whereas Prudential was insured by one carrier for virtually the entire period of injury in Prudential Lines, the injuries in this case spanned a period in which Treadwell was insured by many carriers, under both primary and excess policies, and in which Treadwell lacked insurance altogether. Thus, “a number of factors that often complicate the inquiry” are present here. Prudential Lines, 158 F.3d at 85. In addition, as noted, it appears that the decision to adopt one approach rather than the other here would have no impact on the number of deductibles that apply to each claim. Further, Treadwell already assumed responsibility in the Settlement Agreement for AMLIC’s share of the loss, so the selection of approach would have no effect on who bears the risk of insurer insolvency.

In fact, only one thing turns on the choice of which approach to apply in the present case: whether there will be a second round of litigation. If the joint and several approach were applied, U.S. Fire would be obligated to indemnify Treadwell for its share of future losses. But, as noted above, when the dust settled and the Asbestos Claims were paid in full, U.S. Fire would have the right to bring Tread-well back to court to determine whether the proration-to-the-insured approach applied. The outcome of that second round of litigation, based on the same record as is presented here, would then determine whether U.S. Fire’s policies should have been triggered in the first place; that, in turn, would determine whether Treadwell’s loss should be re-allocated from U.S. Fire back to Treadwell. Thus, the only consequence of applying joint and several liability would be to postpone resolution of the central dispute in this case, at significant additional expense to the parties, not to mention the effort to be expended by the court. The law does not require such a perverse result.

*100 To be sure, like the American Club policies in Prudential Lines, the policies at issue here employ “broad language” of indemnification. Prudential Lines, 158 F.3d at 86. 18 Moreover, as in Prudential Lines, there is no evidence in this case “of a contractual intent to require allocation ... in the first instance.” Id. at 86. But these factors, although they helped support the Prudential Lines Court’s decision, were not dispositive. Additionally, whatever import they might have had in a case involving only one insurer and no periods of self-insurance, these factors do not necessarily provide support for the joint and several approach in a case involving multiple insurers and an extended period of self-insurance. See, e.g., Owens-Illinois, 650 A.2d at 988-89 (concluding that the phrase “all sums” does not support joint and several liability); see also Stonewall, 1992 WL 163180, at *1 n. 2; cf. Forty-Eight Insulations, 633 F.2d at 1224-25. Indeed, in Stonewall, the Second Circuit itself endorsed the view that “[t]he ‘all sums’ language .... “was never intended to cover apportionment when continuous injury occurs over multiple years.’ ” Stonewall, 73 F.3d at 1203 (quoting Owens-Illinois, 650 A.2d at 988-89). 19

C. Treadwell’s Additional Arguments

Notwithstanding the overwhelming considerations of convenience and common sense favoring allocation in the first instance here, analysis of the Second Circuit’s opinion in Prudential Lines does not exhaust the necessary inquiry. Treadwell presses several arguments addressed to contractual intent and interpretation that were not treated explicitly by the Prudential Lines Court. 20 Because, under most circumstances, parties can contract around even convenience and common sense, it is therefore necessary to consider whether any of these arguments has merit.

Treadwell’s first argument relies on the putative “drafting history” of the CGL policies. Specifically, Treadwell submits several internal documents—memo-randa and minutes of meetings from the 1960s and 1970s—from the National Bureau of Casualty Underwriters and the Insurance Services Office, industry associations of which U.S. Fire is or was a member. (See 9/17/98 Warshauer Aff. ¶¶ 1-13 & Exs. A-I) To the extent relevant here, these documents contain various statements along the following lines: (1) that, in cases of cumulative injury, “it is possible that more than one policy will afford coverage” (id. ¶ 8 & Ex. E; see also id. ¶ 7 & Ex. D); (2) that “[t]here is no proration formula in the policy, as it seemed impossible to develop a formula which would handle every possible situation with complete equity” (id. ¶ 9 & Ex. *101 F); and (3) that “each carrier on the risk during any part of [the period of time an asbestosis condition developed] could be fully responsible for the cost of defense and loss.” (Id. ¶ 11 & Ex. H); see also Owens-Illinois, 650 A.2d at 990-91 (quoting several of these statements and others from industry association documents); Gillespie, Allocation of Coverage Responsibility, supra, at 570-71 (same). These statements, Treadwell argues, indicate that the “ ‘all sums’ language was drafted and interpreted to mean each insurance company whose policy was activated or triggered would pay ‘all sums’ to the policyholder for which the policyholder was liable and any allocation would be only among insurance companies.” (9/17/98 Warshauer Aff. ¶ 3)

Treadwell’s argument is unpersuasive, however, for two reasons. First, there is “inherent mischief’ in heavy reliance on selected statements from industry meetings and memoranda. Beeson v. Fishkill Correctional Facility, 28 F.Supp.2d 884, 891 (S.D.N.Y.1998) (discussing the perils of relying heavily on legislative history to interpret a statute). But see American Home Prods., 565 F.Supp. at 1500-03 & n. 3 (“[G]iven the similar language and concepts in the CGL and [the plaintiffs] policies, the CGL drafting process and the intent of its drafters provides [sic ] probative evidence of the meaning attributed in the industry to the [clause at issue] of [the plaintiffs] policies.”). Treadwell bought a particular policy from U.S. Fire, and the parties’ dispute centers on the meaning of that policy's language. Even assuming the relevance of U.S. Fire’s own views on that meaning, industry discussions in which U.S. Fire itself did not actively participate are unlikely to prove much. Cf. American Home Prods., 565 F.Supp. at 1500 n. 3 (justifying reliance on the CGL drafting history in part on the ground that the defendant carrier “was an active participant in the CGL drafting sessions”). The statements on which Treadwell relies represent little more than the individual views of particular speakers employed by insurers who happen to belong to the same industry association as U.S. Fire. 21 Accordingly, those statements deserve little, if any, weight.

Second, even if one were to give significant weight to the statements of the CGL drafters, the statements at issue do not unambiguously support Treadwell’s argument for joint and several liability. To say that it is “possible” that more than one policy will “afford” coverage is not to say that any one policy is actually hable in full in the first instance. Nor is the statement that each carrier on the risk during any part of an injury “could” be fully responsible for the loss necessarily anything more than a prediction of what courts might do, rather than an expression of what courts should do. Finally, to say that “[t]here is no proration formula in the policy” is to say nothing more than the obvious, that the CGL policies do not definitively settle what to do in a situation like the present one. Cf. Owens-Illinois, 650 A.2d at 990 (“Although the [CGL] drafters seemed to *102 acknowledge that some continuum existed between exposure and manifestation of disease when coverage was provided, they did not (or could not) decide how to apportion the responsibility.”)- That is the reason for the present dispute, not the basis for its resolution.

