JOSÉ A. CABRANES, Circuit Judge:

This insurance case raises two issues. First, we consider our appellate jurisdiction. Although we usually may not review voluntary dismissals of claims or denials of motions for summary judgment, this case presents the unusual situation in which we are asked to review the voluntary dismissal of a claim following the denial of a motion for summary judgment. Our review is appropriate in these circumstances because (1) the United States District Court for the Southern District of New York (Richard J. Sullivan, Judge) rejected the legal basis for the appellants' counter-claim; (2) the District Court disposed of all claims with prejudice; and (3) the appellants consented to the final judgment solely to obtain immediate appeal of the prior adverse decision, without pursuing piecemeal appellate review.

Second, we interpret several "excess" liability insurance policies, which provide insurance protection beyond the protection provided by underlying policies. Each excess liability insurance policy at issue includes an exhaustion clause, which states that the excess insurance coverage attaches only after a certain amount of underlying insurance coverage is exhausted "as a result of payment of losses thereunder." Based on this language, the insured appellants argue that their liability must reach the attachment point in order to trigger the excess coverage. By contrast, the insurer appellees argue that the excess liability coverage is only triggered when liability payments reach the attachment point. We conclude that the plain language of the insurance policies supports the view of the insurer appellees. Accordingly, the judgment of the District Court is affirmed.

BACKGROUND

The appellants are the former directors and officers (collectively, "the Directors") of Commodore International Limited ("Commodore"), a computer technology company that in 1994 ceased operations and filed for bankruptcy.1 By the time that Commodore filed for bankruptcy, it had purchased a series of insurance policies designed to protect the Directors from potential liability. The "primary" insurance policy covered the first $10 million in liability, and each successive "excess" insurance policy provided a discrete level of coverage in excess of the coverage in the "underlying" agreements, thus creating a layered "tower" of liability protection.2 For instance, the first excess policy provided $5 million of protection in excess of $10 million in liability payments (the first excess policy's "attachment point"), the second excess insurance policy provided $5 million of protection in excess of $15 million in liability payments, and so on. This suit arose because two of the underlying insurers — Reliance Insurance Company ("Reliance") and the Home Insurance Company ("Home") — have ceased operations and liquidated their assets.3

Appellee Federal Insurance Company ("FIC") is the still-operational provider of the Directors' second and fifth excess insurance policies. See note 2, ante. Anticipating that the Directors would file claims relating to a suit pending in the Supreme Court of the Commonwealth of the Bahamas (the "Bahamas Litigation"),4 FIC filed a declaratory relief action against the Directors in the Southern District of New York, seeking a declaration that, under the terms of the relevant insurance policies, FIC is not required to "drop down" to cover liability that would have otherwise been covered by Reliance and Home. FIC moved for judgment on the pleadings. The District Court granted FIC the requested declaratory relief in an order dated September 28, 2011. See Fed. Ins. Co. v. Estate of Gould, No. 10 Civ. 1160(RJS), 2011 WL 4552381, at *3-5 (S.D.N.Y. Sept. 28, 2011). The Directors do not appeal this aspect of the District Court's order.

In the same proceedings, the Directors filed a counter-claim against FIC and also sued third-party-defendant Travelers Casualty and Surety Company of America ("Travelers") — the provider of the seventh excess insurance policy in the tower. See note 2, ante. With respect to their counter-claim and third-party suit, and in response to the FIC's declaratory action, the Directors sought a declaration that "Federal and Travelers' coverage obligations are triggered once the total amount of [the Directors'] defense and/or indemnity obligations exceeds the limits of any insurance policies underlying their respective policies, regardless of whether such amounts have actually been paid by those underlying insurance companies." Joint App'x at 417 (emphasis supplied). The Directors then moved for partial summary judgment with respect to this request for declaratory relief.

In the same order granting FIC's motion on the "drop down" issue, the District Court denied the Directors' motion for partial summary judgment. Specifically, the Court held that "[i]n each policy, the excess coverage is not triggered until the underlying insurance is exhausted `solely as a result of payment of losses thereunder,'" and therefore "the excess coverage will not be triggered solely by the aggregation of [the Directors'] covered losses." Fed. Ins. Co., 2011 WL 4552381, at *7. Instead, the Court explained, "the Excess Policies expressly state that coverage does not attach until there is payment of the underlying losses." Id.

