SELYA, Circuit Judge.

In 1998, the City of Everett (the City) retained Barletta Engineering Corporation (Barletta) to construct a new elementary school. Barletta, as general contractor, engaged a myriad of subcontractors to assist in this venture. Among them was appellant B & T Masonry Construction Co., Inc. (B & T). The work consumed the better part of two years.

In the City’s view, the completed structure left something to be desired. It sued Barletta in a state court, alleging that Barletta’s faulty workmanship had allowed water leakage which, in turn, had caused property damage to the school building (including mold contamination of ceilings, walls, floors, and other components). Bar-letta promptly filed a third-party complaint against B &, T and sundry other subcontractors. In the only iteration relevant here, the third-party complaint attributed the damage to B & T’s deficient masonry work.

Appellee Public Service Mutual Insurance Co. (Public Service) had issued two *38 consecutive commercial general liability (CGL) policies to B & T, which were serially in effect during the course of B & T’s work on the school project. B & T tendered the defense against Barletta’s claim to the insurer. Public Service refused the tender and disclaimed any coverage obligation. 1

Stung by this rejection, B & T repaired to the United States District Court for the District of Massachusetts. Invoking that court’s diversity jurisdiction, see 28 U.S.C. § 1332(a), it initiated an action seeking a declaration that Public Service had a duty to defend and indemnify it with respect to Barletta’s claim. In due course, the insurer moved for summary judgment. See Fed.R.Civ.P. 56. The district court granted this motion, holding that all the damages described in Barletta’s third-party complaint fell within the compass of the exclusions contained in the CGL policies. 2 B & T Masonry Constr. Co. v. Pub. Serv. Mut. Ins. Co., No. 02-10595, slip op. at 10 (D.Mass. Sept. 26, 2003) (unpublished) (D.Ct.Op.). B & T appeals from this ruling.

We need not tarry. The insuring agreement, section 1(A)(1)(a), provides in pertinent part that Public Service will “pay those sums that the insured becomes legally obligated to pay as damages because of ... ‘property damage’ to which this insurance applies.” This insuring agreement is, however, subject to certain so-called “business risk” exclusions. These include section I(A)(2)(j)(5) (which excludes coverage for property damage to “[t]hat particular part of real property on which [the insured] or any contractors or subcontractors working directly or indirectly on [the insured’s] behalf are performing operations” so long as “the ‘property damage’ arises out of those operations”); section I(A)(2)(j)(6) (which excludes coverage for property damage to “[t]hat particular part of any property that must be restored, repaired or replaced because [the insured’s work on it] was incorrectly performed”); section I(A)(2)(1) (which excludes coverage, with a limitation not relevant here, for “‘[property damage’ to ‘[the insured’s] work’ arising out of it or any part of it”); section I(A)(2)(m) (which excludes coverage for “ ‘[pjroperty damage’ ... arising out of ... [a] defect, deficiency, inadequacy or dangerous condition” in the insured’s product or work); and section I(A)(2)(n) (which excludes coverage for “[d]amages claimed for any loss, cost or expense incurred by [the insured] or others for the loss of use, withdrawal, recall, inspection, repair, replacement, adjustment, removal or disposal of ... ‘[the insured’s] work’ ”). The question presented in this case is whether Barletta’s derivative claim (seeking, in effect, indemnification or contribution anent the City’s claim for damages to the school building) falls within the purview of some or all of these exclusions.

Because this is a diversity case, Massachusetts law controls. United States Liab. Ins. Co. v. Selman, 70 F.3d 684, 688 (1st Cir.1995). Under the Massachusetts cases, the interpretation of an insurance policy is normally a question of law for the court. Ruggerio Ambul. Serv., Inc. v. Nat’l Grange Ins. Co., 430 Mass. 794, 724 N.E.2d 295, 298 (2000). Where, as here, the material facts upon which a coverage question is based are not genu *39 inely in dispute, the application of the policy to those facts is likewise a question of law (and, thus, properly resolved on summary judgment). Liberty Mut. Ins. Co. v. Metro. Life Ins. Co., 260 F.3d 54, 61 (1st Cir.2001).

Massachusetts courts apply the traditional rules of contract interpretation to the construction of insurance policies. Brazas Sporting Arms, Inc. v. Am. Empire Surplus Lines Ins. Co., 220 F.3d 1, 4 (1st Cir.2000). The first principle is to afford the language of the policy its plain meaning. Id. Because the duty of an insurance carrier to defend the insured is broader than its duty to indemnify, see id., we focus on that duty.