Next, Treadwell contends that, under New York law, the absence of a “pro rata limitation” in U.S. Fire’s policies means that U.S. Fire cannot limit its obligations to a share of Treadwell’s liabilities. (Treadwell Mem. at 38) In essence, Tread-well argues that the “absence of a contractual intent to require allocation ... in the first instance,” Prudential Lines, 158 F.3d at 86, decides the present dispute, and is not merely a factor to be considered.

Here, Treadwell relies in major part on the New York Court of Appeals decision in York-Buffalo Motor Express v. National Fire & Marine Insurance Co., 294 N.Y. 467, 63 N.E.2d 61 (1945). In that case, the plaintiff common carrier purchased insurance from National Fire and Marine Insurance Co. (“National”) after receiving notice of cancellation from the Rhode Island Insurance Company (“Rhode Island”) with respect to its original insurance. Unbeknownst to the plaintiff, however, Rhode Island’s cancellation of the original policy was technically invalid, so when a loss occurred thereafter the plaintiff was actually insured by both carriers. National agreed to pay the full loss less the policy limits of the Rhode Island policy, and the plaintiff sued both insurers for that difference. After winning only part of the difference, from Rhode Island, the plaintiff appealed. The Court of Appeals reversed, holding that the plaintiff was entitled to the full amount of the difference from Rhode Island. Quoting an insurance law treatise, the Court stated in relevant part:

“Most policies of fire insurance contain a clause providing that the insurer shall not be liable for any greater proportion of any loss which may occur than the amount named in the policy shall bear to the entire amount of insurance upon the property.... By inserting this clause the insurer limits the amount of recovery upon that particular policy to the proportionate amount which that policy bears to the entire amount of the policies. In the absence of such a clause, the insured could recover the whole amount from any one of the insurers, and leave him to obtain contribution from the other insurers. ”

Id. at 473, 63 N.E.2d 61 (quoting Joyce on the Law of Insurance 4166 (2d ed.1918)) (emphasis added).

Treadwell’s reliance on York-Buffalo is misplaced. First, given that the plaintiff in that case had recovered most of its loss from National and was seeking only the remainder from Rhode Island, the language quoted is technically dictum with respect to whether allocation in the first instance is warranted. Second, in the 54 years since York-Buffalo was decided, the case has been cited in only three cases, see Lewis Mach. Co. v. Aztec Lines, 172 F.2d 746, 750 (7th Cir.1949); Ruzicka v. Rager, 305 N.Y. 191, 199, 111 N.E.2d 878 (1953); Associated Mut. Ins. Co. v. Firemen’s Fund Ins. Co., 81 A.D.2d 949, 950, 439 N.Y.S.2d 706, 707 (3d Dep’t 1981), aff'd, 56 N.Y.2d 676, 451 N.Y.S.2d 731, 436 N.E.2d 1333 (1982), and never for the proposition that when a loss is covered by more than one insurer, the insured can recover its full loss from any one insurer. Thus, it is by no means clear that the cited, dictum in York^Buffalo remains good law. Finally, even assuming that the Court’s language quoted above is binding and good law, it would not apply to this case. Whereas York-Buffalo involved two carriers providing concurrent coverage, the present case involves multiple carriers who provided successive coverage. See Owens-Illinois, 650 A.2d at 991 (“Generally speaking, pro-rata provisions are intended to apply only ‘when the coverage is concurrent.’ If the policies do not overlap, such clauses are not generally applicable.”) (quoting St. Paul Fire & Marine Ins. Co. v. Vigilant *103 Ins. Co., 919 F.2d 235, 241 (4th Cir.1990)); cf. Gulf Chem., 1 F.3d at 372 (adopting pro rata allocation in the first instance and distinguishing cases that adopted joint and several liability on the ground that they “coneern[ed] multiple claims arising from a single incident”); Forty-Eight Insulations, 633 F.2d at 1224-25 (same).

Treadwell’s final argument is premised on the contra proferentem rule, which states that “ ‘where a policy of insurance is so framed as to leave room for two constructions, the words used should be interpreted most strongly against the insurer.’ ” Haber v. St. Paul Guardian Ins. Co., 137 F.3d 691, 697 (2d Cir.1998) (quoting Liverpool & London & Globe Ins. Co. v. Kearney, 180 U.S. 132, 136, 21 S.Ct. 326, 45 L.Ed. 460 (1901)); see also Gillespie, Allocation of Coverage Responsibility, supra, at 569-73 (arguing that the contra proferentem rule supports joint and several liability in cases of continuous injury). But that rule of construction applies when there is a dispute over the terms of a particular contract between an insured and insurer. It has no application to a case involving multiple insurers and multiple insurance contracts, when the question to be decided arises altogether outside the scope of any particular contract. See Doherty, Allocating Progressive Injury Liability, supra, at 268-69; see also Owens-Illinois, 650 A.2d at 991 (declining to apply the contra proferentem rule because it “can produce uneven results” depending on “the configuration of insurance coverage” in a given case). 22

• [20] The conclusion that allocation in the first instance is warranted presents, in turn, the question of whether Treadwell’s payments pursuant to the Settlement Agreement should be allocated to all the years in which it actually or effectively lacked insurance, i.e., to the AMLIC policy years and the years prior to 1967. As noted, the answer to this question depends on whether Treadwell should be treated as a self-insurer for the years prior to 1967. Under the Second Circuit’s decision in Stonewall, it should.

In Stonewall, a case decided under New York (and Texas) law, the National Gypsum Company (“NGC”), a former asbestos product manufacturer, and certain of its liability insurers sought declaratory relief clarifying the extent to which NGC was entitled to indemnification for asbestos-related claims asserted against it. See Stonewall, 73 F.3d at 1186. Confronted with multiple insurance policies covering each claim, the District Court decided, on a motion for summary judgment, to allocate in the first instance among all the triggered policies. Specifically, as described by the Court of Appeals, the District Court “ruled that each triggered policy was responsible for only a pro rata share of NGC’s liability as to a particular claimant. The share was determined by multiplying the judgment or settlement by a fraction that has as its denominator the entire number of years of the claimant’s injury, and as its numerator the number of years within that period when the policy was in effect.” Id. at 1202. Additionally, *104 Even if Treadwell had invoked die reasonable expectations doctrine with respect to the issue in dispute, that would not have changed the result. "Assessing the objectively reasonable expectations of a policyholder in this context of long-tail injuries is ... very difficult,” Owens-Illinois, 650 A.2d at 991, if not impossible. See Keene, 667 F.2d at 1058 (Wald, J., concurring in part); American Home Prods., 565 F.Supp. at 1511; cf. Doherty, Allocating Progressive Injury Liability, supra, at 268; Gillespie, Allocation of Coverage Responsibility, supr a, at 566-68.