Following that decision, the parties submitted a letter to the District Court agreeing that "`all remaining claims and third-party claims should be dismissed with prejudice.'" Fed. Ins. Co. v. Estate of Gould, No. 10 Civ. 1160(RJS) (S.D.N.Y. filed Oct. 30, 2011), ECF No. 69 (quoting the parties' letter of Oct. 28, 2011). Pursuant to that agreement, the District Court ordered "that this case is dismissed with prejudice but without costs." Id.; see also Fed.R.Civ.P. 41(a)(2).5

The Directors then appealed the judgment, contesting only the Court's denial of their motion for partial summary judgment with respect to their request for declaratory relief.

DISCUSSION

A.

This case comes to us in an unusual posture — an appeal from a voluntary dismissal of a claim following the denial of a motion for partial summary judgment. We generally lack appellate jurisdiction to review voluntary dismissals of claims or denials of motions for summary judgment. See Empire Volkswagen, Inc. v. World-Wide Volkswagen Corp., 814 F.2d 90, 94 (2d Cir.1987) (voluntarily dismissed claims); DiStiso v. Cook, 691 F.3d 226, 239 (2d Cir.2012) (denials of motions for summary judgment); see also Steel Co. v. Citizens for a Better Env't, 523 U.S. 83, 93-94, 118 S.Ct. 1003, 140 L.Ed.2d 210 (1998) (reciting the familiar rule that jurisdiction must exist before reviewing the merits). Nonetheless, for the reasons stated below, this case presents the unusual circumstances where we may review a final judgment that resulted from a voluntary dismissal following a denial of a motion for summary judgment.

Orders granting "Rule 41(a)(2) motions for voluntary dismissal are not usually appealable, since it is presumed that plaintiffs obtained that which they sought." Coliseum Square Ass'n, Inc. v. Jackson, 465 F.3d 215, 249 (5th Cir.2006); see also Empire Volkswagen, 814 F.2d at 94. The rationale for this rule has little weight, however, where the appellant "lost on the merits and [is] only seeking an expeditious review." United States v. Procter & Gamble Co., 356 U.S. 677, 681, 78 S.Ct. 983, 2 L.Ed.2d 1077 (1958). In that situation, an appellant has not "`consent[ed] to a judgment..., but only that, if there was to be such a judgment, it should be final in form instead of interlocutory, so that [an appeal may be taken] without further delay.'" Id. (quoting Thomsen v. Cayser, 243 U.S. 66, 83, 37 S.Ct. 353, 61 L.Ed. 597 (1917)).

For that reason, "`[w]hen the dismissal is with prejudice, plaintiffs have been allowed, in limited circumstances, to appeal from a voluntary dismissal when the plaintiffs' solicitation of the formal dismissal was designed only to expedite review of a prior order which had in effect dismissed plaintiffs' complaint.'" Chappelle v. Beacon Commc'ns Corp., 84 F.3d 652, 653 (2d Cir.1996) (alterations and internal quotation marks omitted) (quoting Empire Volkswagen, 814 F.2d at 94).6 In order to qualify as an "effective dismissal" of the claim, Empire Volkswagen, 814 F.2d at 95, the adverse ruling must have rejected the claim "as a matter of law," Palmieri v. Defaria, 88 F.3d 136, 140 (2d Cir.1996).7 Because the invitation to dismiss must be designed only to secure immediate appellate review of an adverse decision, parties cannot appeal "a joint stipulation to voluntary dismissal, entered unconditionally by the court pursuant to a settlement agreement." Concha v. London, 62 F.3d 1493, 1507 (9th Cir.1995). If claims unaffected by the adverse ruling are also pending, "[a] party who loses on a dispositive issue that affects only a portion of his claims may elect to abandon the unaffected claims, invite a final judgment, and thereby secure review of the adverse ruling." Rabbi Jacob Joseph Sch. v. Province of Mendoza, 425 F.3d 207, 210 (2d Cir.2005) (quotation marks omitted). These strict requirements allow plaintiffs and counter-claimants to retain control of their own claims while also ensuring that voluntary dismissals are not used to obtain piecemeal appellate review. See Smith v. Half Hollow Hills Cent. Sch. Dist., 298 F.3d 168, 172 (2d Cir.2002) ("[T]he federal policy against piecemeal appeals is not implicated where an entire case can be decided in a single appeal." (citing Cuoco v. Moritsugu, 222 F.3d 99, 110 (2d Cir.2000))).

