WALKER, Circuit Judge:

General Reinsurance Corporation (General Re) appeals from a judgment and order of the United States District Court for the Southern District of New York (Hon. John F. Keenan, Judge) directing that it reimburse United States Fire Insurance Company (U.S. Fire) for funds paid in settlement of a malpractice claim asserted against South Nassau Communities Hospital (Hospital). At the time the malpractice cause of action accrued, the Hospital was covered under three liability insurance policies. The Insurance Company of North America (INA) provided the Hospital’s primary layer of insurance. In the event that the Hospital was exposed to liability that exceeded the limits of the INA policy, it was covered by two excess liability insurers— General Re and U.S. Fire. The two parties are at odds in this case as to the order in which their respective excess policies should come into play.

The issue of which insurer had initial excess liability exposure turns on the construction of the excess insurance contract entered into between the Hospital and General Re. The district court concluded that the language of the General Re policy unambiguously obligated General Re to provide an immediate second layer of insurance coverage. On appeal, General Re argues that the district court, in construing the General Re policy, erred in declining to consider extrinsic evidence that would demonstrate the intent of the Hospital and General Re as to the point at which General Re’s excess coverage would attach. The appellant also contends that the district court erroneously applied the doctrine of contra proferentem. We agree with the appellant on both points and, therefore, we reverse.

BACKGROUND

On June 27, 1967, Michael Lane was born at the Hospital but, as a result of nursing staff’s negligence, he suffered severe and permanent brain damage. In May of 1981, Lane sued the Hospital and other defendants in state court for damages. On May 15, 1987 the parties reached a settlement in the amount of $2.6 million, $2.2 million of which was attributable to the Hospital. As stated above, the Hospital’s insurance coverage was multi-layered, with three policies effective at the time of Lane’s injuries and potentially applicable to the Hospital’s $2.2 million liability.

The primary layer provided by INA insured against professional liability with a primary limit of $300,000 for each claim and a $1 million cap on an annual aggregate of claims. The INA policy also insured against bodily injury, setting coverage limits at $300,000 for each person injured, $1 million for each occurrence, and $1 million for the annual aggregate.

The excess coverage, that is coverage for liability sustained by the Hospital that surpassed the limits of the INA policy, was provided by U.S. Fire and General Re. Along with other forms of coverage, not relevant here, the U.S. Fire “Comprehensive Catastrophe Liability Policy,” protected the Hospital against hospital professional liability within excess limits of $3 million per claim, and an annual aggregate of $3 million.

*571 The limits of General Re’s excess liability policy were set forth in its “Excess Reinsurance Certificate” in the following cryptic provision:

“Bodily Injury liability and Hospital Malpractice Liability

Nil each person or claim/$l,000,000 each occurrence or aggregate.”

In settling the Lane suit, INA contributed $300,000, the full limit of its professional liability per claim coverage. U.S. Fire paid the remaining $1.9 million in return for the Hospital’s subrogation and assignment to U.S. Fire of all rights that the Hospital would have against General Re with respect to the Lane claim. There is no question in this case that, if General Re’s policy does not require it to contribute, U.S. Fire will bear the entire loss sustained by the Hospital in excess of the $300,000 covered by the INA primary layer of insurance.

In September, 1988, U.S. Fire brought this diversity action in the district court to recover from General Re the $1 million aggregate limit of General Re’s policy as contribution towards the Lane settlement. In the alternative, U.S. Fire asked the district court to apply the two excess liability policies on a pro rata basis toward paying the settlement and thereby order General Re to reimburse U.S. Fire $475,000 or 25% of the $1.9 million excess liability. The district court agreed with appellee U.S. Fire’s arguments that pursuant to the provisions of General Re’s “Excess Reinsurance Certificate,” General Re was obligated to pay $1 million immediately upon the exhaustion of the INA $300,000 per claim coverage. It entered judgment accordingly and this appeal followed.

DISCUSSION

I. Ambiguity

General Re argues that the district court erred in excluding extrinsic evidence to clarify the meaning of its policy to the effect that General Re’s liability would not have been triggered in this case. We agree. The district court stated “that as far as this Court can determine, [the General Re] policy ... is an integrated con-tract____ Accordingly, no extrinsic evidence should be considered in determining the parties’ intent in entering into the contract.” While this is a correct statement of the parol evidence rule in relation to unambiguous contracts, it fails to account for the exception accorded agreements that are ambiguous on their face.