On appeal, neither NGC nor the insurers objected to the District Court’s decision to allocate in the first instance, or to the time-on-the-risk formula used by the District Court to determine the carriers’ respective shares. See id. NGC, however, objected to the proration-to-the-insured approach, arguing that the policies promised to pay “all sums” for which NGC became liable because o.f bodily injury and did not contain any provision “permitting the Insurers to shift a portion of a covered loss back to the insured for uninsured periods.” Id. Notwithstanding these arguments, the Second Circuit affirmed. Praising the New Jersey Supreme Court’s decision in Owens-Illinois, which adopted the proration-to-the-insured approach on policy and equity grounds, see Owens-Illinois, 650 A.2d at 995, the Second Circuit described proration-to-the-insured as “a sensible way to adjust the competing contentions of the parties in the context of continuous triggering of multiple policies over an extended span of years.” Stonewall, 73 F.3d at 1203. However, the Court did modify the District Court’s decision in one respect: It held that the proration-to-the-insured approach should not be applied to years “after 1985 when asbestos liability insurance was no longer available.” Id. (citing Owens-Illinois, 650 A.2d at 995; Keene, 667 F.2d at 1058 (Wald, J., concurring in part)); see also Olin Corp. v. Insurance Co. of N. Am., 986 F.Supp. 841, 843-45 (S.D.N.Y.1997) (discussing this limitation).

Treadwell makes various arguments as to why the Second Circuit’s decision in Stonewall is wrong or not controlling. Most of these arguments confuse the question of whether to prorate to an insured for uninsured periods with the analytically distinct question of whether to allocate in the first instance, and thus are inapplicable or have been rejected already. Two of Treadwell’s arguments, however, warrant consideration.

Treadwell’s first argument, that the “precedential effect of Stonewall” was limited by Prudential Lines (Treadwell Reply Mem. at 12-14), is arguably correct, but beside the point. As discussed above, the central issue in Prudential Lines was whether to apply the pro rata allocation approach or the joint and several approach. Prudential was insured for the full period of injury, so the Court had no occasion to pass directly on the proration-to-the-insured approach. Nevertheless, in a footnote, the Court characterized Stonewall in a manner which implies that New York courts are not required to apply the proration-to-the-insured approach: In Stonewall, the Prudential Lines Court wrote, “[w]e held that the district court did not err in allocating liability to the insured ... for periods in which the insured lacked coverage (at least during the period when coverage for asbestos risk was available).” Prudential Lines, 158 F.3d at 84 n. 12 (emphasis added).

Whether the proration-to-the-insured approach is required or merely permitted, however, it should be applied here. To the extent relevant, the facts of this case are almost identical to those in Stonewall. Thus, the Court’s holding, even if not controlling, warrants substantial weight. In any event, applying the proration-to-the-insured approach in this case is supported by sound considerations of equity. Tread-well made a decision to go without insurance for the years prior to 1967, and this decision should have consequences. Otherwise, Treadwell would receive the same treatment as an identically situated compa *105 ny that chose to purchase insurance for the full period. As Judge Weinstein explained with characteristic force and clarity in Uniroyal, “A firm that fails to purchase insurance for a period ... is self-insuring for all the risk incurred in that period; otherwise it would be receiving coverage for a period for which it paid no premium. Self-insurance is called ‘going bare’ for a reason.” Uniroyal, 707 F.Supp. at 1392; see also NL Indus., Inc. v. Commercial Union Ins. Co., 935 F.Supp. 513, 521 (D.N.J.1996) (applying New York law); Reichhold Chems., Inc. v. Hartford Accident & Indem. Co., No. X03CV 880085884S, 1998 WL 811592, at *13 (Conn.Super.Ct. Oct. 1, 1998) (same); Owens-Illinois, 650 A.2d at 992; cf. Forty-Eight Insulations, 633 F.2d at 1224-25 (applying the proration-to-the-insured approach to allocation of defense costs); Gulf Chem., 1 F.3d at 371-72 (same).

Second, Treadwell notes that the Stonewall Court did not directly address the issue of what formula to use when allocating, and argues that allocation should be done here “by policy limits” rather than time on the risk. {See Tread-well Mem. at 43) Although Treadwell’s argument finds support in some cases, see, e.g., Morgan, Olmstead, Kennedy & Gardner, Inc., 83 Cal.App.3d at 608, 148 Cal. Rptr. at 66, it is nevertheless without merit here. First, the argument is premised on the unjustified assumption that the proportion of injury occurring within a given period is somehow related to the proportion of coverage afforded by the policy in that period. See Northern States, 523 N.W.2d at 662; Doherty, Allocating Progressive Injury Liability, supra, at 277. Second, allocation by policy limits is an elusive concept in a case like this, which involves both primary and excess insurance coverage. Finally, given my decision to prorate to Treadwell for the years prior to 1967, allocating by policy limits would require a determination of what Tread-well’s “policy limits” were for those years. Any such determination would be based on a “judicial fiction” that Treadwell “was self-insured under a policy the terms of which are ascertainable,” and would therefore be arbitrary and utterly fanciful. J.H. France, 626 A.2d at 508; see also Keene, 667 F.2d at 1048-49; Armstrong World Indus., 45 Cal.App.4th at 56 n. 21, 52 Cal.Rptr.2d at 711 n. 21.

In contrast, the time-on-the-risk method has been applied by the vast majority of courts allocating liability, including every court to have considered the issue under New York law. See NL Indus., 935 F.Supp. at 521-22 (New York law); Olin Corp., 986 F.Supp. at 842-43 (same); Stonewall, 1992 WL 163180, at *1 (same); Metropolitan Life, 1999 WL 244642, at *9 (same); Reichhold Chems., 1998 WL 811592, at *12-13 (same); Diamond Shamrock, 609 A.2d at 466-67 (same); see also, e.g., Lafarge, 935 F.Supp. at 688 (Texas law); Northern States, 523 N.W.2d at 663 (Minnesota law). More to the point, the method is “predictable, administrable, fundamentally fair, and provides potential insureds with incentives to purchase insurance or rationally self-insure.” Doherty, Allocating Progressive Injury Liability, supra, at 260; see also Northern States, 523 N.W.2d at 662-64 (discussing the pros and cons of several allocation formulas and concluding that time on the risk is the proper method); Doherty, Allocating Progressive Injury Liability, supra, at 281-83 (same); Rob S. Register, Comment, Apportioning Coverage Responsibility of Consecutive Insurers When the Actual Occurrence of Injury Cannot Be Ascertained: Who Has to Contribute in a Settlement?, 49 Mercer L.Rev. 1151, 1163-64 (1998) (same). Accordingly, Treadwell is obligated to contribute toward payment of the Asbestos Claims based on the number of years it was uninsured.

