BARRON, Circuit Judge.

Federal Rule of Civil Procedure 68 allows a party defending against a claim to make an offer of judgment that, if accepted within 14 days, must be enforced upon the filing of the offer, the acceptance, and proof of service. Fed.R.Civ.P. 68. In so providing, the Rule describes the offer that may be made under the Rule as one "to allow judgment on specified terms, with the costs then accrued." Id. The dispute in this case turns largely on that last phrase — "with the costs then accrued" — and the significance that should be attributed to it.

The offeror here, the City of Lawrence ("the City"), is defending in a civil rights action brought by a plaintiff who was sexually assaulted by one of the City's police officers. Prior to trial, the City made a Rule 68 offer of judgment for $300,000 that was silent as to whether that amount was inclusive of the plaintiff's costs or not. Then, within the 14-day period for acceptance, the City attempted to clarify its offer by sending an "amended" offer of judgment that contained the same language as the first offer with an additional sentence stating that the offer was "also inclusive of any costs and fees incurred to date, including attorney's fees." Following this attempted clarification, but before the 14-day period expired, the plaintiff purported to accept the unamended version of the offer. In communicating her acceptance to the City, she informed the City that she would be separately moving for fees and costs. The plaintiff then filed the unamended offer, her purported acceptance, and proof of service with the District Court.

The City moved to strike that filing on the ground that the plaintiff's acceptance was invalid. The District Court granted the motion. In reaching that conclusion, the District Court held that, in consequence of the City's purported clarification of the initial offer, there was no meeting of the minds between the parties as to any offer of judgment. The District Court thus proceeded to address the merits of the defendants' motion for summary judgment, which the District Court granted on the ground that the police officer was not acting "under color of state law" in committing the assault on the plaintiff.

The plaintiff now appeals. She contends that she was entitled to accept the City's original Rule 68 offer and to treat it as a complete offer exclusive of costs. She also contends that the District Court erred in granting summary judgment on the basis of its holding that the officer was not acting under color of state law. Because we agree with the plaintiff's first argument, we we reverse and remand for entry of judgment in accordance with Rule 68.

I.

The plaintiff is Coeurd'Alene LaPierre. Her lawsuit arose out of an incident in which she was sexually assaulted by City Police Officer Kevin Sledge. Sledge was prosecuted for the incident and, in January 2011, was convicted of rape and three counts of indecent assault and battery. In September 2011, LaPierre sued Sledge, the City, and City Police Chief John Romero in Massachusetts Superior Court. Romero and the City removed the case to federal court in November of that year. Sledge never entered an appearance below, and default was entered against him.

On September 5, 2014, after the defendants had moved for summary judgment but before the District Court had ruled on that motion, the City sent a letter to LaPierre's counsel. That letter expressly purported to be an offer of judgment "[p]ursuant to Fed.R.Civ. P. 68." The letter stated that the City offered "judgment against the City of Lawrence and dismissal of all claims against any other Defendant in exchange for $300,000 payable over three (3) years." The letter contained no mention of whether that offer was inclusive of LaPierre's litigation costs or attorneys' fees.

One day later, on September 6, the City sent an e-mail to LaPierre's counsel purporting to withdraw the September 5 offer of judgment. Two days after that, on September 8, the City sent LaPierre's counsel an e-mail explaining that the September 5 offer had to be "clarified." Attached to that e-mail was what the City called an "amended offer of judgment." That document included the exact same language as the prior letter, with one additional sentence: "This $300,000.00 figure also inclusive of any costs and fees incurred to date, including attorney's fees."

The following day, September 9, LaPierre's counsel notified the City that LaPierre was accepting the September 5 offer. In the e-mail informing the City of that acceptance, LaPierre's counsel also stated that her client would be moving for "fees and costs incurred to date." LaPierre then filed the September 5 offer letter, along with a notice of acceptance and proof of service, with the District Court.

Before judgment was entered in accordance with that filing, the City moved to strike LaPierre's filing. In the memorandum in support of its motion to strike, the City argued, among other things, that the parties had not reached a meeting of the minds as to whether costs and fees were included in the Rule 68 offer and thus that there was no accepted offer within the 14-day period established by the Rule. The City also submitted correspondence between the parties — including the attempted "withdrawal" of the September 5 offer and the "amended" offer — which the City asked the District Court to consider as extrinsic evidence that the City had meant to include costs and fees in the September 5 offer.

