The plaintiffs, twelve disabled individuals and a disability rights organization, allege that the defendants’ paratransit system for disabled persons in the Rochester, New York area violated the Americans with Disabilities Act, 42 U.S.C. § 12101 et seq. (“ADA” or the “Act”). The defendants moved for summary judgment in lieu of answering the complaint, and the plaintiffs cross-moved for summary judgment on three of their four claims. The United States District Court for the Western District of New York (Larimer, J.) granted summary judgment in favor of the plaintiffs and enjoined the defendants to comply with their obligations under the ADA. We affirm the grant of injunctive relief, but on grounds somewhat different from those *203upon which the district court relied, grounds which may require the district court to modify the injunction on remand.
BACKGROUND1
Defendant Rochester-Genesee Regional Transportation Authority (“RGRTA”) provides transportation services in the Rochester, New York area. As a public benefit corporation established by New York statute, RGRTA is a “public entity” subject to the requirements of the ADA. See 42 U.S.C. § 12131(1)(B) (defining “public entity” as including “any department, agency, special purpose district, or other instrumentality of a State or States or local government”). Through a subsidiary, Regional Transit Service, Inc. (“RTS”), RGRTA operates a “fixed route system” of bus lines, defined by the ADA as “a system of providing designated public transportation on which a vehicle is operated along a prescribed route according to a fixed schedule.” 42 U.S.C. § 12141(3).
Through a second subsidiary, defendant Lift Line, Inc. (“Lift Line”), RGRTA operates a complementary paratransit system for disabled persons. This service consists of a fleet of thirty-six buses that provide curb-to-curb transportation along a corridor three-quarters of a mile wide on each side of RTS’s fixed bus routes. See 49 C.F.R. § 37.131(a)(1).
To be eligible for paratransit service, a disabled Rochesterian must submit an application and a health-care or rehabilitation professional’s certification for approval by Lift Line. Lift Line has been liberal in its approval of such applications. From 1992 through 1999, the company received 6,539 applications and granted all but 444 (or 6.8%) of them. Lift Line has not endeavored to recertify its paratransit riders or pare its rolls. When this action was commenced, approximately 6,200 people were certified for paratransit service, including each individual plaintiff. These individuals depend on Lift Line for work, worship services, family visits, medical appointments, errands, and other activities.
To schedule a paratransit ride, certified individuals must make a phone reservation the day before or up to 14 days in advance.2 The November 1999 “RTS Bus Guide & Map” for the Rochester area advised Lift Line users to call “between 7:00 am and 5:00 pm, seven days a week” to schedule a ride. It cautioned that “[reservations are made on a first-call, first-serve basis.”
The parties have presented a largely undisputed series of data about Lift Line’s paratransit service from May 26 to June 14, 2000 (the “sample period”). The plaintiffs appear to have selected this period at random to collect data in support of the claims stated in their June 15, 2000 complaint. No party contends that the data collected during this period are unrepresentative.
During the sample period, Lift Line received 8,962 ride requests and scheduled 8,452 (or 94.4%) of them. Nearly 75% of *204these requests were made fourteen days in advance and, of those, 99.54% were scheduled. The scheduling rates declined, however, with the period of advance notice. Of the 181 rides requested seven days in advance, 154(85%) were scheduled. Of those rides requested two days in advance, only 62.78% were scheduled. And of the 161 rides requested one day in advance, only 69 (42.86%) were scheduled. Thus, by its own admission, Lift Line denied 57.14% of the next-day ride requests during the relevant period. When Lift Line denied these requests, it did so because “all spaces on the buses assigned to the area had been reserved.” (Pls.’ Statement of Undisputed Facts, dated Oct. 31, 2000, at 21.)
Each individual plaintiff requested a paratransit ride during the sample period. Some of those who called the day before were told that Lift Line could not provide a ride. The others, including those who called several days in advance, were told to call a second time to confirm their rides. When they called the second time, they were told that Lift Line could not provide a ride. Each time, the explanation was a lack of capacity.
According to the defendants, Lift Line’s capacity constraints are attributable to some riders’ abuse of the system. For purposes of this summary judgment motion, it is uncontested that (1) riders who are not truly eligible for paratransit service take space away from those who are truly eligible under the regulations; (2) although Lift Line is authorized to re-certify riders and de-certify those who are no longer eligible, Lift Line has not done so; and (3) Lift Line canceled 1,694 rides (19% of all reservations) during the relevant period, though the parties disagree about whether this problem is a cause or a symptom of Lift Line’s capacity constraints.
On June 15, 2000, the plaintiffs filed this class action, alleging that a substantial number of eligible riders who called to schedule rides one or more days in advance were not accommodated due to a lack of capacity. Specifically, the plaintiffs alleged that the defendants violated the ADA by (1) failing to provide next-day service to eligible persons, in violation of 42 U.S.C. § 12143(a)(2) and 49 C.F.R. § 37.131(b); (2) requiring riders to call a second time to confirm ride availability and thereby maintaining waiting lists for para-transit service, in violation of 49 C.F.R. § 37.131(f)(2); (3) engaging in an “operational pattern or practice” that significantly limits the availability of paratransit service, in violation of 49 C.F.R. § 37.131(f)(3); and (4) fading to provide paratransit service in accordance with the plan defendants submitted to the Secretary of Transportation, in violation of 42 U.S.C. § 12143(e)(4).