The duty to defend is, of course, “based on the facts alleged in the complaint and those facts which are known by the insurer.” Boston Symph. Orch., Inc. v. Comm’l Union Ins. Co., 406 Mass. 7, 545 N.E.2d 1156, 1158 (1989). For the duty to arise, “the underlying complaint need only show, through general allegations, a possibility that the liability claim falls within the insurance coverage.” SCA Servs., Inc. v. Transp. Ins. Co., 419 Mass. 528, 646 N.E.2d 394, 397 (1995) (citation and internal quotation marks omitted). The insured bears the initial burden of showing coverage under the policy’s insuring agreements. Highlands Ins. Co. v. Aerovox Inc., 424 Mass. 226, 676 N.E.2d 801, 804 (1997). Once the insured has accomplished this feat, the burden shifts to the carrier to prove the applicability of one or more separate and distinct exclusionary provisions. Id. To the extent (if at all) that any ambiguity permeates a policy exclusion, it must be construed strictly against the insurer. Brazas Sporting Arms, 220 F.3d at 4.

Here, B & T satisfied its threshold burden of showing coverage under an insuring agreement. The question reduces, then, to whether the business risk exclusions avoid the application of that coverage. On that question, Public Service had the devoir of persuasion and relied upon the plain language of the exclusions to show that they applied. In arguing against that proposition before us, B & T asserts a nascent theory that departs dramatically from what it argued in the court below. We explain briefly.

In the lower court, B & T acknowledged that the business risk exclusions applied to damage to the school building caused by its workmanship but posited that whether the damage claimed by the City (and, derivatively, by Barletta) was caused by B & T’s workmanship or that of another subcontractor remained an open question. This open question, it asseverated, precluded summary judgment. The district court rejected that asseveration, concluding (correctly, in our view) that any liability that might attach to B & T under the third-party complaint necessarily would stem from its own workmanship and, thus, would be excluded from coverage. D. Ct. Op. at 10. If another firm were negligent and B & T were not, that fact would in no way alter the coverage equation. Id.

B & T did not renew this specific theory in its appellate briefs 3 but, rather, relied *40 upon a newly contrived theory. On appeal, it suggests for the first time that the exclusion clauses, taken in the ensemble, render the insurance policy illusory (and, accordingly, that the exclusions are unenforceable). We cannot countenance such a bald-faced switching of horses in midstream.

Advancing one theory in the trial court and jettisoning it in favor of another (previously unarticulated) theory in the court of appeals is unacceptable. Such a praxis violates a prudential principle firmly embedded in our jurisprudence: that in the absence of extraordinary circumstances—and none exist in this case—“legal theories not raised squarely in the lower court cannot be broached for the first time on appeal.” Teamsters Union v. Superline Transp. Co., 953 F.2d 17, 21 (1st Cir.1992). Cases holding to that effect are legion. See, e.g., Vargas-Ruiz v. Golden Arch Dev., Inc., 368 F.3d 1, 3 (1st Cir.2004); United States v. Bongiorno, 106 F.3d 1027, 1034 (1st Cir.1997); United States v. Dietz, 950 F.2d 50, 55 (1st Cir.1991); Clauson v. Smith, 823 F.2d 660, 666 (1st Cir.1987); Johnston v. Holiday Inns, Inc., 595 F.2d 890, 894 (1st Cir.1979). B & T’s tactics transgress that prudential principle.

In an attempt to place its neoteric theory beyond the range of the case law enforcing the raise-or-waive rule in this sort of situation, B & T makes three arguments. We find all of them unpersuasive.

First, B & T claims that it actually raised the “illusory coverage” theory below. The record belies that claim. The reference in B & T’s reply brief is to an exchange that took place during the summary judgment hearing. ' In that exchange, its counsel questioned Public Service’s interpretation of the policy by asking rhetorically, “what did we buy this insurance for?” In posing this rhetorical question, however, the lawyer was arguing for a particular interpretation of the policy language. He never mentioned the possibility that the breadth of the exclusions rendered the coverage illusory and, thus, that the exclusions were void as a matter of law.

Even if the rhetorical question was intended to start the argument down this path—and that is a stretch—the court was not provided a roadmap. That omission would doom the argument here. To preserve a point for appeal, some developed argumentation must be put forward in the nisi prius court—and a veiled reference to a. legal theory is not enough to satisfy this requirement. See, e.g., United States v. Slade, 980 F.2d 27, 31 (1st Cir.1992) (“A litigant cannot ignore her burden of developed pleading and expect the district court to ferret out small needles from diffuse haystacks.”); Rivera-Gomez v. Adolfo de Castro, 843 F.2d 631, 635 (1st Cir.1988) (“Judges are not expected to be mindread-ers. Consequently, a litigant has an obligation to spell out its arguments squarely and distinctly or else forever hold its peace.”) (citation and internal quotation marks omitted).