The District Court agreed with the City that the parties had not reached a meeting of the minds, noting that, as a result of the City's "unilateral clarification" of the September 5 offer, "plaintiff was on notice of defendant's interpretation of its offer when she purportedly `accepted' the offer, though she understood the terms differently." Shortly thereafter, the District Court granted summary judgment in favor of the City and Romero. In granting that motion, the District Court concluded that LaPierre's civil rights claims under § 1983 could not succeed because Sledge had not been acting "under color of state law" when he assaulted and raped LaPierre.1

LaPierre moved for reconsideration of that decision, but the District Court denied that motion without explanation on May 13, 2015. LaPierre filed this timely appeal five days later,2 and we now reverse on the ground that the District Court erred in not entering judgment pursuant to the accepted Rule 68 offer of judgment.3

II.

The crux of the parties' dispute is whether LaPierre's purported acceptance of the September 5 offer was valid. In arguing that it was not, the City contends4 that extrinsic evidence demonstrates that the parties attached two different meanings to the offer. Specifically, the City points to the City's "amended" offer of judgment and the parties' settlement negotiations as evidence that the City interpreted the September 5 offer, which the parties agree was silent on its face as to costs and fees, to be inclusive of costs and fees. And the City directs us to LaPierre's stated intent to move for "fees and costs incurred to date" as proof that LaPierre interpreted the September 5 offer to be exclusive of those sums.

A threshold question, however, is whether we can consider extrinsic evidence in interpreting the September 5 offer. The resolution of that question turns on the proper interpretation of both Rule 68 and the September 5 offer. As those interpretive issues are legal ones, our review of the District Court's decision to consider extrinsic evidence in granting the motion to strike is de novo. See Garayalde-Rijos v. Municipality of Carolina, 799 F.3d 45, 47 (1st Cir.2015) (noting that courts interpret Rule 68 offers of judgment according to "ordinary contract principles"); King v. Rivas, 555 F.3d 14, 17 (1st Cir.2009) ("Rivas has now appealed, arguing that the district court misconstrued Rule 68, and our review of such a question is de novo."); Rodriguez-Abreu v. Chase Manhattan Bank, N.A., 986 F.2d 580, 586 (1st Cir. 1993) ("Determining whether contract language is ambiguous is also a question of law.").

Ordinarily, courts "must" enter judgment on an accepted Rule 68 offer of judgment once it has been filed with the court along with the acceptance and proof of service "regardless of what took place... between the parties in the time between the offer of judgment and [the offeree's] acceptance" — that is, without regard to what such extrinsic evidence might show. Garayalde-Rijos, 799 F.3d at 48. The City does not challenge that general proposition.5 The City instead stakes its argument on our prior statement that "an offeror may in some circumstances clarify an offer after making it." Id. at 48 n. 3 (citing Radecki v. Amoco Oil Co., 858 F.2d 397, 402-03 (8th Cir.1988)). And because the City contends that the "amended" offer it put forth on September 8 was a permissible clarification of the September 5 offer, the City concludes that we must affirm the District Court's ruling on the motion to strike in light of what that and the other extrinsic evidence shows about whether there was a meeting of the minds.

The case we cited for the proposition on which the City relies, however, limited its holding to cases in which a Rule 68 offer was "incomplete or ambiguous." See Radecki, 858 F.2d at 402-03. And, here, contrary to the City's contention, we conclude that the September 5 offer was not "incomplete or ambiguous." The District Court therefore committed an error of law in ruling that the City was allowed to "clarify" its initial offer in its "amended" offer that added a new term that addressed costs and fees.6 Accordingly, we agree with LaPierre that her acceptance of the September 5 offer must be enforced, "with the costs then accrued."7

To be sure, the text of the September 5 offer did not refer to costs one way or the other. It merely set forth a judgment amount of $300,000. For that reason, if this offer were made outside of the context of Rule 68, one would not be able to discern from the face of the offer whether it was intended to be inclusive of costs or not. But the offer was made pursuant to Rule 68. We thus must read the offer in light of the Rule and the precedent construing the Rule. And a review of the text of the Rule and the precedent interpreting the Rule convinces us that the City's offer, by virtue of its silence as to whether it was inclusive of costs, must be read to be exclusive of costs and thus to be neither "incomplete [n]or ambiguous" as to that issue.

Rule 68 states that "a party defending against a claim may serve on an opposing party an offer to allow judgment on specified terms, with the costs then accrued." Fed.R.Civ.P. 68. The Rule thus makes clear, through its trailing language, that a Rule 68 offer must be one that allows an offeree to recover costs.

Moreover, by its terms, Rule 68 separates the "specified terms" on which a party may offer judgment from the "costs then accrued." The Rule thus does not specify that "costs" must be a required "term[]" of the offer. Instead, the Rule separates out an offer's "terms" from the "costs." The language therefore suggests that if an accepted offer specifies particular "terms" without mentioning costs, "the costs then accrued" will be included by the court in the judgment along "with" those "specified terms" by operation of the Rule. In other words, the Rule itself renders unambiguous and complete what otherwise might be ambiguous or incomplete.