The defendants moved for summary judgment in lieu of filing an answer; and the plaintiffs cross-moved for summary judgment on their first, third, and fourth claims. On August 14, 2001, the district court denied the defendants’ motion and granted summary judgment in favor of plaintiffs on the three claims for which they sought it. See Anderson v. Rochester-Genesee Reg’l Transp. Auth., 206 F.R.D. 56, 71 (W.D.N.Y.2001) (“Anderson I ”). As to the first claim, the court held that the defendants failed to meet all next-day ride requests as required by 42 U.S.C. § 12143(a) and 49 C.F.R. § 37.131(b). Id. at 62-68. As to the third claim, the court held that the defendants engaged in an operational pattern or practice that substantially limited the availability of para-transit service by maintaining a capacity level insufficient to meet demand. Id. at 69-70. The court held that these rulings also supported summary judgment for *205plaintiffs on their fourth claim, failure to comply with the plan submitted to the Secretary of Transportation. Id. at 70. As to the second cause of action — the “waiting list” claim, on which the plaintiffs did not seek judgment as a matter of law — the court denied the defendants’ motion for summary judgment and ordered that the parties conduct discovery.3 Id. at 69.
Having so ruled, the district court enjoined the defendants to “take immediate steps to comply with their obligations under the ADA and federal regulations implementing that Act,” and ordered the parties to “attempt to work together to formulate a comprehensive plan to effectuate” its ruling. Id. at 71-72. The court also granted the plaintiffs’ motion for conditional class certification, defining the class as “all persons who are now or in the future will be eligible for ADA paratransit services in the geographical area served by defendants.” Id. at 72. Defendants filed a timely notice of appeal. The injunction has not been stayed and, though the defendants challenge the basis for the injunction, they do not contest its particular terms.
On April 26, 2002, after full briefing in this Court, the district court issued an order to supplement and implement its August 14, 2001 order. See Anderson v. Rochester-Genesee Reg’l Transp. Auth., 205 F.Supp.2d 106 (W.D.N.Y.2002) (“Anderson II ”). For reasons set forth in the margin, we give consideration to that order in this appeal.4 In it, the court noted that “defendants [had] undertaken various steps to improve their paratransit services,” having “increased the number of buses during peak ridership times, increased the number of schedulers on staff, and hired additional bus drivers.” Id. at 107. “As a result of these and other measures,” the court noted, “defendants report that they have been able to schedule 99.86% of all rides requested from November 5, 2001 through January 31, 2002, and 98.8% of all next-day ride requests during that same period.” Id.
Nonetheless, while “the parties worked diligently and in good faith to resolve the litigation” and adopt a “mutually satisfactory plan,” they could not reach agreement. Id. The court therefore ordered remedial measures:
*206• “The company must provide next-day ride service to all ADA paratransit eligible individuals who require such service ....’’Id. at 108.
• “[T]he company shall take whatever steps are necessary to obtain more buses, drivers and schedulers to comply with all of the requirements concerning provision of paratransit service.” Id.
• “[T]he company will phase in modifications to its reservation system to permit advance reservations to be made not more than three days prior to the desired trip.” Id.
• The company shall “provide the Court with [monthly] reports” on demand rides, subscription rides, and the certification/recertification process. Id. at 109-10.
The court also endorsed the following permissive measures:
• The company may “mak[e] its entire fixed-route fleet of buses wheelchair accessible,” and it should do so “with dispatch.” Id. at 109.
• The company may implement a recer-tification process through a third party, “as long as the process conforms to all applicable regulations and is not used as a vehicle for retaliation.” Id.
• The company may “establish an administrative process to suspend para-transit services to individuals who persistently miss scheduled trips or cancel them in an untimely manner,” as long as such process is “in full compliance with the regulations.” Id.
The court declined to “impose a schedule of stipulated penalties for noncompliance by the company” or to rule on any fare increase that Lift Line might adopt in the future. Id. at 110-11. The court retained jurisdiction, however, to monitor compliance. Id. at 110.
On July 26, 2002, this Court invited the Department of Transportation (“DOT”) to submit a letter-brief detailing its views on the meaning of the relevant paratransit service regulations. The Justice Department’s Civil Rights Division responded on the DOT’s behalf in a letter-brief dated October 25, 2002. The parties submitted responsive letter-briefs on November 8, 2002. We also received amicus curiae briefs from the Eastern Paralyzed Veterans Association (urging affirmance) and the New York City Transit Authority (urging reversal).
DISCUSSION
Our consideration of the relevant statutory and regulatory provisions for para-transit service leads us to accept portions of the district court’s reasoning and reject other portions; affirm the grant of summary judgment on the plaintiffs’ first and third claims, and reverse on their fourth claim; and remand for proceedings on the fourth claim and any re-framing of the injunction that may be justified by this opinion or circumstances that have developed during the pendency of the appeal.
I. Standard of Review
We review the district court’s grant of summary judgment de novo. See Young v. County of Fulton, 160 F.3d 899, 902 (2d Cir.1998). In doing so, we construe the evidence in the light most favorable to the non-moving party and draw all reasonable inferences in its favor. See Anderson v. Liberty Lobby, Inc., 477 U.S. 242, 255, 106 S.Ct. 2505, 91 L.Ed.2d 202 (1986); Maguire v. Citicorp Retail Servs., Inc., 147 F.3d 232, 235 (2d Cir.1998). Summary judgment is appropriate only 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).
*207The meaning of the relevant ADA provisions and DOT regulations are questions of law that we review de novo. See United States v. Mitchell, 328 F.3d 77, 81 (2d Cir.2003) (interpretation of statutes); Winter Storm Shipping, Ltd. v. TPI, 310 F.3d 263, 267 (2d Cir.2002) (interpretation of statutes and rules), cert. denied, — U.S. -, 123 S.Ct. 2578, 156 L.Ed.2d 605 (2003); Auburn Housing Auth. v. Martinez, 277 F.3d 138, 143 (2d Cir.2002) (interpretation of statutes).