VI.

One final issue requires consideration: what impact, if any, Treadwell’s settlements with its other insurers have on the present dispute. As noted, Treadwell en *106 tered into two settlements with its other insurers. First, pursuant to the AMLIC Agreement, Treadwell settled all claims against AMLIC for a single payment of $475,000 from the New York Insurance Fund (the “AMLIC Payment”). That the AMLIC Payment was made by the New York Insurance Fund and not by AMLIC itself is immaterial for present purposes. Second, pursuant to the Settlement Agreement, CIGNA, Travelers and Treadwell assumed 71.4%, 13.4% and 15.2%, respectively, of Treadwell’s total liability. 23 Under the Settlement Agreement, Treadwell is the sole beneficiary of the AMLIC Payment.

Treadwell asserts that both agreements are binding on U.S. Fire for allocation purposes. First, with respect to the AM-LIC Agreement, Treadwell argues that because AMLIC contracted to cover the 1970-1972 period, the AMLIC Payment of $475,000 should be allocated to those years. (See Treadwell Mem. in Opp’n at 7 n. 6; see also Treadwell Mem. at 19-20) Second, with respect to the Settlement Agreement, Treadwell contends that because its share of the total loss was based on the number of years AMLIC was on the risk, its $944,984 of payments should be allocated to those years only. (See Treadwell Mem. 16-20) U.S. Fire disputes both propositions, contending that the liability for each claim that Treadwell assumed under the Settlement Agreement should be allocated pro rata to all years of the claimant’s injury in which Treadwell was actually or effectively (because of AM-LIC’s insolvency) uninsured, including periods before 1967. (See U.S. Fire Mem. at 15-18; see also U.S. Fire Reply Mem. at 12-14)

A. The AMLIC Agreement

The first question to be resolved is whether a primary insurer’s agreement to pay a portion of the total liability arising from continuing injury is binding on the insured and its excess insurers for allocation purposes. That is, in determining whether primary insurance coverage has been exhausted, thereby triggering excess coverage, what amount should be allocated to the primary insurer’s policy period: the amount it actually paid or the amount it would have been contractually obligated to pay had it not settled? The answer to this question determines not only whether the AMLIC Payment should be allocated to the AMLIC policy period, but also whether the shares assumed by CIGNA and Travelers pursuant to the Settlement Agreement are properly allocated to their respective periods. 24

Treadwell’s argument that a primary insurer’s settlement should be allocated to that insurer’s policy period finds some support in the case law, all of which comes, coincidentally, from this district. See Maryland Cas. Co. v. W.R. Grace & Co., No. 88 Civ. 2613(JSM), 1996 WL 109068 (S.D.N.Y. Mar.12, 1996) (“Insurers contract to cover a particular period. If they settle before a final determination as to whether or not the injury actually or reasonably occurred within that period and it is later shown that the injury in fact occurred outside of the policy period, the settlement amount is still allocated to the period that the settling insurer contracted to cover.”); E.R. Squibb & Sons, Inc. v. Accident & Cas. Ins. Co., 853 F.Supp. 98, 101 (S.D.N.Y.) (“Absent collusive arrangements to defraud an excess carrier, ... [an *107 excess carrier] must pay amounts due the insured which are unpaid for any reason, including a compromise reached by a first-tier carrier through an arms-length settlement.”), clarified, 860 F.Supp. 124 (S.D.N.Y.1994); see also Stonewall Ins. Co. v. National Gypsum Co., No. 86 Civ. 9671(JSM), 1992 WL 47363, at *1 (S.D.N.Y. Mar. 4, 1992). Although these cases are arguably distinguishable and not controlling in any event, Treadwell’s argument finds support also in sound public policy. Specifically, treating a primary insurer’s settlement with an insured as binding for allocation purposes, at least in the absence of evidence of collusion to defraud an excess insurer, furthers the strong public interest in promoting settlement. See, e.g., McDermott, Inc. v. AmClyde, 511 U.S. 202, 215, 114 S.Ct. 1461, 128 L.Ed.2d 148 (1994) (“[P]ublic policy wisely encourages settlements.... ”); United States v. Glens Falls Newspapers, Inc., 160 F.3d 853, 856 (2d Cir.1998) (discussing the “strong public policy which encourages the settlement of cases through a negotiated compromise” (internal quotation marks and citation omitted)).

To see why allocating an insurer’s settlement amount to its policy period promotes settlement, consider the following hypothetical. Assume that several people suffering from asbestos-related diseases sue a company, C, exactly 10 years to the day after they were initially exposed to asbestos. Assume further that C was insured in only the first three years, or 30%, of the 10-year period of the claimants’ injuries. In those three years, C was covered by primary policies, issued by insurer P and covering up to $150,000 in liability per year — $450,000 in the aggregate for all three years. Also during those years, C was covered by excess policies, issued by insurer E and triggered by exhaustion of the underlying primary insurance. Finally, assume that the claimants’ injuries thus far have cost C $1 million in liability payments and that there is a chance the total liability will eventually exceed $2 million.

Now consider three scenarios. In Scenario 1, the parties cannot reach settlement and bring their dispute to a court, which allocates liability pro rata by time on the risk, with C contributing for the years it was uninsured. In this scenario, therefore, P will assume $300,000, or 30%, of the existing $1 million liability and 30% of the next $500,000 in liability, at which point it will owe the maximum amount allowable under its policies ($450,000); C will assume 70% of all liability; and E will be off the hook until the total liability reaches $1.5 million, when P’s policies will be exhausted. At that point, E will assume 30% of all subsequent liability.

In Scenario 2, P settles with C for the full coverage under P’s policies, $450,000. Although this amount exceeds P’s contractual liability of $300,000 at the time of settlement, it is plainly binding on P and C with respect to the first $1 million in liability; thus, of the first $1 million in liability, P will assume $450,000 and C will assume $550,000. C’s and E’s respective shares of the liability in excess of $1 million, however, will differ depending on whether P’s $450,000 is allocated entirely to its policy period or not. If it is — that is, if the settlement is binding on C and E for allocation purposes — the excess policies will be triggered, even though the total liability is only $1 million. Thus, E and C will assume 30% and 70%, respectively, of all liability in excess of $1 million. If the settlement is not binding for allocation purposes, E would not be liable until the total liability exceeded $1.5 million, at which point it would assume 30% of all future liability. Thus, C would have to pay all losses until the total reached $1.5 million, and 70% of liability thereafter.