The parties have jointly proceeded on the basis that New York law applies. According to New York law,

while the parol evidence rule requires the exclusion of evidence of conversations, negotiations and agreements made prior to or contemporaneous with the execution of a written [contract] which may tend to vary or contradict its terms ... such proof is generally admissible to explain ambiguities therein____

67 Wall Street Co. v. Franklin National Bank, 37 N.Y.2d 245, 248, 333 N.E.2d 184, 186-87, 371 N.Y.S.2d 915, 918 (1975) (citations omitted). Integration and ambiguity are not mutually exclusive. Even though a document may be fully integrated with respect to the ultimate terms of the agreement, the meaning of those terms may remain unclear. Therefore, “[e]ven where there is a complete integration, the rule will not rise up to bar ... [the consideration of extrinsic evidence] if the terms of the prior agreement are not inconsistent with the terms of the written integration.” Lee v. Joseph E. Seagram & Sons, Inc., 413 F.Supp. 693, 701 (S.D.N.Y.1976), aff'd, 552 F.2d 447 (2d Cir.1977) (applying New York Law).

Thus, the threshold question for us is whether the General Re policy is ambiguous. The district court made no explicit finding on this point. However, it appears to have made an indirect finding to that effect when it stated: “[t]o the degree [the General Re policy] contains ambiguities ... they are to be construed against General Re.” Whether or not the district court made such a finding, however, is not important since “the determination of whether a contract is ambiguous — and thus whether parol may be considered — is a threshold question of law for the court.” Garza v. *572 Marine Transport Lines, Inc., 861 F.2d 23, 27 (2d Cir.1988). See also Pantone, Inc. v. Esselte Letraset, LTD., 878 F.2d 601, 605 (2d Cir.1989). On appeal, we are free to examine the issue of ambiguity de novo. Garza, 861 F.2d at 27.

As with contracts generally, a provision in an insurance policy is ambiguous when it is reasonably susceptible to more than one reading. As we reiterated in Garza,

[a] word or phrase is ambiguous when it is capable of more than a single meaning “ ‘when viewed objectively by a reasonably intelligent person who has examined the context of the entire integrated agreement and who is cognizant of the customs, practices, usages and terminology as generally understood in the particular trade or business.’ ”

Id. (citing Walk-In Medical Centers, Inc. v. Breuer Capital Corp., 818 F.2d 260, 263 (2d Cir.1987)) (quoting Eskimo Pie Corp. v. Whitelawn Dairies, Inc., 284 F.Supp. 987, 994 (S.D.N.Y.1968)). With the forgoing in mind, we turn to the General Re policy.

Clauses A and C, and Item 4 of the Declarations contained in General Re’s “Excess Reinsurance Certificate” provide as follows:

A. Whereas certain insurance carriers have issued to the Reinsured a policy or policies of underlying excess insurance providing coverage as described in Item 2 of the Declarations,

******

C. Now Therefore, this Certificate is to further indemnify the Reinsured against ultimate net loss in excess of the total of all applicable limits of insurance described in A ... above, but only up to an amount not exceeding the limit shown in Item 4 of the Declarations.

******

Item 4. Limit(s) and Application of Coverage Hereunder

Bodily Injury Liability and Hospital Malpractice Liability

Nil each person or claim/$l,000,000 each occurrence or aggregate

In referring to Item 2 of the Declarations, Clause A incorporates the limits of INA’s primary coverage into the General Re policy. However, upon reading Clause C in conjunction with Clause A and Item 4 of the Declarations, the policy becomes ambiguous. Clause C provides that General Re will indemnify the Hospital “against ultimate net loss in excess of the total of all applicable limits [of the INA policy,] ... but only up to an amount not exceeding the limit shown in Item 4 of the Declarations.” By its reference to Clause A and Item 4, Clause C establishes both the starting and endpoints of the General Re excess coverage. Unfortunately, Clause A and Item 4 do not clearly define these important boundaries.