II. Statutory and Regulatory Framework
Title II of the ADA provides that “no qualified individual with a disability shall, by reason of such ¿disability, be excluded from participation in or be denied the benefits of the services, programs, or activities of a public entity, or be subjected to discrimination by any such entity.” 42 U.S.C. § 12132. The Act expressly bars such discrimination in public transportation:
It shall be considered discrimination ... for a public entity which operates a fixed route system ... to fail to provide with respect to the operations of its fixed route system, in accordance with this section, paratransit and other special transportation services to individuals with disabilities ... that are sufficient to provide to such individuals a level of service (1) which is comparable to the level of designated public transportation services provided to individuals without disabilities using such system; or (2) in the case of response time, which is comparable, to the extent practicable, to the level of designated public transportation services provided to individuals without disabilities using such system.
42 U.S.C. § 12143(a).
Pursuant to the Act, see 42 U.S.C. §§ 12143(b) & (c), the Secretary of Transportation has issued regulations prescribing minimum service criteria for paratran-sit service. See 49 C.F.R. § 37.121 et seq. Two of the Secretary’s implementing regulations are of particular relevance here. They are in some tension with each other because one seemingly requires next-day service for every user every time without fail, while the other contemplates a lesser level of service so long as the failures are not substantial in number.
First, the Secretary has established standards for paratransit service “response time.” 49 C.F.R. § 37.131(b). Under § 37.131(b), a public entity providing transportation services “shall schedule and provide paratransit service to any ADA paratransit eligible person at any requested time on a particular day in response to a request for service made the previous day.” Id. “Reservations may be taken by reservation agents or by mechanical means.” Id. The regulation provides further:
(1) The entity shall make reservation service available during at least all normal business hours of the entity’s administrative offices, as well as during times, comparable to normal business hours, on a day when the entity’s offices are not open before a service day.
(2) The entity may negotiate pickup times with the individual, but the entity shall not require an ADA paratransit eligible individual to schedule a trip to begin more than one hour before or after the individual’s desired departure time.
(3) The entity may use real-time scheduling in providing complementary para-transit service.
(4) The entity may permit advance reservations to be made up to 14 days in advance of an ADA paratransit eligible individual’s desired trips.
Id.
Second, the Secretary has established standards for paratransit service “capacity *208constraints.” 49 C.F.R. § 37.131(f). A public entity “shall not limit the availability of complementary paratransit service to ADA paratransit eligible individuals” by “(1) [r]estrictions on the number of trips an individual will be provided; (2)[w]aiting lists for access to the service; or (3)[a]ny operational pattern or practice that significantly limits the availability of service to ADA paratransit eligible persons.” Id. (emphasis added). The regulation defines a “pattern or practice” as including, but not limited to, “(A) [substantial numbers of significantly untimely pickups for initial or return trips; (B) [substantial numbers of trip denials or missed trips; [and] (C) [substantial numbers of trips with excessive trip lengths.” 49 C.F.R. § 37.131(f)(3)(i). It excludes “[operational problems attributable to causes beyond the control of the entity (including, but not limited to, weather or traffic conditions affecting all vehicular traffic that were not anticipated at the time a trip was scheduled).” 49 C.F.R. § 37.131(f)(3)(ii).
Thus, one regulation requires that para-transit providers “shall schedule and provide paratransit service to any ADA para-transit eligible person at any requested time on a particular day in response to a request for service made the previous day,” 49 C.F.R. § 37.131(b) (emphasis added), which seems to require providers actually to meet 100% of all next-day ride requests. The other regulation, by expressly prohibiting only the denial of “[substantial numbers” of rides, 49 C.F.R. § 37.131(f)(i), appears to contemplate some permissible number of ride denials.
in the summary judgment decision under review, the district court construed § 37.131(b) literally to require 100% next-day service. Anderson I, 206 F.R.D. at 62-63. The court did not “see any inconsistency between” § 37.131(b) and § 37.131(f). Id. at 63. The latter, it held, “simply provides a prohibition separate and distinct from the next-day requirement contained in § 37.131(b).” Id. It observed that § 37.131(f) “does not state that a public entity may deny ride requests as long as the number of denials is not ‘substantial,’ ” and it saw “no reason to think that either of these subsections modifies or limits the other.” Id. (emphasis in original).
We appear to be the first circuit court to consider and apply these regulations.5 We do not think that the text of the regulations, taken together, supports the district court’s view that they require unfailing service. We read the relevant statutory and regulatory provisions, in light of agency opinion letters and with the benefit of the government’s letter-brief to this Court, as follows: § 37.131(b) requires the formulation and implementation of a plan to meet 100% of the demand for next-day ride requests by eligible riders, while § 37.131(f) grants limited leeway for occasional failures of such well-laid plans to meet demand. The regulations require a provider to rethink its plan and implement changes whenever a pattern of noncompliance develops. This analysis requires some exposition.
As a threshold matter, the text of the ADA itself offers little guidance. Section 12143 requires that the “level of [paratran-*209sit] service” be “comparable to the level of designated public transportation services provided to individuals without disabilities,” and that response time be “comparable, to the extent practicable, to the level of designated public transportation services provided to individuals without disabilities.” 42 U.S.C. § 12143(a). What level of service would make a paratransit system “comparable” to a public transportation system used by individuals without disabilities? Comparability seems impossible to achieve because, as one district judge has observed, “a constraint on a fixed route system never results in a patron being denied a ride altogether, absent an uncontrollable force.” Liberty Resources, 155 F.Supp.2d at 256.
Some guidance is found in the commentary that accompanied the “minimum service criteria” regulations promulgated by the DOT under 42 U.S.C. § 12143(c)(3). See 56 Fed.Reg. 45584, 45606-08 (Sept. 6, 1991). The DOT’S discussion of the “response time” regulation is cast in terms of scheduling systems and their periods of operation. Id. at 45606. The DOT viewed “the next-day scheduling provision” as “a good balance of minimizing inconvenience to users and allowing providers sufficient time to schedule trips to maximize efficiency,” id., and viewed § 37.131(b) as requiring paratransit service providers to implement some form of next-day scheduling system.