In Scenario 3, P settles with C for $150,-000, less than both P’s maximum exposure and its legal share. C would thus be liable for $850,000 of the first $1 million in losses. Again, however, C’s and E’s respective shares of the liability in excess of $1 million would differ depending on whether the settlement is binding for allocation *108 purposes. If the settlement is binding, C would have to assume the next $1 million in losses; only then, when the total liability exceeded $2 million, would E be liable for 30% of future losses. If the settlement is not binding, however, E’s liability would be triggered when the total losses reached $1.5 million. Thus, again, C would have to pay all losses until the total reached $1.5 million, and 70% thereafter.

Table 1 depicts each party’s liability under each of these three scenarios, and the effects in Scenarios 2 and 3 of treating P’s settlements as either binding (shaded areas) or not binding (unshaded areas) for allocation purposes. In addition, Table 1 lists for each scenario the parties’ respective liability shares when the total loss equals $2 million.

*109 [[Image here]]

As this hypothetical illustrates, if C’s settlement with P is not binding for allocation purposes, C will have little or no incentive to settle. If P settles for more than its legal share (Scenario 2), C will have to pay the same ($1.4 million) as it would have owed in the absence of a settlement. If P settles for less than its legal share (Scenario 3), C will owe more than it would have in the absence of a settlement. Thus", C stands to gain nothing by settling. 25 In contrast, if P’s settlement is *110 binding for allocation purposes, C has the chance of obtaining through settlement a better outcome than it could by going to court.

Of course, because P’s exposure is capped at $450,000, C’s gain is E’s loss. That is, if P settles for more than its legal share (Scenario 2) and P’s settlement is binding for allocation purposes, E will end up paying more than it would have in the absence of a settlement ($300,000 versus $150,000). But this consequence is not as unfair as it might first appear. For one thing, if P settles for less than its legal share (Scenario 3), E stands to gain at C’s expense; that is, if total liability reaches $2 million, E will end up owing nothing as opposed to $150,000. In such a situation, it is unlikely the excess carrier would argue against treating P’s settlement as binding for allocation purposes. 26 Moreover, absent collusion on the part of C and P, there is nothing preventing E from participating in the settlement negotiations with both of the other parties. Indeed, if any settlement with P would be binding for allocation purposes, E would have an incentive to participate in settlement negotiations to avoid an increase in its liability. With both insurers participating in settlement negotiations, the parties are likely to reach an agreement that approximates that the outcome would have been in the absence of settlement and without incurring the litigation costs of reaching that result.

In the present case, there is no evidence of collusion between Treadwell and AMLIC (or, more precisely, the Superintendent). To the contrary, U.S. Fire was given notice of the ongoing negotiations and was invited to participate. (See, e.g., 9/16/98 Mensch Aff. Ex. A5) Under the circumstances, therefore, the $475,000 AMLIC Payment should be allocated entirely to the 1970-1972 period. 27

B. The Settlement Agreement

Having decided that the $475,000 AMLIC Payment—which was made directly to Treadwell-—should be allocated to the 1970-1972 period, I need decide only whether Treadwell’s payments in excess of that amount, totaling $469,984, also should be allocated to the 1970-1972 period. As noted, Treadwell argues that because its share of the total loss under the Settlement Agreement was based on the number of years AMLIC was on the risk, it should be permitted to allocate its payments to AMLIC’s policy period. I disagree.

Treadwell relies here primarily on the Second Circuit’s decision in Stonewall, 28 *111 In that case, the insured, NGC, entered into an agreement, known as the “Wellington Agreement,” with 33 other former asbestos products producers and 16 insurers. See Stonewall, 73 F.3d at 1188. Under the terms of the Wellington Agreement, a claims-handling facility was established “to evaluate, defend, and settle all asbestos-related bodily injury claims” against its subscribing producers and “to pay settlements, judgments, and legal expenses incurred in the handling” of these claims. Id. Costs incurred by the claims-handling facility in settling each claim were allocated to each subscribing producer according to a formula, regardless of whether the producer was named as a defendant in that claim. See id. NGC’s share of such costs was, in turn, “borne by those of its insurers that were also subscribers to the Wellington Agreement, to the extent of the insurance coverage afforded to NGC under its policies and pursuant to the terms of the Wellington Agreement.” Id.

Little more than three years after the Wellington Agreement was executed, the claims-handling facility established by the agreement was dissolved. See id. Simultaneously, NGC entered into another agreement, the “CCR Producer Agreement,” with ,21 former asbestos products producers, all of which had been parties to the Wellington Agreement. See id. Like the Wellington Agreement, the CCR Producer Agreement established a claims-handling facility with responsibility for evaluating, defending and settling asbestos-related bodily injury claims against the subscribing producers. See id. Again, the costs incurred by the facility were allocated to the subscribing producers according to a formula, which formula eventually was revised so that producers would pay a share of only those claims in which they were named. See id. No insurer was a signatory to the CCR Producer Agreement, but several insurers who had been signatories to the Wellington Agreement entered into separate agreements with the producers concerning the new claims-handling facility. See id. In addition, notwithstanding the dissolution of the first claims-handling facility, the insurance coverage provisions of the Wellington Agreement remained in effect. See id. at 1189.

The insurers seeking relief in Stonewall were not signatories to the Wellington and CCR Agreements. See id. Thus, the District Court had to determine “whether NGC’s decision to resolve the asbestos-related bodily injury claims against it by joining these claims-handling facilities was reasonable, and whether all amounts paid by NGC pursuant to these agreements ... could be recovered from these non-signatory Insurers under the terms of their policies.” Id. The District Court found, in the Court of Appeals’s words, that NGC “enjoyed a number of benefits” as a result of its participation in the claims-handling facilities and held that NGC’s decision to participate was reasonable. Id. at 1207. Notwithstanding that the agreements allocated to NGC losses for some claims in which it was not even a named defendant, the Second Circuit affirmed. NGC’s payments, the Court held, “were ‘consistent with NGC’s rights under its policies to enter into reasonable and good faith settlements.’ ” Id. (quoting the District Court’s opinion). Indeed, the Court argued, had NGC declined to join the claims-handling facilities, the insurers likely would have complained “that NGC’s failure to use these settlement mechanisms was unreasonable.” Id.