U.S. Fire argues that the phrase in Clause C, “in excess of the total of all applicable limits,” includes INA’s $300,000 per claim sublimit on professional liability coverage. Therefore, as soon as the Hospital exhausted its INA per claim sublimit, General Re was obliged to pay the remaining liability on the Lane claim.

U.S. Fire also contends that, for both bodily injury and hospital malpractice insurance, Item 4 denies coverage on a per claim or per person basis, but provides $1 million per occurrence or upon the exhaustion of the INA aggregate limit. If the Lane incident were considered an “occurrence,” it appears that U.S. Fire could avoid the policy’s troublesome “Nil each person or claim” restriction. In characterizing the Lane incident as an “occurrence,” U.S. Fire argues that “[s]ince South Nassau had a duty [to General Re] under Notice of Loss to report Hospital Malpractice ‘occurrences' there is no textual reason to suggest that General Re did not insure Hospital Malpractice on an ‘occurrence’ basis.”

General Re offers a different reading of its policy. It asserts that the language of Clause C concerning the underlying “applicable limits” — the limits that trigger its own obligation — solely refers to INA’s aggregate limit and not to the INA per claim restriction. In support of this interpretation, General Re points out that the *573 limits established by Item 4 specifically preclude malpractice coverage on a per claim basis. General Re also insists that the terms “person” and “occurrence,” employed in Item 4, relate to bodily injury insurance and not to its malpractice provisions. The construction urged upon us by General Re provides the Hospital with the following excess coverage: Bodily Injury Liability — Nothing per each person/$l million per each occurrence/$l million aggregate; Malpractice Liability — Nothing per each claim/$l million aggregate.

General Re concedes that if the Hospital had exhausted its INA $1 million aggregate, it would have had to pay, up to its own $1 million limit, all remaining malpractice claims for which the Hospital was liable. Since the INA limit had not been exhausted for the period in question, General Re denies any liability with respect to the Lane claim.

We hold that the General Re “Certificate of Reinsurance” is ambiguous. In reaching this conclusion we need not consider the relationship between the term “occurrence” and the two types of coverage provided by the General Re policy. The terms of the policy regarding “all applicable limits,” taken in conjunction with Item 4 of the Declarations, are sufficiently unclear to warrant the consideration of parol evidence.

Clause G indemnifies the Hospital against “the total of all applicable limits of insurance described in [Clause] A----” However, that indemnification is specifically made subject to the “limit shown in Item 4 of the Declarations.” While Clause A arguably incorporates the INA $300,000 per claim sublimit into the General Re coverage, Item 4 denies any coverage on a “per claim” basis. A policy that takes back with one provision what it gives with another is ambiguous. Nor do we necessarily have to read the two sections as contradictory. While Item 4 specifically negates per claim coverage, Clause C speaks in terms of “all applicable limits.” These two sections are capable of being harmonized if read together as simply providing that INA’s “per claim” limits are not “applicable under the General Re policy. In any event, the policy’s provisions are “capable of more than a single meaning” and, therefore, the contract is ambiguous. Garza, 861 F.2d at 27.

II. Application of Contra Proferentem

The district court ruled that to the extent the Certificate of Reinsurance was ambiguous it must be construed against General Re. Here, the court invoked the rule of contract construction known as contra proferentem, which literally means “against the offeror.” In the insurance context, the rule requires that an ambiguous policy be construed against the insurer.

The district court relied heavily upon the older New York cases of Kratzenstein v. Western Assurance Co., 116 N.Y. 54, 22 N.E. 221 (1889), and Janneck v. The Metropolitan Life Insurance Co., 162 N.Y. 574, 57 N.E. 182 (1900). These cases, however, describe the rule’s earlier and more rigid application. Presently, “contra preferen-tem [sic] is used only as a matter of last resort after all aids to construction have been employed but have failed to resolve the ambiguities in the written instrument.” Schering Corp. v. Home Insurance Co., 712 F.2d 4, 10 n. 2 (2d Cir.1983) (citing Hartford Accident & Indem. Co. v. Wesolowski, 33 N.Y.2d 169, 172, 350 N.Y.S.2d 895, 305 N.E.2d 907 (1973)).