B & T next maintains that the raise-or-waive rule should not apply because it is not advancing a new issue on appeal, but merely a new argument. In mincing words in this fashion, B & T attempts to align its new theory with its old one, arguing in the face of obvious differences that these two theories are “the same” because *41 both relate to the general issue of whether the exclusions govern this case.

We have decanted this wine before. In Slade, we explicitly rejected the notion that “only new facts and not new arguments about those facts are prohibited from debuting in the court of appeals,” calling that notion “grounded more in hope than in precedent.” 980 F.2d at 31. We held, citing numerous cases, that “a party is not at liberty to articulate specific arguments for the first time on appeal simply because the general issue was before the district court.” Id. That holding is disposi-tive here.

Finally, B & T suggests that even if it failed to preserve its late-emerging theory for appeal, we should entertain that theory because the theory is uniquely important. We have recognized that an appellate court has the authority, in its discretion, to consider theories not articulated below. See, e.g., United States v. LaGuardia, 902 F.2d 1010, 1013 (1st Cir.1990). We also have recognized, however, that exceptions of this kind to the raise-or-waive rule should be “few and far between,” Nat’l Ass’n of Soc. Workers v. Harwood, 69 F.3d 622, 627 (1st Cir.1995), and, accordingly, this power is to be used sparingly. The typical case involves an issue that is one of paramount importance and holds the potential for a miscarriage of justice. See id. at 628; United States v. Krynicki, 689 F.2d 289, 292 (1st Cir.1982).

B & T implores us to entertain the “illusory coverage” theory here, predicting that any other course will result in perpetuating the underwriting of “[t]housands, if not tens of thousands,” of other illusory policies. Appellant’s Reply Br. at 3. We reject these importunings. We simply do not see how a straightforward application of the raise-or-waive rule in this garden-variety coverage dispute either rises to a level of great importance or threatens to work a miscarriage of justice.

We add an eschatocol of sorts. Even though we are not compelled to speak to the merits, we note in the interest of completeness that B & T’s new theory would not have prevailed even if it had been properly preserved.

B & T contends that the district court’s reading of the business risk exclusions would eliminate all coverage for negligence claims, even though that is the very type of coverage that B & T purchased and that a CGL policy purports to provide. Appellant’s Br. at 16. That contention is sheer sophistry. The exclusions leave most negligence claims unaffected; they merely bar coverage as to any damages to the project itself caused by B & T’s faulty workmanship. While these exclusions do limit liability, they do not completely vitiate the bargained-for coverage (indeed, they do not come close to achieving so drastic a result). Many negligence claims are undoubtedly covered. If, for example, a wall of the school building collapsed due to B & T’s negligence and damaged an adjacent structure (not part of the school complex), or if a B & T employee carelessly dropped a trowel and struck a passing vehicle, coverage would attach. Consequently, the grant of coverage is not illusory. See, e.g., Bagley v. Monticello Ins. Co., 430 Mass. 454, 720 N.E.2d 813, 817 (1999) (holding that as long as “the policy still provides coverage for some acts, it is not illusory simply because of a potentially wide exclusion”).

We need go no further. For the reasons elucidated above, we hold that the district court did not err in entering summary judgment in Public Service’s favor.

Affirmed.

Notes

. B & T made a similar tender to the insurer when the City later filed amended complaints and B arietta, in turn, filed amended third-party complaints. Public Service rejected these tenders as well. Nothing in the amended pleadings changes the coverage analysis.

. Because the two policies are substantially identical with respect to the matters at issue, we hereinafter refer, for simplicity’s sake, only to the first policy.

. To be sure, B & T’s counsel did make a passing mention of the theory during oral argument in this court. We have no need to respond to that allusion. The district court correctly determined that Barletta's complaint sought to hold B & T liable only for damage to the school building caused by B & T's own work and that any such damage would be completely excluded from coverage under the policy. D. Ct. Op. at 10. Where, as here, a trial court accurately evaluates an argument and convincingly dispatches it, there is no need for a reviewing court to prepare a palimpsest. See, e.g., Vargas—Ruiz v. Golden Arch Dev., Inc., 368 F.3d 1, 2 (1st Cir.2004); Cruz-Ramos v. P.R. Sun Oil Co., *40 202 F.3d 381, 383 (1st Cir.2000); Ayala v. Union de Tronquistas, 74 F.3d 344, 345 (1st Cir.1996).