Treadwell’s rebanee on Stonewall is misplaced. The question in Stmeivall was effectively whether the non-settling insurers were bound by the sums paid by NGC to the asbestos claimants through the claims-handbng facibties. To be sure, NGC did not enter into agreements with the claimants themselves, or even pay *112 them directly. But the costs NGC incurred were directly related to the resolution of the underlying claims. In essence, the Court treated the claims-handling facilities as NGC’s agents for the purposes of resolving the underlying claims and held that the facilities’ settlements of the underlying claims were within the terms of NGC’s insurance policies. Crucially, the non-settling insurers were not bound by the terms of NGC’s settlements with its other insurers. Indeed, as discussed in the previous section of this opinion, the non-settling insurers in Stonewall were allocated shares of the loss based on the time each was on the risk.

However, in the present case, the Settlement Agreement itself has nothing to do with resolving the Asbestos Claims themselves. Instead, the agreement is concerned primarily with how to allocate the separately determined costs of the underlying claims among Treadwell and its other insurers. Thus, the Settlement Agreement does not compromise the liability insured by the U.S. Fire policies, which indemnify Treadwell for losses due to the settlement of covered claims themselves. Moreover, whereas the agreements in Stonewall saved transaction costs that would otherwise have been borne by the insurers, the Settlement Agreement in this case does not produce similar efficiency gains. Thus, while the non-settling insurers in Stonewall might have complained had NGC not entered into the Wellington and CCR Producer Agreements, see Stonewall, 73 F.3d at 1207, U.S. Fire would have had no cause for complaint if Treadwell failed to enter into the Settlement Agreement.

Nor, as an additional matter, would allowing Treadwell to allocate its own payments to the 1970-1972 period further the worthy goal of promoting settlement. Assuming that Treadwell’s share of the total loss was, in fact, based on the proportion of years AMLIC was on the risk during the Coverage Block — a proposition nowhere stated in the Settlement Agreement — Treadwell received a windfall in the Settlement Agreement. That is, CIGNA and Travelers assumed responsibility for a substantial amount of the loss that, in the absence of settlement, would have been borne by Treadwell. Thus, Treadwell would have had sufficient incentive to settle even if it had known that its payments would have to be allocated across all years it was uninsured. To allow Treadwell to allocate all its payments to the AMLIC policy period, therefore, would be to give Treadwell a double windfall, the second at U.S. Fire’s expense, without any countervailing justification.

In short, while Treadwell can allocate $475,000 of its payments — the amount of the AMLIC Payment — to the 1970-1972 policy period, the remainder of its payments must be allocated across all the years of each claimant’s injury in which Treadwell was uninsured, including the period prior to 1967.

VII.

The consequences of this ruling are as follows. First, $475,000 of Treadwell’s payments are allocated to the 1970-1972 policy period, prorated evenly across the three years. Second, notwithstanding Treadwell’s complaint of impracticability Csee Treadwell Mem. in Opp’n at 7-11), Treadwell’s payments in excess of $475,000 (currently $469,984) are allocated pro rata across all years in which Treadwell was uninsured during each Asbestos Claimant’s period of injury.

The parties have not submitted comprehensive data with respect to when each Asbestos Claimant was first exposed to asbestos at a Treadwell powerhouse. Accordingly, it is impossible for me to determine with certainty how much of Tread-well’s payments in excess of $475,000 are attributable to the 1970-1972 period, when the U.S. Fire policies were in effect. Nevertheless, it can be inferred from the parties’ arguments and from the limited data that is in the record (see Reilly Aff. Ex. D), that according to the rulings announced in *113 this opinion, none of AMLIC’s policies has yet been exhausted, and none of U.S. Fire’s obligations to defend or indemnify triggered. That is, Treadwell’s payments and the portion of the AMLIC Payment attributable to any one year of the AMLIC policy period do not yet exceed $300,000.

Thus, summary judgment is granted to U.S. Fire, contingent upon a determination that the payments attributable to the AM-LIC policy period do not in fact exceed $300,000 in any one year. The parties are ordered to determine, based on the relevant data and the rulings set forth in this opinion, the actual amount of Treadwell’s payments in excess of $475,000 attributable to the AMLIC policy years and to settle judgment accordingly. To the extent that the relevant data are unavailable — -that is, if some of the Asbestos Claimants’ initial exposure dates cannot be determined — the parties are directed to use random sampling or other statistical methods to allocate those claims based on the known data. Cf. UNR Indus., Inc. v. Continental Cas. Co., 942 F.2d 1101, 1107 (7th Cir.1991) (sanctioning the use of statistical methods in allocating liability to particular policy periods when the relevant data are unknown or prohibitively expensive to obtain); Eagle-Picher Indus., Inc. v. Liberty Mut. Ins. Co., 829 F.2d 227, 235-37 (1st Cir.1987) (same); Maryland Cas. Co., 1996 WL 109068, at *9-10 (same). In the unfortunate event that the parties cannot settle judgment on their own, I will appoint a special master at the parties’ expense to make the relevant calculations. See Fed.R.Civ.P. 53 (authorizing the appointment of a special master at the expense of the parties in a complex case); cf. Squibb, 853 F.Supp. at 102-03 (stating that if the parties could not agree on the defendants’ liability in light of the Court’s opinion, the Court would consider appointment of a special master at their expense).

i|< ‡ ‡ ;¡:

For the reasons stated above, Tread-well’s motion for summary judgment is denied, U.S. Fire’s motion is granted and Treadwell’s amended third-party complaint is dismissed, all contingent upon a determination based on the rulings set forth in this opinion that none of the AMLIC policies has been exhausted. I will confer with the parties to establish a schedule for settling a judgment.

Notes

. "Slip.” refers lo the "Stipulation of Material Facts Not in Dispute for Purpose of Summary Judgment Motions," so ordered August 26, 1998.

. "Compl." refers to the Amended Cross-Claim and Amended Third-Party Complaint of Treadwell Corporation, dated August 27, 1997.

. The parlies agreed by stipulation that, as of July 22, 1998, more than 5000 asbestos-related lawsuits were pending against Treadwell. (Stip-¶ 2) Citing this agreement, U.S. Fire states that it "has not confirmed that any additional Asbestos-Related Claims have been asserted against Treadwell.” (U.S. Fire Local Rule 56.1 Statement ¶ 7) Because U.S. Fire has not produced " 'specific facts indicating’ that a genuine factual issue exists,” however, I have accepted Treadwell’s figure for the purposes of these motions. Scotto v. Almenas, 143 F.3d 105, 114 (2d Cir.1998) (quoting Wright v. Coughlin, 132 F.3d 133, 137 (2d Cir.1998)). For present purposes, this distinction is immaterial. See, e.g., Michael Dore, Insurance Coverage for Toxic Tort Claims; Solving the Self-Insurance Allocation Dilemma, 28 Tort & Ins. L.J. 823, 829 (1993).