The New York courts have specifically stated that the rule “is not applicable in a contest between two insurance companies.” Loblaw, Inc. v. Employers’ Liability Assurance Corp., 85 A.D.2d 880, 881, 446 N.Y.S.2d 743, 745 (4th Dep’t 1981), aff'd, 57 N.Y.2d 872, 442 N.E.2d 438, 456 N.Y.S.2d 40 (1982); Standard Marine Insurance Co., LTD v. Federal Insurance Co., 39 A.D.2d 444, 446, 336 N.Y.S.2d 692, 695 (1st Dep’t 1972) (per curiam). Indeed, the circumstances of Standard Marine are quite similar to the ones involved in this case. Standard Marine concerned a dispute over reimbursement for a fire loss sustained' by a parent company and its wholly owned subsidiary. The parent’s insurer claimed that the subsidiary’s carrier was obliged to pay for the loss. The sub *574 sidiary’s insurer denied liability and argued that the parent’s company was responsible to cover the claims. Eventually, each carrier paid its insured and then turned on its counterpart for reimbursement. On appeal, the sole issue was whether the language of subsidiary’s policy obligated its insurer to pay for the entire loss. While the court ultimately decided that the subsidiary’s policy was unambiguous and did not provide the disputed coverage, it nevertheless went on to reject the argument that contra proferentem is applicable in a case between two insurers. Standard Marine, 39 A.D.2d at 446, 336 N.Y.S.2d at 695.

In Loblaw, the court more fully explained the rationale behind its refusal to apply the rule in inter-insurer disputes. It stated:

Loblaw argues that there is a patent ambiguity which must be construed against the insurer and in favor of the insured ... That rule, however, is not applicable in a contest between two insurance companies____ While it is true that Loblaw is not an insurance company, where, as here, it acts as a self-insurer with respect to Workers Compensation claims through its agent, a licensed insurance adjusting company, its status is more akin to that of an insurance company than to that of an individual who is inexperienced in matters of insurance coverage for whose benefit the rule was promulgated.

Loblaw, 85 A.D.2d at 881, 446 N.Y.S.2d at 745. (citations omitted).

Loblaw suggests that the touchstone for applying contra proferentem is the insured’s lack of sophistication. Where the dispute is between two insurance companies, both parties are sophisticated business entities, familiar with the market in which they deal and armed with relatively equivalent bargaining power; hence, the contra insurer rule serves little purpose. See Schering Corp., 712 F.2d at 10 n. 2 (noting that “a number of courts have recognized that in cases involving bargained-for contracts, negotiated by sophisticated parties, the underlying adhesion contract for the doctrine rationale is inapposite”).

Where, as here, the justifications for applying the rule seem to be lacking, and there exists ample extrinsic evidence, which, properly considered, clarifies the policy's “per claim”/“applicable limit” ambiguity, we find that the district court erred in applying the doctrine of contra proferentem.

III. The Extrinsic Evidence

Having determined that a contract is ambiguous, and that parol evidence must be employed to elucidate the parties’ contractual intent, we usually remand the case to the district court for any necessary consideration and findings. However, since all relevant extrinsic evidence concerning the parties’ intent has already been presented to the trial court, and is contained in the record, a remand is unnecessary here. See Adams v. Agnew, 860 F.2d 1093, 1097 (D.C.Cir.1988); Otto v. Variable Annuity Life Ins. Co., 814 F.2d 1127, 1138 & n. 11 (7th Cir.1986); King v. C.I.R., 458 F.2d 245, 249 (6th Cir.1972); 9 Wright & Miller, Federal Practice and Procedure § 2577 (1971 & Supp.1990). “As we have before us the same record, and as no part of the decision below turned on credibility, we are in as good a position to determine the question as is the district court.” Concord Fabrics, Inc. v. Marcus Brothers Textile Corp., 409 F.2d 1315, 1317 (2d Cir.1969).

Numerous documents were admitted at trial to clarify the parities’ intent. Two documents are dispositive: 1) the Johnson & Higgins insurance binder regarding the General Re policy, and 2) the Hospital’s own insurance committee minutes.