Objections received during the comment period emphasized that unfailing next-day service for paratransit riders was unrealistic.6 Some commenters “suggested a performance standard (e.g., meeting an average 98 percent of trip requests per day).” Id. at 45608. The DOT nevertheless retained its capacity constraint regulations in their present form. While conceding that “there are capacity constraints on fixed route transit,” the DOT observed that “[cjapacity constraints of this kind are already reflected in the requirements for paratransit, given the service area and hours and days criteria.” Id. Also, while overcrowding may prevent fixed route passengers from boarding particular buses or trains, “all the passengers have to do is wait a little longer for the next bus or train- to come,” whereas there is no next bus or train for paratransit riders. Id. In short, paratransit would not be “a comparable system” if overcrowding prevented paratransit riders from reaching their destinations. Id. “The capacity constraints provision” was designed to “provide adequate redress for systemic problems in service delivery.” Id. Thus, while § 37.131(b) concerns the system a para-transit service provider must design and implement, the provisions of § 37.131(f) gauge whether a provider has fulfilled its obligation to meet demand.
This understanding is confirmed by the government’s persuasive October 25, 2002 letter-brief to this Court.7 Section *21037.131(b), according to the government, “imposes an affirmative obligation on transit agencies to design, fund, and implement a next-day service to meet the foreseeable needs of all ADA-eligible individuals .... The regulation accordingly forecloses any planned non-coverage.” (Letter from Jessica Dunsay Silver, Dep’t of Justice, dated Oct. 25, 2002, at 4 (emphasis added).) The government views § 37.131(b) and § 37.131(f) as “complementary” but “addressing] different aspects of administering a paratransit service,” as follows:
Section 37.131(b) addresses a transit provider’s responsibilities from a- conceptual perspective and imposes an affirmative obligation on transit authorities to design, fund, and implement a paratran-sit program that will fully meet the anticipated needs of ADA-eligible individuals for next-day paratransit service. Section 37.131(f), by contrast, addresses the transit provider’s responsibilities from the practical perspective of “capacity constraints” and specifically imposes a prohibition on “[a]ny operational pattern or practice , that significantly limits the availability of service to ADA para-transit eligible persons.” 49 C.F.R. § 37.131(f)(3).
(Id. at 4-5 (emphasis added).) Thus, the government recognizes that “[e]ven a well conceived paratransit service, designed, •funded, and implemented to meet 100% of projected need, may occasionally experience trip denials.” (Id. at 5.) Under § 37.131(f), however, “‘substantial numbers’ of trip denials can establish that a paratransit service — no matter how well-designed, funded, or implemented in theory — is inadequate as a matter of actual operation.” (Id.)
DOT’S advice to paratransit service providers, as expressed in opinion letters issued by the Federal Transit Administration (“FTA”),8 has been to the same effect, consistently and over a period of years. These letters show that the FTA expects paratransit providers to plan, design, and operate their systems to meet their full next-day ride demand, and that § 37.131(f) permits an insubstantial number of trip denials, so long as those denials are unplanned and do not result from the provider’s operational decisions.9
*211This view was articulated persuasively in the only other opinion to consider these regulations in detail. See Liberty Resources, Inc. v. Southeastern Pa. Transp. Auth., 155 F.Supp.2d 242 (E.D.Pa.2001), vacated, 54 Fed.Appx. 769 (3d Cir.2002) (unpublished disposition) (dismissing defendant’s appeal as moot and vacating judgment after defendant complied with, and district court terminated, an injunction order). The Eastern District of Pennsylvania held that the regulations, taken together, “indicate that DOT expected agencies ... to attempt to provide properly requested rides to all ADA-eligible riders, i.e., without exception.” Id. at 255 (emphasis in original). It concluded that “the ‘substantial number’ language [of § 37.131(f)] cannot be used as a green light to intentionally create a system that denies rides.” Id. at 256.
*212In short, § 37.131(b) requires paratran-sit service providers to plan to meet 100% of the demand for next-day ride requests. Section 37.131(f) recognizes that even well-laid plans may misfire on occasion and permits the denial of an insubstantial number of trips, so long as those denials were not attributable to the design of the para-transit system. And, as necessary, para-transit service providers must modify their plans with the goal of achieving the 100% service level.
III. Next-Day Service Claim
The plaintiffs’ first claim alleges that the defendants violated 42 U.S.C. § 12143(a)(2) and 49 C.F.R. § 37.131(b) by failing to provide next-day paratransit rides to all eligible individuals who requested them. As noted above, the district court construed § 37.131(b) as requiring paratransit service companies to satisfy 100% of the demand for next-day ride requests,- and granted summary judgment to the plaintiffs primarily because some “eligible persons are being completely denied rides on the days requested.” Anderson I, 206 F.R.D. at 65.
Under our interpretation of the relevant regulations, however, a paratransit provider may not be held liable for denying next-day ride requests solely on the basis of a lack of capacity unless it denies a substantial number sufficient to constitute a pattern or practice under § 37.131(f). We take up that issue in Part IV of this opinion.
The, question under § 37.131(b) is whether the paratransit company planned, designed, and implemented a system to meet 100% of its next-day ride demand. The record supports the finding that the defendants foresaw a growing inability to meet demand. The defendants’ 1993 ADA Paratransit Plan Update recorded that “there are now 1,432 clients making an average of 8.8 trips per month or a projected 147,000 trips per year,” and that “[t]his projection exceeds the estimated supply of 130,000 trips by 13%.” (1993 ADA Paratransit Plan Update, at 2.) The update “projected that all requests for service by ADA eligible clients ... cannot be accommodated within the resources presently available to Lift Line,” even as it “anticipated that the number of eligible clients will continue to grow in 1993 by perhaps 300(2%).” (Mat 3.)'