. To be precise again, Treadwell did not purchase any insurance directly from CIGNA. Instead, CIGNA assumed coverage responsibility as a successor to several other insurance carriers. (Treadwell Local Rule 56.1 Statement ¶ 33)

. To be precise, Treadwell has been unable to identify any insurance coverage prior to 1967.

. The allocation established in the Interim Agreement corresponds only roughly to the primary insurers’ respective proportions of time on the risk between January 1, 1967 and July 1, 1986. Calculated based on the number of days that each insurer provided coverage, CIGNA, AMLIC and Travelers were on the risk 69.1%, 15.4% and 15.5%, respectively, of the so-called Coverage Block.

. “1996 Compl." refers to Treadwell's initial Third-Party Complaint, attached as Exhibit V to the Affidavit of Vincent E. Reilly.

. In addition to allocating responsibility for prospective costs, the Settlement Agreement provides for some reimbursement by USF & G and CU to CIGNA and Travelers for payments made by the latter prior to January 26, 1996, presumably pursuant to the Interim Agreement. (Agrmt. at 8-10, 14-16)

. It may be recalled that CIGNA, Travelers and AMLIC were on the risk 69.1%, 15.5% ■and 15.4%, respectively, of the Coverage Block. See supra note 6.

. Citing a stipulation between the parties that, as of December 31, 1997, Treadwell had paid or promised an aggregate of approximately $850,000 in indemnity payments (StipA 10), U.S. Fire states that it “has not confirmed that any additional payments have been made by Treadwell.” (U.S. Fire’s Local Rule 56.1 Statement ¶ 24) Again, because U.S. Fire has not produced specific facts indicating that a genuine issue exists, I have accepted Treadwell's figure for the purposes of these motions. See Scotto, 143 F.3d at 114.

. Under New York law, which the parties agree applies here (StipJ 13), an excess insurer is not required to drop down to provide coverage merely because the underlying primary insurer is insolvent. See Zeig v. Massachusetts Bonding & Ins. Co., 23 F.2d 665, 666 (2d Cir.1928) (Augustus Hand, J.); see also St. Vincent's Hosp. & Med. Ctr. v. Insurance Co. of N. Am., 117 Misc.2d 665, 457 N.Y.S.2d 670, 672 (Sup.Ct. N.Y. County 1982). Nevertheless, the excess policy is triggered when aggregate payments by the primary insurer, and by the insured in lieu of the insolvent primary insurer, exceed the underlying policy’s liability limits. See Zeig, 23 F.2d at 666. The question presented here is whether the AMLIC policies have been exhausted in this manner.

.By stipulation so ordered August 26, 1998 — the same day as the aforementioned Stipulation of Material Facts Not in Dispute for Purpose of Summary Judgment Motions— U.S. Fire abandoned the argument that it is not obligated to indemnify or defend until Treadwell has exhausted all of its primary insurance. (See also Treadwell Local Rule 56.1 Statement ¶ 60; 9/16/98 Johnson Aff. ¶ 18) U.S. Fire has not raised the pollution exclusion clause argument. Therefore, I have deemed that argument abandoned.

. I assume arguendo that judicial estoppel applies where the alleged prior inconsistent position was advanced either by a party or, as in this case, by its privy.

. To the extent Treadwell’s argument might be premised on North River’s failure to advocate the proration-to-the-insured approach specifically, it is without merit also. In Mad-sen & Howell, the plaintiff was insured for the entire relevant period. (See 9/17/98 War-shauer Aff. Ex. K at 19) Thus, North River’s silence with respect to the proration-to-the-insured approach is without significance.

. Treadwell appeals also to a common law doctrine called "mend the hold,” so named for a “nineteenth-century wrestling term, meaning to get a better grip (hold) on your opponent.” Harbor Ins. Co. v. Continental Bank Corp., 922 F.2d 357, 362 (7th Cir.1990) (Posner, J.). The doctrine, which was first enunciated by the Supreme Court in Ohio & Maryland Railway v. McCarthy, 96 U.S. 258, 24 L.Ed. 693 (1877), and has been applied only infrequently since, prohibits a party to a contract suit from taking one position and, after litigation has begun, changing its ground. See id. at 267-68; see also Harbor Ins., 922 F.2d at 362.

The doctrine’s reach, however, is "uncertain.” Harbor Ins., 922 F.2d at 364. Viewed as prohibiting a party from changing its position in litigation, the doctrine "is a cousin to judicial estoppel.” Id. at 364. Viewed more broadly, the doctrine "can be seen as a corollary of the duty of good faith that the law ... imposes on the parties to contracts.” Id. at 363. Nevertheless, either way the doctrine is inapplicable here. For the reasons discussed above, it cannot be said that U.S. Fire has taken inconsistent positions in this litigation; nor has Treadwell shown that U.S. Fire acted in bad faith generally.

. The crucial point, not recognized by Tread-well, is that the two issues — whether to allocate among all potentially liable parties in the first instance and whether or not to prorate to the insured based on uninsured periods — are analytically distinct. See Keene, 667 F.2d at 1058 & n. 6 (Wald, J., concurring in part) (advocating the joint and several approach, but concluding that the insured should be obligated to contribute for years it was uninsured); cf. Prudential Lines, 158 F.3d at 84 n. 12 (recognizing implicitly that the two questions are analytically distinct). Several courts also have made the mistake of confusing the question of allocation generally with allocating some liability to the insured. See, e.g., J.H. France, 626 A.2d at 507-09.

. The parties spend many pages discussing the effects of the Second Circuit’s decision in Stonewall on the allocation issue generally. The allocation issue, however, was not presented to, or decided by, the Stonewall Court. See Stonewall, 73 F.3d at 1202; see also Prudential Lines, 158 F.3d at 84 n. 12. To the extent relevant here, the only issue decided in Stonewall was whether the lower court erred in applying the proration-to-the-insured ap *98 proach. See Prudential Lines, 158 F.3d at 84 n. 12. As noted, that issue is analytically distinct from the prior question of whether to allocate in the first instance.