The Supreme Court has read the Rule similarly. In Marek, the Court considered an offer of judgment that expressly purported to include "costs now accrued and attorney's fees" within its offer of $100,000 but did not separately delineate the amount offered for the substantive claim and the amount offered for costs. 473 U.S. at 3-4, 105 S.Ct. 3012. The Court made clear that such "lump-sum offers" are permissible under Rule 688 because a timely offer is valid under Rule 68 "[a]s long as the offer does not implicitly or explicitly provide that the judgment not include costs." Id. at 6, 105 S.Ct. 3012. For that reason, according to the Court, "it is immaterial whether the offer recites that costs are included, whether it specifies the amount the defendant is allowing for costs, or, for that matter, whether it refers to costs at all." Id. And the Court went on to state that "if the offer does not state that costs are included and an amount for costs is not specified, the court will be obliged by the terms of the Rule to include in its judgment an additional amount which in its discretion, it determines to be sufficient to cover the costs." Id. (citation omitted).

The Marek Court was not considering an offer that was — like the one at issue here — silent on the issue of whether the offer was inclusive of costs. It thus was not faced with a contention that extrinsic evidence should be consulted to interpret such an offer. But the Court's statement about how courts are "obliged by the terms of the Rule" to react to such offers was stated clearly and without limitation. And we have made clear that we "are bound by the Supreme Court's considered dicta almost as firmly as by the Court's outright holdings." Cuevas v. United States, 778 F.3d 267, 272-73 (1st Cir.2015) (quoting McCoy v. Mass. Inst. of Tech., 950 F.2d 13, 19 (1st Cir.1991)); see also Igartúa v. United States, 626 F.3d 592, 605 n. 15 (1st Cir.2010) ("Carefully considered Supreme Court dicta, though not binding, must be accorded great weight and should be treated as authoritative. Although the Supreme Court may ignore its own dicta, we are a lower court bound by the Supreme Court." (citation and internal quotation marks omitted)). Moreover, the circuits that have addressed the issue appear to have uniformly followed Marek on this point in determining that they could not consider extrinsic evidence to interpret a Rule 68 offer that is silent as to the inclusion of costs.9

Finally, reading the Rule to dictate that an offer that is silent as to costs is exclusive of costs is consistent with the purposes of the Rule. Rule 68 contains a "rather finely tuned balance" that is "designed to encourage the settlement of private disputes." Garayalde-Rijos, 799 F.3d at 47 (internal quotation marks omitted). That aim is furthered by construing the Rule, where supported by its text, to set out a clear interpretation for offers that might be unclear outside the context of the Rule. Moreover, allowing preacceptance clarifications always runs the risk of enabling offerors to send clarifications for the purpose of reducing the offeree's response period from the 14 days contemplated by the Rule to the number of days remaining after such a clarification has been sent. Thus, where, as here, the text of the Rule supports a reading that would limit the opportunities for offerors to game the system in that way, the administration of the Rule is best served by adopting that reading.

Against this interpretation of the Rule's text and the precedent construing it, the City relies on Radecki, the out-of-circuit precedent that we favorably cited for the proposition that "an offeror may in some circumstances clarify an offer after making it." See Garayalde-Rijos, 799 F.3d at 48 n. 3. But Radecki involved a very different species of claimed ambiguity.

In Radecki, the original Rule 68 offer provided for judgment "in the amount of $525,000.00, including costs now accrued." 858 F.2d at 399. The Eighth Circuit held that the original offer "subsum[ed] within the amount offered any liability for `costs.'" Id. at 400. The Eighth Circuit then went on to state that, because the statute under which the lawsuit was brought (the Petroleum Marketing Practices Act) did not define attorneys' fees as part of costs, the original offer had not been clear as to whether it was inclusive of attorneys' fees. Id. at 400 & n. 2. For that reason, the Eighth Circuit concluded that the preacceptance clarification in that case was valid and operative and that the Court would consider extrinsic evidence to determine whether the defendant intended the offer to be inclusive of attorneys' fees. Id. at 400.

Here, by contrast, there is no dispute that 42 U.S.C. § 1988 subsumes attorneys' fees within costs. Radecki thus provides no basis for allowing a preacceptance clarification to the September 5 offer and thus no basis for examining the extrinsic evidence that the City contends shows that there was no meeting of the minds.10 Rather, in accordance with the Rule's text and the precedent construing it, we conclude that the September 5 offer was unambiguously exclusive of both costs and, as a subset of costs, attorneys' fees.

III.

For the reasons set forth above, we vacate the District Court's July 10, 2015 order granting judgment in favor of Romero and the City and the District Court's October 1, 2014 order granting the City's motion to strike. We remand to the District Court with instructions to enter judgment in accordance with the offer of judgment filed on September 10, 2014. Costs on appeal are awarded to appellant. See Fed. R.App. P. 39(a)(4).