The 1993 update proposed measures designed “to achieve full compliance,” including tests of the eligibility process, closer management of client cancellations, and efforts to increase public funding and private partnerships. {Id. at 3-4.) Yet the 1994 plan update stated that “[tjhere were no significant changes made in paratransit service since the 1993 submission.” (1994 ADA Paratransit Plan Update, at Sec. VII.) The 1995 update reported that, “[djuring calendar 1994, Lift Line[] continued to operate within existing policies, procedures, fleet, fares and service area.”10 (1995 ADA Paratransit Plan Update, at 1.) Unquestionably, then, the defendants failed to respond adequately to the increasing demand they foresaw in 1993.
In the affidavit submitted in support of the defendants’ motion for summary judgment, RGRTA’s chief executive officer acknowledged Lift Line’s persistent ride denial rate. (Affidavit of Donald J. Riley, dated Aug. 30, 2000, at 11-14.) Between May and June 2000, he noted, Lift Line scheduled over 99% of the rides requested 14 days in advance, but “[a]s the ride day approaches, ... the percentage of *213rides that can be scheduled inevitably falls because there is less and less capacity in the system.” (Id. at 11.) He conceded that “only 69 of the 161 rides requested with 1 day notice (approximately 43%) were scheduled” because “all spaces on the buses assigned to the area had been reserved.” 11 (Id. at 11-12.)
The defendants attributed their ride denials to capacity constraints that were “not unusual”:
First, Lift Line riders that are not truly “eligible” for paratransit service (and who would not be eligible if a rigorous recertification process were employed ...) continue to ride and thus use reservation spaces for those that are truly “eligible.” Second, Lift Line riders are not required to ride accessible RTS bus routes whenever available (even though they could be) .... Finally, an exorbitant number of Lift Line riders ... reserve spaces only to cancel the ride, or not show up at all, at a later date.
(Id. at 12.) Defendants concede that “Lift Line could reduce its denial rate even further, and perhaps eliminate it altogether, if it recertified the eligibility of its riders, required riders to use accessible RTS buses whenever possible, or raised fares to the statutory limit.” (Id. at 14.) The record thus establishes that the defendants foresaw increasing demand, recognized that they failed to schedule all next-day ride requests from eligible riders, and declined to institute reforms that would allow them to meet 100% of the eligible next-day ride demand.
We therefore conclude that the defendants violated § 37.131(b) by failing to design and implement a system to schedule all next-day ride requests from eligible riders. On this ground, we affirm the district court’s grant of summary judgment in favor of plaintiffs on the first claim. However well-intentioned may have been their efforts to make Lift Line flexible and available to as many individuals as possible, the defendants failed to comply with the baseline requirement of § 37.131(b)’s next-day service provision.
IY. Operational Pattern or Practice Claim
The third claim alleges that the defendants violated 49 C.F.R. § 37.131(f)(3) by engaging in an “operational pattern or practice” that significantly limited the availability of paratransit service. To repeat: § 37.131(f) provides that “[s]uch patterns or practices include, but are not limited to, ... [substantial numbers of trip denials or missed trips.” 49 C.F.R. § 37.131(f)(3)(i)(B). The regulation exempts “[ojperational problems attributable to causes beyond the control of the entity (including, but not limited to, weather or traffic conditions affecting all vehicular traffic that were not anticipated at the time a trip was scheduled).” 49 C.F.R. § 37.131(f)(3)(ii).
The district court ruled that, “based upon the number of ride denials, particularly for next-day service, defendants have engaged in an operational pattern or practice that significantly limits the availability of service to ADA paratransit eligible persons.” Anderson I, 206 F.R.D. at 70. “Even looking at the total number of denials over the course of the 14-day reservation period, the 6% of requests that are denied, or 510 out of 8962 requests from *214May 26 to June 14, 2000, cannot reasonably be considered ‘insubstantial.’” Id. The court reasoned that “rides are regularly denied not because of matters outside the defendants’ control, but because of a lack of available seats, which in turn is attributable to defendants’ insufficient capacity and its booking practices.” Id.
We agree with the district court’s reasoning and conclusion. Section 37.131(f) gives no clue as to how many trip denials is “substantial,” but the DOT has provided some guidance. In its letter-brief, the government advised that “there is no ‘magic number,’ whether expressed in absolute terms or as a percentage, that can be used to determine whether a transit authority has denied or missed a substantial number of trips.” (Letter from Jessica Dunsay Silver, Dep’t of Justice, dated Oct. 25, 2002, at 5-6.) “[A] factual case-by-case determination” is therefore required, (Letter from William P. Sears, Chief Counsel, Fed. Transit Admin., dated Jan. 9, 2002, at 2), “within the context of each agency’s service profile,” (Letter from Jessica Dunsay Silver, Dep’t of Justice, dated Oct. 25, 2002, at 6). Relevant factors may include the time period over which the denials occurred, changes implemented by the provider to address them, the trend and persistence of denials, foreseeability of the denials, causes of the denials, and the reasonableness of the provider’s demand estimates and plans.12 (Id. at 6-7.)
In Liberty Resources, the court considered whether “the number and nature of [a paratransit agency’s] trip denials” violated the DOT’S capacity constraint regulation. 155 F.Supp.2d at 243. The undisputed evidence revealed that the agency (“Septa”) denied 29,472 (or 2.8%) of the 1,050,770 rides requested over a thirteen month period. Id. at 245. It denied 11,-948 (or 13.4%) of the 89,131 next-day ride requests it received during this period. Id. at 246. This amounted to approximately 30 next-day ride denials each day. Id. Septa argued that it had met 97.2% of all ride requests, but the court fairly observed that the proper focus is on the number of rides denied and the reasons for those denials. See id. at 257. The court concluded that Septa had engaged in “a pattern and practice [in] violation of the capacity constraint provision” of § 37.131(f). Id.