The New York Court of Appeals has not yet considered the allocation issue directly. The closest it came to doing so was in Continental Casualty Co. v. Rapid-American Corp., 80 N.Y.2d 640, 593 N.Y.S.2d 966, 609 N.E.2d 506 (1993), which held that "pro rata sharing of defense costs may be ordered,” but that there was "no error or unfairness in declining to order such sharing, with the understanding that the insurer may later obtain contribution from other applicable policies.” Id. at 655-56, 593 N.Y.S.2d at 974, 609 N.E.2d 506, (emphasis added). The Court did not decide whether pro rata allocation of indemnification was warranted, let alone at what stage that issue should be considered. See id. at 655, 593 N.Y.S.2d at 973-74, 609 N.E.2d 506. Nor did the Court decide whether an insured must contribute to defense costs for periods in which it was uninsured, stating that this question “is appropriately deferred at least until such time as the underlying lawsuits are shown to involve ‘occurrences' during self-insured periods.” Id. at 656, 593 N.Y.S.2d at 974, 609 N.E.2d 506.

. The policy language in this case (“all sums”) is slightly different from the policy language in Prudential Lines ("any loss”). This difference, however, is immaterial for present purposes. Cf. Prudential Lines, 170 B.R. at 235 (opining that there is “no material difference between ... [t]he term 'any loss' in the [American Club] policies ... [and] the 'all sums' language in [other CGL] policies”).

. Strictly speaking, because the Stonewall Court did not consider which approach to allocation was warranted, this statement is dictum with respect to the present issue, but it is the kind of dictum that warrants "considerable weight.” United States v. Bell, 524 F.2d 202, 206 (2d Cir.1975) (distinguishing between " 'obiter dictum,’ which constitutes an aside or an unnecessary extension of comments, and considered or ‘judicial dictum' ”); see also United States v. Oshatz, 912 F.2d 534, 540 (2d Cir.1990) ("[I]n some contexts expressions of views by an appellate court must be regarded as the law of the circuit, even though not an announcement of a holding or even of a necessary step in the reasoning leading to a holding.”).

. To the extent that these arguments were adopted or rejected in opinions cited by the Prudential Lines Court, it might be argued that the Second Circuit implicitly rejected them. Nevertheless, I decline to read into the Court's opinion what is not actually there. Cf. ITT Corp. v. United States, Nos. 84 CIV. 5458 PKL to 84 CIV. 5461 PKL, 1990 WL 71475, at *2 (S.D.N.Y. May 22, 1990), rev’d on other grounds, 963 F.2d 561 (2d Cir.1992).

. Indeed, the speakers themselves rarely professed to offer more than their own individual opinions. For example, one of the documents on which Treadwell relies, the minutes of a September 1964 meeting of the Joint Forms Committee of the National Bureau of Casualty Underwriters and the Mutual Insurance Rating Bureau, reads in relevant part:

Mr. Schoen [of Hartford Accident & Indemnity Company] said that as a fundamental principle we want to cover ... everything flowing from an injurious exposure during the policy period. Mr. Schmalz [of Liberty Mutual Insurance Company] said his understanding was the same, though .it was not the approach he would choose. He thought Mr. Katz [of Aetna Casualty & Surety Company] believed that as to a protracted exposure, the policy in effect at the time the injury became manifest should pay and there should not be proration. Mr. Katz said he did not completely agree with Mr. Schmalz's remarks, and went on to explain that prorating cannot be effectuated between the insurer and the claimant. Between two insurers, of course, they would prorate....

(9/17/98 Warshauer Aff. Ex. C at 11)

. Treadwell invokes also the "reasonable expectations doctrine,” which holds that "if an ambiguity arises that cannot be resolved by examining the parties' intentions, then the ambiguous language should be construed in accordance with the reasonable expectations of the insured when he entered into the contract.” Haber, 137 F.3d at 697. But Tread-well states only that it reasonably expected "U.S. Fire would pay upon exhaustion of the AMLIC policies” (Treadwell Mem. at 49), a proposition which is not in dispute.

Even if Treadwell had invoked die reasonable expectations doctrine with respect to the issue in dispute, that would not have changed the result. "Assessing the objectively reasonable expectations of a policyholder in this context of long-tail injuries is ... very difficult,” Owens-Illinois, 650 A.2d at 991, if not impossible. See Keene, 667 F.2d at 1058 (Wald, J., concurring in part); American Home Prods., 565 F.Supp. at 1511; cf. Do-herty, Allocating Progressive Injury Liability, supra, at 268; Gillespie, Allocation of Coverage Responsibility, supra, at 566-68.

. It may be recalled that USF & G and CU agreed to contribute toward Treadwell’s 15.2% share in connection with claims arising from the powerhouse sites for which they provided coverage. These contributions are immaterial for present purposes.

. Interestingly—and significantly, as may be seen later in this opinion, see infra note 26— neither Treadwell nor U.S. Fire questions the allocation of CIGNA’s and Travelers's shares to those insurers’ respective policy periods. Notwithstanding this silence, if the AMLIC Payment should not be allocated entirely to the AMLIC policy period, it follows that CIG-NA’s and Travelers’s payments should not be allocated entirely to their policy periods either.

. By settling, C will save the costs of liliga-lion. For the purposes of comparing the ef- *110 feels of one rule versus another, however, such savings are immaterial.

. Indeed, it is notable in this regard that U.S. Fire does not question the allocation of CIGNA’s and Travelers’s shares to those insurers’ respective policy periods. See supra note 24. Because U.S. Fire is an excess insurer for a different policy period, U.S. Fire stands to gain from the fact that these insurers assumed more liability through the Settlement Agreement than they would have been allocated in the absence of settlement.

. Strictly speaking, the AMLIC Agreement did not limit the AMLIC Payment to the 1970-1972 period. Rather, the payment was made in exchange for a general release from liability under “any and all insurance policies which may have been issued by [AMLIC] to Treadwell, known or unknown(Slip. Ex. E ¶ 2 (emphasis added)) Nevertheless, there is no evidence in the record that AMLIC con-traded to cover any period other than 1970 through 1972. Accordingly, the AMLIC Payment should be allocated in its entirety to those years.

. Each of the parties relies as well on Judge Martin's decision in E.R. Squibb & Sons, Inc. v. Accident & Casualty Insurance Co., No. 82 CIV. 7327(JSM), 1997 WL 251548 (S.D.N.Y. May 13, 1997). In that case, also involving insurance coverage for continuous injury, Judge Martin rejected an argument by the defendant insurers that they were entitled to set-offs based on the amounts paid by other insurers who settled for what turned out to be more than they were legally obligated to pay. See id. at *2. The non-settling insurers, Judge Martin held, were liable for the amount that they were contractually obligated to pay, even if such payment resulted in a windfall for the insured. See id. Squibb, however, is distinguishable from this case in that it did not *111 involve excess insurance. Further, the holding is in tension with the conclusion reached above that settlements should be binding for allocation purposes on both the insured and its excess insurers.