The only claim at issue in this appeal is the Directors' request for a declaration that the relevant "coverage obligations are triggered once the total amount of [the Directors'] defense and/or indemnity obligations exceeds the limits of any insurance policies underlying their respective policies, regardless of whether such amounts have actually been paid by those underlying insurance companies."8 Joint App'x at 417. On September 28, 2011, the District Court rejected this request as a matter of law.9 The Court held that the "express language" of the relevant contract terms "establishes a clear condition precedent to the attachment of the Excess Policies," by "expressly stat[ing] that coverage does not attach until there is payment of the underlying losses." Fed. Ins. Co., 2011 WL 4552381, at *7. In sum, the Court held, "the relief sought by [the Directors] contradicts the plain language of the Excess Policies." Id. at *6.

Although the Court's order denying the Directors' motion for summary judgment did not constitute a "final decision" appealable under 28 U.S.C. § 1291,10 see Ortiz v. Jordan, ___ U.S. ___, 131 S.Ct. 884, 891, 178 L.Ed.2d 703 (2011) ("Ordinarily, orders denying summary judgment do not qualify as `final decisions' subject to appeal."), the parties subsequently informed the District Court that they wished to dismiss with prejudice all pending claims and counter-claims pursuant to Rule 41(a)(2) of the Federal Rules of Civil Procedure in order to obtain immediate appellate review, see note 5, ante. The District Court then issued an order to that effect. See Fed. Ins. Co. v. Estate of Gould, No. 10 Civ. 1160(RJS) (S.D.N.Y. filed Oct. 30, 2011), ECF No. 69.

Once the District Court dismissed all pending claims and counter-claims with prejudice, an appeal became appropriate because (1) the District Court's order denying the Directors' motion for summary judgment plainly rejected the legal basis for the Directors' counter-claim; (2) the District Court had disposed of all claims with prejudice; and (3) the Directors' consent to the final judgment was designed solely to obtain immediate appeal of the prior adverse decision, without pursuing piecemeal appellate review. In these circumstances, we may review the District Court's judgment dismissing the Director's counter-claim.11 See Chappelle, 84 F.3d at 653 (citing Empire Volkswagen, 814 F.2d at 94).

B.

i.

Turning to the merits, we review de novo a grant or denial of summary judgment, construing the record in the light most favorable to the non-moving party. Mullins v. City of New York, 653 F.3d 104, 113 (2d Cir.2011). As in other contract disputes, insurance policies are interpreted according to their plain terms. See Fieldston Prop. Owners Ass'n, Inc. v. Hermitage Ins. Co., 16 N.Y.3d 257, 264, 920 N.Y.S.2d 763, 945 N.E.2d 1013 (2011); Harleysville Ins. Cos. v. Aetna Cas. & Sur. Ins. Co., 568 Pa. 255, 260-61, 795 A.2d 383 (2002).12 Because the plain meaning of contractual terms can depend on context, see Int'l Multifoods Corp. v. Commercial Union Ins. Co., 309 F.3d 76, 87 n. 4 (2d Cir.2002), we begin with a brief, general overview of excess liability policies, and then turn to the particular contractual language at issue.