Similarly, in Martin v. Metropolitan Atlanta Rapid Transit Authority, 225 F.Supp.2d 1362 (N.D.Ga.2002), the defendant transportation company (“MARTA”) was enjoined to improve its paratransit services to “a level of service which is comparable to that MARTA provides to the non-disabled.” Id. at 1383. The record showed systemic scheduling and service problems and the initial denial of 38% of next-day ride requests due to a lack of capacity. Id. at 1371. The court concluded that “operational patterns and practices in MARTA’s paratransit service have significantly limited the availability of service to paratransit eligible persons in violation of the ADA.” Id. at 1380.
We conclude that Lift Line denied a “substantial” number of paratransit rides *215in violation of § 37.131(f)(3)(i)(B). While Lift Line scheduled over 94% of all requests received during the sample period, the success rate declined sharply with the number of days of advance notice: Lift Line denied 37 of the 130 rides requested four days in advance, 38 of the 105 rides requested three days in advance, 67 of the 180 rides requested two days in advance, and 92 of the 161 rides requested for the next day. Overall, Lift Line denied 436 of the 8,839 rides requested in the twenty-day period tracked by the plaintiffs before they commenced this action. These statistics are unrefuted and comport with the trip denial data included in the defendants’ DOT submissions over the last several years.
As discussed in the previous section, the defendants foresaw increasing ride demand and failed to modify their paratran-sit service plan to meet it. They acknowledge that they could take steps to improve their ability to meet demand, such as paring their certification rolls to eliminate ineligible riders. The defendants attribute the problem to their indulgence of ineligible riders and frequent rider cancellations, and they argue that these causes bespeak their good faith, and that may be so. But as the government advised in its letter-brief:
[A]n excusable cause [of operational problems] must truly be beyond the control of the transit provider. A transit agency is expected to anticipate recurrent traffic congestion, seasonal variations in weather, and the need to maintain vehicles.... Indeed, once a seemingly unforeseeable pattern develops, ... the recurring event becomes foreseeable, and the transit authority can no longer claim the matter is beyond its ability to address.
(Letter from Jessica Dunsay Silver, Dep’t of Justice, dated Oct. 25, 2002, at 5.) The defendants must fulfill their obligation to avoid recurring problems by any appropriate measures, possibly including a tough-minded enforcement of rider eligibility.
We therefore affirm the conclusion that the defendants violated § 37.131(f) by maintaining a pattern or practice that significantly limits the availability of para-transit service for eligible riders.
V. Claim for Noncompliance with Plan Submitted to the Secretary of Transportation
The ADA’s paratransit scheme requires providers to submit service plans to the Secretary of Transportation. Section 12143(c)(7) provides in pertinent part:
The regulations issued under this section shall require that each public entity which operates a fixed route system— (A) ... submit to the Secretary, and commence implementation of, a plan for providing paratransit and other special transportation services which meets the requirements of this section; and (B) on an annual basis thereafter, submit to the Secretary, and commence implementation of, a plan for providing such services,,
42 U.S.C. § 12143(c)(7). The DOT has promulgated detailed regulations to implement these plan requirements. See 49 C.F.R. §§ 37.135-37.149. Each plan must contain, among other things, “[a] description of the plan to provide comparable paratransit,” including “[a] brief description of planned modifications to existing paratransit and fixed route service and the new paratransit service planned to comply with the ADA paratransit service criteria,” as well as “[a] description of the planned comparable paratransit service as it relates to each of the service criteria described in § 37.131 of this part — service area, absence of restrictions or priorities based on trip purpose, response time, *216fares, hours and days of service, and lack of capacity constraints.” 49 C.F.R. §§ 37.139(d)(3) & (d)(4).
The ADA’s definition of “discrimination” includes a public entity’s “failure ... to provide paratransit or other special transportation services in accordance with the plan or modified plan the public entity submitted to the Secretary under this section.” 42 U.S.C. § 12143(e)(4). A provider therefore may be held liable under the ADA for failing to comply with its own plan.
The plaintiffs claim that RGRTA and Lift Line violated § 12143(e)(4) by failing to provide paratransit service in accordance with the plan they submitted to the DOT. The district court regarded this cause of action as derivative of the other claims and granted summary judgment in favor of the plaintiffs on that ground: “[sjince I have found that plaintiffs are entitled to summary judgment on their first and third claims for relief, I will grant summary judgment in their favor on this claim as well.” Anderson I, 206 F.R.D. at 70. We respectfully disagree.
The plaintiffs argue broadly that the “defendants falsely affirmed in their plan that Lift Line was in compliance with the regulations requiring next-day service, prohibiting waiting lists, and not engaging in operational patterns and practices of discrimination.” (Pls.’ Br. at 61; see also Complaint, at 34-36.) However, these affirmations amount in great part to legal conclusions as to matters that are disputed in this case. The DOT concluded that these affirmations complied with DOT regulations after it reviewed the defendants’ annual submissions. (Defs.’ Reply Br. at 23-24.) In one representative compliance letter, the DOT informed RGRTA that it had “completed its review of the paratransit plan update [RGRTA] submitted” and “determined that [its] plan update [was] in compliance with the requirements of DOT’s regulation.” (Letter from Letitia Thompson, Deputy Reg’l Adm’r, Federal Transit Admin., dated May 30, 1995.) The DOT approved the defendants’ 1995 plan update even though it included information about trip denial rates that did not materially differ from those now at issue in this litigation.