Upon reading the insurance binder prepared by the Hospital’s insurance brokers, Johnson & Higgins, the cloud of ambiguity lifts and the terms of the General Re excess coverage become remarkably clear. It provides:

*575 Excess Bodily Injury Liability:

Underlying Limits Excess Limits Total Limits

CGL 300,000 each person nil each person 300,000each person

1,000,000 each occurrence 1,000,000 each occurrence 2,000,000 each occurrence

1,000,000 aggregate 1,000,000 aggregate 2,000,000 aggregate

HPL 300,000each claim nil each claim 300,000each claim

1,000,000 aggregate 1,000,000 aggregate 2,000,000 aggregate

The relevant section is that following the caption “HPL.” HPL is an abbreviation for “Hospital Professional Liability.” As set out, the HPL limits corroborate General Re’s reading of its excess malpractice policy. The binder demonstrates that the Hospital’s HPL coverage is comprised of an underlying $300,000 INA per claim limit, a General Re excess limit of “nil each claim,” and a total coverage limit of $300,000 per claim. It also establishes that General Re’s aggregate coverage does not become active until the Hospital’s underlying INA aggregate limit is exhausted, thereby giving the Hospital total aggregate coverage of $2 million. According to the binder agreement, the parties’ intent with respect to the “applicable 3imit[ ]” discussed in Clause C seems to have been the INA $1 million aggregate. Apparently it was not, as U.S. Fire contends, the INA $300,000 per claim sublimit.

In rejecting the construction that we find persuasive, the district court stated that such a reading would lead to “strange results.” However, the potential results over which the district court was disturbed seem to be not so much “strange” as they are a function of the Hospital’s poor planning. The fact that under General Re’s policy the Hospital had only $300,000 worth of malpractice coverage so long as the INA aggregate had not been exhausted appears to be the motivating factor behind the Hospital’s purchase of the U.S. Fire Comprehensive Catastrophe Policy.

The second controlling piece of parol evidence is the minutes of the Hospital’s insurance committee meeting, held on May 18,1965. The minutes recount the meeting as follows:

1. Mr. Kirkwood discussed the need for greater limits on the Hospital’s General Public Liability and Professional Liability Insurance coverage which now for Bodily Injury amounts to $300,000 each person/$2,000,000 aggregate.

The Committee authorized the placement of an additional $1,000,000 “Umbrella” coverage, increasing the $300,000 to $1,300,000 and increasing the $2,000,000 to $3,000,000, at an approximate annual premium cost of $1,500. (Note A)

2. The Committee expressed interest in obtaining even greater limits of coverage and authorized Mr. Kirkwood to place the increased coverage which seemed reasonable in relation to the premium cost. (Note B)

* * * * * *

Note A: On May 19, 1965 a binder was placed for $1,000,000 additional excess liability coverage by the U.S. Fire Insurance Company.

Note B: On May 21, 1965 a binder was placed for an additional $2,000,000 excess *576 liability coverage, bringing total limits to $3,300,000/$5,000,000, at an estimated annual premium cost of $1,000.

(emphasis added).

The minutes show that prior to its purchase of the U.S. Fire policy the Hospital’s malpractice coverage was $300,000 per person/$2 million aggregate. In its own view, the committee’s authorization of an additional $1 million policy brought the per claim limit up to $1.3 million, and the total aggregate limit from $2 million to $3 million. “Note B” reiterates the point by concluding that the subsequent purchase of yet another $2 million of excess insurance brought the Hospital’s total coverage to $3.3 million per person/$5 million aggregate. This evidence proves that the Hospital was fully aware that its General Re excess coverage incepted only after its underlying INA aggregate had been exhausted.

In light of the binder agreement and the evidence regarding the Hospital’s own understanding of its General Re insurance — an understanding that prompted it to purchase further insurance from U.S. Fire — it is obvious that the General Re policy was never intended to cover the Lane claim.

CONCLUSION

For the reasons discussed in this opinion, we hold that the General Re Certificate of Reinsurance is ambiguous. We further hold that the extrinsic evidence, properly construed, demonstrates that the Hospital’s General Re malpractice coverage did not incept until after the Hospital had exhausted the aggregate limit of its primary insurer. Therefore, we reverse the judgment of the district court, and vacate the award in favor of U.S. Fire.