In this context, "primary" insurance refers to the first layer of insurance coverage that attaches immediately upon the occurrence of a policy-defined liability or loss. See Horace Mann Ins. Co. v. Gen. Star Nat'l Ins. Co., 514 F.3d 327, 329 (4th Cir.2008). "Excess liability policies, by contrast, ... provide an additional layer of coverage for losses that exceed the limits of a primary liability policy. Coverage under an excess policy thus is triggered when the liability limits of the underlying primary insurance policy have been exhausted." Id.; see also Olin Corp. v. Am. Home Assurance Co., 704 F.3d 89, 93 (2d Cir.2012) (describing how excess liability policies operate). And, as illustrated by this case, "[e]xcess insurance may also be designed to operate above another excess policy," with coverage under the higher-layer excess policies triggered once the lower-layer excess policies are exhausted. Horace Mann Ins. Co., 514 F.3d at 329 n. 1. Accordingly, "the very nature of excess insurance coverage is such that a predetermined amount of underlying primary coverage must be paid before the excess coverage is activated." Gabarick v. Laurin Mar. (Am.), Inc., 649 F.3d 417, 422 (5th Cir.2011) (alteration and quotation marks omitted). "Because coverage is only triggered after the primary insurance limit has been exhausted, excess insurance is generally available at a lesser cost than the primary policy since the risk of loss is less than for the primary insurer." Id. (alteration and internal quotation marks omitted).

ii.

We now turn to the relevant language in the excess policies. Both FIC policies state that excess liability coverage "shall attach only after all ... `Underlying Insurance' has been exhausted by payment of claim(s)," Joint App'x at 278, 289 (emphasis supplied), and that "exhaustion" of the underlying insurance occurs "solely as a result of payment of losses thereunder."13 Id. at 273, 283 (emphasis supplied). Similarly, the Travelers policy states that excess liability coverage "shall attach only after all such Underlying Insurance has been exhausted," and that exhaustion occurs "solely as a result of payment of losses thereunder."14 Id. at 398 (emphasis supplied).

The Directors sought a declaration that these excess liability coverage obligations are triggered when "defense and/or indemnity obligations" reach the attachment point. But "obligations" are not synonymous with "payments" on those obligations. To hold otherwise would make the "payment of" language in these excess liability contracts superfluous. Accordingly, we agree with the District Court's conclusion that the "express language" of the relevant contract terms "establishes a clear condition precedent to the attachment of the Excess Policies," by "expressly stat[ing] that coverage does not attach until there is payment of the underlying losses." Fed. Ins. Co., 2011 WL 4552381, at *7. Because the plain language of the contracts specifies that the coverage obligation is not triggered until payments reach the respective attachment points, the District Court properly denied the Directors' request for a declaration that coverage obligations are triggered once the Directors' defense and indemnity obligations reach the relevant attachment point.

The Directors make several arguments attacking the reasoning of the District Court, but their arguments are not persuasive. In fact, most of their arguments are inapposite because they are based on a misunderstanding of the District Court's order. The Directors' view is summarized in their reply brief:

Reply Br. 8. This argument ignores the language and context of the District Court's order. The District Court never held that the underlying insurers must make payments before the obligations under the relevant excess policies are triggered. Rather, the District Court — echoing the terms of the relevant insurance policies — described the exhaustion requirement in the passive voice and did not specify which party was obligated to make the requisite payments. See Fed. Ins. Co., 2011 WL 4552381, at *7 ("[T]he Excess Policies expressly state that coverage does not attach until there is payment of the underlying losses.").

The District Court did not err in doing so. Denying the Directors' request did not require ruling on whether the underlying insurers, in particular, were required to make payments; the Directors simply sought a declaration that the excess policies' coverages are triggered once the respective attachment points are reached — i.e., once the amount of "defense and/or indemnity obligations exceeds the limits of any insurance policies underlying their respective policies."15

Nor do we find persuasive the Directors' reliance on Zeig v. Massachusetts Bonding & Insurance Co., 23 F.2d 665 (2d Cir. 1928).16 In that case, Manhattan dressmaker Louis Zeig had purchased property insurance totaling $15,000 in coverage, plus an excess policy that attached after the primary insurance was "exhausted in the payment of claims to the full amount of the expressed limits." 23 F.2d at 666 (quotation marks omitted). In a subsequent burglary, Zeig lost more than $15,000 in property. He initially filed claims for $15,000 with the primary insurance providers but ultimately settled those claims for $6,000. Id. Because the losses from the burglary were greater than $15,000, however, Zeig also filed a claim under the excess policy, attempting to recover his losses in excess of $15,000. The legal dispute turned on how the excess policy was triggered — namely, whether it applied even though Zeig settled the primary claims for less than their face value.