We decline to construe § 12143(e)(4) to impose liability whenever a court finds that a transportation service provider has not complied with other provisions of the DOT’s regulations. So applied, § 12143(e)(4) would be redundant. Cf. State Street Bank & Trust Co. v. Salovaara, 326 F.3d 130, 139 (2d Cir.2003) (“It is well-settled that courts should avoid statutory interpretations that render provisions superfluous .... ”). In order to give § 12143(e)(4) independent force, we read it as describing a failure to take some action or to implement some procedure that is included in a plan or annual update.
This understanding finds support in the single case we have found applying § 12143(e)(4). In O’Connor v. Metro Ride, Inc., 87 F.Supp.2d 894 (D.Minn.2000), the defendants “incorporated door-through-door service in the paratransit plan they proposed to [the DOT].” Id. at 900. The district court denied the defendants’ motion for summary judgment because, whether or not the ADA requires door-through-door service, a “jury could reasonably find that [the defendants’] alleged failure to provide service ‘in accordance with the plan’ constituted unlawful disability discrimination under Title II.” Id.
The plaintiffs here identify no specific action or procedure in the defendants’ DOT submissions that the defendants faked to implement. The defendants’ affirmations of ADA compliance constituted legal conclusions with which the DOT at one time agreed. We therefore reverse *217the grant of summary judgment in favor of plaintiffs on their § 12143(e)(4) claim.
CONCLUSION
For the foregoing reasons, we affirm the grant of summary judgment on the plaintiffs’ claims for violation of 49 C.F.R. §§ 37.131(b) and 37.131(f), and we reverse on their claim for violation of 42 U.S.C. § 12143(e)(4). We remand for proceedings on the latter claim, for any reframing of the injunction that may be justified by this opinion or circumstances that have developed during the pendency of the appeal, and for any other proceedings consistent with this opinion.
. We draw these facts from the Defendants' Statement of Material Facts Not in Dispute, dated August 30, 2000; the Plaintiffs’ Statement of Undisputed Facts, dated October 31, 2000; and other materials filed in connection with the parties' summary judgment motions.
. For several years, Lift Line conducted "real-time” scheduling, a system comprised of live operators who answered calls, received requests, and arranged rides while customers remained on the phone. Because the schedulers made trip arrangements on the spot, callers often spent a long time on hold. In August 1999, Lift Line switched to a reservation system in which customers call once to give their ride request information and then call a second time to confirm that a ride is available and obtain pickup details.
. The district court’s denial of summary judgment on the plaintiffs’ "waiting list” claim under 49 C.F.R. § 37.131(f)(2) is not before us on this appeal.
. The Anderson II opinion postdated — and therefore was not part of — the record submitted on appeal, hut we take judicial notice of it. See Shuttlesworth v. City of Birmingham, 394 U.S. 147, 157, 89 S.Ct. 935, 22 L.Ed.2d 162 (1969) (taking judicial notice of record in prior litigation between same parties); New York ex rel. Spitzer v. Operation Rescue Nat’l, 273 F.3d 184, 199 (2d Cir.2001) (taking judicial notice of district court’s decision in related proceeding); In re Holocaust Victim Assets Litig., 225 F.3d 191, 195 n. 3 (2d Cir.2000) (noting approval of addition to record on appeal of district court order filed approximately six months after appeal was filed); Jacques v. United States R.R. Retirement Bd., 736 F.2d 34, 40 (2d Cir.1984) (taking judicial notice of official court record in related case of inferior court in same jurisdiction). We have appellate jurisdiction over defendants’ appeal from the district court’s August 14, 2001 order as implemented by the April 26, 2002 order. See 28 U.S.C. § 1292(a)(1); Original Great Am. Chocolate Chip Cookie Co. v. River Valley Cookies, Ltd., 970 F.2d 273, 276 (7th Cir.1992) ("The acid test of whether a purported injunction is appealable is whether it is in sufficient though not exact compliance with Rule 65(d) that a violation could be punished by contempt or some other sanction.”); Fed.R.Civ.P. 65(d) (requiring that injunctions be "specific in terms” and "describe in reasonable detail ... the act or acts sought to be restrained”).
. Two other district court decisions have applied these paratransit regulations, and one of those has been vacated. See Martin v. Metropolitan Atlanta Rapid Transit Auth., 225 F.Supp.2d 1362 (N.D.Ga.2002); Liberty Resources, Inc. v. Southeastern Pa. Transp. Auth., 155 F.Supp.2d 242 (E.D.Pa.2001), vacated, 54 Fed.Appx. 769 (3d Cir.2002) (unpublished disposition) (dismissing defendant’s appeal as moot after defendant’s compliance with injunction). We consider these decisions in our analysis to the extent that they constitute persuasive authority.
. As summarized in the Federal Register, commenters observed that "the provisions concerning consistent denials or untimeliness were too vague;” that, "[g]iven fluctuations in demand, a system could not avoid some trip denials without having substantial excess capacity;” that "it was unreasonable to expect any system to meet all demand, which would inevitably require the addition of more vehicles and keep costs spiraling upward;" and, since "there are capacity constraints on fixed route systems (e.g., a full bus passes up peo-pie waiting at a stop),” that "capacity constraints were likewise reasonable for para-transit.” 56 Fed.Reg. at 45608.