Writing for the Court, Judge Augustus N. Hand explained that "[i]t is doubtless true" that the parties could, "if they chose to do so," require actual payment of $15,000 as a condition precedent to liability. Id. But imposing this obligation, Judge Hand noted, would be "unnecessarily stringent" and serve "no rational interest" of the excess insurer, "so long as it was only called upon to pay such portion of the loss as was in excess of the limits of those [primary] policies." Id. Indeed, as Zeig had suffered out-of-pocket losses valued over $15,000, he could only damage his own interest by settling his primary claims for less than their face value, not damage the interest of the excess insurers. Because a natural reading of the contract would be "harmful to the insured, and of no rational advantage to the insurer," the Court construed the contract to mean that Zeig still had to exhaust his primary claims for $15,000, and that this could be done not only through full cash payment but also through a settlement agreement. Id. Accordingly, the Court held that Zeig "should have been allowed to prove the amount of his loss, and, if that loss was greater than the amount of the expressed limits of the primary insurance, he was entitled to recover the excess to the extent of the policy in suit." Id.

The Directors argue that Zeig controls here. But their argument neglects important differences between Zeig and this case. In fact, nothing is inherently errant or unusual about interpreting an exhaustion clause in an excess liability insurance policy differently than a similarly written clause in a first-party property insurance policy. "[I]n interpreting contractual language," like language in any other legal text, "[t]he text should always be read in its context." Int'l Multifoods Corp., 309 F.3d at 87 n. 4 (quotation marks omitted). It is a "well-established rule of construction ... that words can take on different meanings in different contexts." Am. Home Assurance Co. v. Republic Ins. Co., 984 F.2d 76, 78 (2d Cir.1993); cf. Robinson v. Shell Oil Co., 519 U.S. 337, 341, 117 S.Ct. 843, 136 L.Ed.2d 808 (1997) ("The plainness or ambiguity of statutory language is determined by reference to the language itself, the specific context in which that language is used, and the broader context of the statute as a whole.").

Moreover, as the District Court explained, Zeig and the other related cases on which the Directors rely "principally address situations in which a policy was deemed exhausted as a result of an insured's below-limit settlement of indemnity claims with an underlying carrier." Fed. Ins. Co., 2011 WL 4552381, at *7; see Fed. Ins. Co. v. Srivastava, 2 F.3d 98, 103 (5th Cir.1993) ("Judge [Augustus N.] Hand [in Zeig] assumed that the insured's loss was fixed before any settlement with the primary insurers. With the loss set, there was little danger that primary insurers could, contrary to the contracted-for risk, shift any part of their burden to excess carriers. With a burglary of property, the insured loss was established."); see also Great N. Ins. Co. v. Mount Vernon Fire Ins. Co., 92 N.Y.2d 682, 688, 685 N.Y.S.2d 411, 708 N.E.2d 167 (1999) ("[T]he goal of first-party property coverage ... is to reimburse the insured for the insured's actual property loss...."). In those cases, the insured suffered out-of-pocket losses (for instance, through the loss of property, or through liability payments to a third party) for which the insured sought indemnification. The Directors' requested relief, by contrast, focuses on their obligations to pay third parties. In these circumstances, we agree with the District Court that this difference is relevant when structuring (and interpreting) a liability insurance policy.17 As the District Court noted, FIC and Travelers

Fed. Ins. Co., 2011 WL 4552381, at *7. In other words, the excess insurers here had good reason to require actual payment up to the attachment points of the relevant policies, thus deterring the possibility of settlement manipulation. In this context, the plain meaning of the phrase "payment of losses" refers to the actual payment of losses suffered by the Directors — not the mere accrual of losses in the form of liability.

CONCLUSION

To summarize, we hold that:

Accordingly, the judgment of the District Court is AFFIRMED. Additionally, the appellees' motion for judicial notice is DENIED.18