. Agency opinions do not constitute binding authority and receive less deference than regulations, see Chevron, U.S.A., Inc. v. Natural Resources Defense Council, Inc., 467 U.S. 837, 843-44, 104 S.Ct. 2778, 81 L.Ed.2d 694 (1984), but we "give substantial deference to an agency’s interpretation of its own regulations ... 'unless it is plainly erroneous or *210inconsistent with the regulation.’ ” Thomas Jefferson Univ. v. Shalala, 512 U.S. 504, 512, 114 S.Ct. 2381, 129 L.Ed.2d 405 (1994) (citations omitted). Such interpretations "are 'entitled to respect’ ... to the extent that [they] have the 'power to persuade.’ ” See Catskill Mts. Chapter of Trout Unlimited, Inc. v. City of New York, 273 F.3d 481, 491 (2d Cir.2001) (quoting Christensen v. Harris County, 529 U.S. 576, 587, 120 S.Ct. 1655, 146 L.Ed.2d 621 (2000)).
. The Office of Civil Rights in the Federal Transit Administration, a division of the Department of Transportation, "monitors the implementation of and compliance with the American with Disabilities Act [sic] of 1990 by investigating complaints and conducting compliance reviews.” See Federal Transit Admin. Website <available at http:/ /www.fta.dot.gov/office/civrights/index.html> (accessed July 22, 2003).
. First, an April 1996 opinion letter advised a provider that, "[c]ontrary to a widely-held perception, the [DOT’s] ADA regulation does not require that all trip requests (from eligible riders) must be served in order for an operator to be in full compliance, neither does it provide a number or percentage of trip denials that is considered to be acceptable.” (Letter from Gordon J. Linton, Adm'r, Fed. Transit Admin., dated Apr. 15, 1996, at 1.)
In response to an inquiry as to whether "DOT interprets its regulations to mean that a transit provider is in violation of the ADA complementary paratransit regulations if it does not have sufficient capacity to service 100% of the demand at all times” (Letter from Patrick W. Reilly, Chief Counsel, Fed. Transit Admin., dated Mar. 23, 1999, at 1), the FTA advised in March 1999 that "[a] transit agency must be able to deal with the swings in demand when administering its ADA comple*211mentary paratransit service, just as it would on its fixed routes. How a transit agency deals with these swings in demand is its prerogative.” (Id.) For example, it can "have an extra contractor available” or “increase the size of its fleet.” (Id.) "However, if a transit agency has not adequately dealt with this issue, and the transit agency denies ADA complementary paratransit service to a qualified individual with a disability because it does not have the capacity to respond to demand, the denial of ADA complementary paratransit service is discrimination within ... the ADA.” (Id.) Thus, the FTA advised that paratransit service providers must plan for swings in demand.
A December 1999 opinion letter advised that § 37.131(f) recognizes "that forces outside a transit agency’s control will lead to an insubstantial number of denials”:
[Tjhose matters which the transit agency controls, such as decisions on resources for paratransit services, must be designed to meet the demand by all eligible riders, rather than some subset of total demand.... Further, the term "substantial number” as used in section 37.131 cannot be read to allow a transit agency to make operational decisions to serve less than all eligible riders. The assumption of section 37.131 is that operational decisions designed to serve all eligible riders will lead to an insubstantial number of denials because of elements beyond the transit agency's control.... Consequently, if a denial is the result of a force outside the transit agency’s control, it is not a violation of the ADA. If a denial is the result of a decision the transit agency made, i.e., if the denial could have been avoided, then it is a violation of the ADA.... An example of an unacceptable denial is if the transit agency denied a trip to an eligible rider for lack of vehicles. (Letter from Patrick W. Reilly, Chief Counsel, Fed. Transit Admin., dated Dec. 28, 1999, at 2-3 (emphasis added).) Further, "ADA complementary paratransit service should be designed [to accommodate increases in demand] in a comparable manner [to fixed route systems], Operators must monitor current ADA complementary paratransit usage, acquire additional service based on projected demand, and maintain the ability to respond to surges in demand.” (Id. at 3 (emphasis added).)
Most recently, a January 2002 opinion letter offered guidance to an inquiring transit company that read § 37.131(b) "not to preclude all denials, but instead to require that a transit agency design, budget, and operate its system with a goal of having no jjsservation denials or other significant capacity constraint.” (Letter from William P. Sears, Chief Counsel, Fed. Transit Admin., dated Jan. 9, 2002, at 1.) The FTA advised that § 37.131(b) "concerns the timing of reservation requests and subsequent service. If an eligible rider requests a paratransit trip reservation any time today, the transit provider must provide the trip at any time tomorrow.” (Id. (emphasis in original).) The FTA clarified that § 37.131(b) prohibits policies that prevent a transit provider from accepting next-day ride requests: "For example, a provider policy that refused to accept reservations any time today for a trip tomorrow would be facially inconsistent with this criterion. Likewise, a policy that required eligible passengers to call in two days or a week before they wished to travel would also violate this provision.” (Id. (emphasis added).) Thus, the FTA contemplates that there will be ride denials, but counsels that the significance of a particular ride-denial rate must be evaluated under § 37.131(f)'s prohibition on capacity constraints. (Id. at 2.)
. The consolidation of certification forms and procedures implemented by the FTA in 1995 prevents us from tracking these specific statements into later years.
. As previously noted, the November 1999 “RTS Bus Guide & Map” for the Rochester area advised Lift Line users to call "between 7:00 am and 5:00 pm, seven days a week” to schedule a ride. It cautioned that "[rjeserva-tions are made on a first-call, first-serve basis." This presumably had the practical effect of increasing speculative reservations and frequent cancellations.
. After listing these factors, the government suggested that this case presents an example of a situation where “it may be obvious from empirical data that a transit authority has denied a substantial number of trips.” (Id. at 7.) The government expressed the view that, if RGRTA “failed to provide 57 percent of the next-day reservation requests, if that denial rate pertains to ADA-eligible individuals, and if the denials are attributable to factors within the transit provider’s control, then there can be no serious disagreement that the provider has engaged in an 'operational pattern or practice that significantly limits the availability of service to ADA paratransit eligible persons,’ ” in violation of § 37.131(f)(3). (Id.)