DIANE P. WOOD, Circuit Judge.

It is well known that the Fair Labor Standards Act (FLSA), 29 U.S.C. § 201 et seq., requires employers to pay their employees for overtime work at a rate of time and a half. 29 U.S.C. § 207(a). Some employees, however, do not work a standard 40-hour week, and in their case application of this principle becomes more complicated. This case involves 28 firefighters from Evansville, Indiana, who have been pursuing their FLSA suit against the City since September 1989. The plaintiffs believe that their collective bargaining agreement with the City entitles them to more overtime compensation (principally in the form of compensatory time off) than the City was paying from 1987 to 1993, and also (under a different collective bargaining agreement) from 1994 to 1996. The district court, after a bench trial on part of the case, entered judgment for the City. It also granted summary judgment for the City on the claims relating to the 1994-1996 time period, and it granted summary judgment dismissing the International Association of Professional Fire Fighters, Local 357, from the case. We agree that the plaintiffs received all that was coming to them under the statute, and we therefore affirm.

I.

In Evansville, the firefighters for many years have worked shifts that run nine days, 24 hours a day. The Evansville Fire Department maintains three such shifts over a 27-day tour of duty. Each individual firefighter therefore has always worked roughly 216 hours (24 x 9) over each 27-day cycle. (Time spent during the other 18 days of the cycle when they are on call for emergencies apparently does not count toward this total.) Firefighters are not paid by the hour; instead, they receive a paycheck bi-weekly, the amount of which is calculated by taking an annual salary and dividing it up. Because they are paid on a salary basis, the amount they receive does not vary depending on the actual number of hours worked. Nevertheless, the plaintiff firefighters agree that the Evansville firefighters had always worked 216 hours in a 27-day period for 22 years prior to trial.

For all that appears, everything was running smoothly under this system until the Supreme Court decided Garcia v. San Antonio Metro Transit Authority, 469 U.S. 528 (1985), which held that the Commerce Clause did not prevent Congress from imposing maximum hours and minimum wages on state and municipal employees under the FLSA. The next year, Congress amended the FLSA to give governmental employers more flexibility in meeting their overtime obligations, by allowing them to pay in the form of compensatory time off. 29 U.S.C. § 207(o). Against this background, in 1987 the City and Local 357 negotiated their collective bargaining agreement (CBA) for 1987. For the first time, the CBA included the following clause:

Both parties agree that all time worked beyond the allowable straight time maximum as provided by the Fair Labor Standards Act (FLSA) will be compensated with compensatory time as allowed by the FLSA.

The same clause appeared in the 1988, 1989-1990, and 1991-1993 CBAs.

The FLSA addresses the subject of the unorthodox work-week in 29 U.S.C. § 297(k), which provides that a firefighter with a work period of at least seven days but less than 28 days shall receive overtime compensation for all hours worked in excess of a number bearing the same ratio to the total days worked as 212 hours bears to 28 days. As 29 C.F.R. § 553.230(c) spells out, for a 27-day work period, the total number of regular hours for firefighters is 204 (because 212/28, or 7.57 hours per day, is roughly equal to 204/27, or 7.55). Initially, the City took the position that the firefighters' salary corresponded to 216 hours of work. Beginning in 1987, therefore, with the new CBA and Garcia governing its actions, it began giving the firefighters one-half hour of compensatory time off for each hour worked between 204 and 216 during each work period. This effectively meant, according to the City, that the firefighters were receiving their statutory "time and a half" for those overtime hours in a mixed form: 2/3 monetary compensation, 1/3 compensatory time.

The plaintiffs did not see it this way. In 1989, an Evansville city firefighter (whose name is not known from the record) filed a complaint with the U.S. Department of Labor on behalf of the firefighters, claiming that the City was incorrectly computing the compensatory overtime credits. In September of that year, three firefighters — Ron Tabor, Don Brown, and Fred Taylor — filed this suit in district court on behalf of themselves and others similarly situated. In response to the complaint lodged with the Department of Labor, Alice Hertli, an investigator from the Wage and Hour Division, met with representatives of the City and Fire Department administrators. She agreed with the firefighters and directed the City to begin crediting each firefighter with 18 hours of overtime pay for the hours worked between 204 and 216. Hertli threatened the City with fines if it did not comply. The City acquiesced for a period of time, but it eventually balked and returned to its former position of crediting only six hours overtime for the hours between 204 and 216. Meanwhile, this litigation was progressing. In 1994 many of the original plaintiffs settled their claims against the City (which had become concerned about its exposure for cash payments to retiring firefighters entitled to cash in accumulated compensatory overtime hours). After the settlement, the City apparently paid even the non-settling plaintiffs at the full 18 hour (time and a half) rate for a time, although it eventually again stopped this practice and returned to the six hour rate.

The language of the CBA remained unchanged until the Association and the City negotiated the 1994-1996 agreement. This time, they inserted the following specific language about overtime into the text:

The parties agree that all firefighters in suppression [i.e. on duty] receive straight-time monetary compensation to work two hundred sixteen (216) hours in each twenty-seven (27) day work period. The parties agree that in addition to straight time monetary compensation, all firefighters in suppression shall continue to receive additional premium pay of fifty percent (50%) for each hour worked in excess of the maximum hour standard of two hundred four (204) hours as established by the Fair Labor Standards Act. The parties agree that all firefighters in suppression shall receive compensation at a rate of no less than one and one half (1 1/2) the firefighters' regular rate for each hour worked in excess of two hundred sixteen (216) in each twenty-seven (27) day work period. The parties agree that any and all overtime compensation required pursuant to this agreement and/or required pursuant to the Fair Labor Standards Act may be awarded in compensatory time off rather than monetary compensation at the option of the City. Both parties further agree that this language reflects the intent and past practices of the parties and does not circumvent or violate the requirements of the Fair Labor Standards Act.

Under this agreement, the City consistently paid its firefighters monetary compensation for their 216-hour shift and it credited them with six hours overtime for the hours from 205 to 216.

The plaintiffs' complaint initially included two counts, in which they argued (1) the City owed them additional overtime compensation for the period from September 1987 through September 1993, (2) the City owed additional overtime compensation for time the firefighters spent on call (i.e. beyond the 216 hours), (3) the captains in the department were not exempt from the FLSA as "bona fide executives," and (4) individual firefighter overtime compensation banks were being improperly reduced whenever a firefighter worked fewer than 204 hours in a 27-day period. After the settlements reduced the number of plaintiffs considerably, the remaining plaintiffs amended the complaint. The new Count III alleged that the 1994-1996 CBA also violated the FLSA's overtime compensation rules. The plaintiffs later added Count IV, which raised the same argument but added Local 357 as a party.

The first two counts were tried to the court on February 13 and 14, 1995. The court found against the plaintiffs and for the City on the first two overtime compensation issues, and it found for the plaintiffs on the question of the captains' entitlement to overtime as non-exempt employees. It also found for the plaintiffs on their claim regarding treatment of the overtime compensation banks, finding that it was improper for the City to deduct time not worked during one tour of duty from overtime compensation earned from hours worked in a prior tour of duty. Later, Local 357 moved for summary judgment, which the court granted, and at the same time it granted summary judgment for the City with respect to the 1994-1996 contract. With all claims resolved, the plaintiff firefighters appealed to this court. The City has not cross-appealed with respect to the status of the captains or the individual overtime accounts; thus, those parts of the judgment are not before us.

II.

Because of the change in language from the 1987 CBA (and later agreements based on it) to the 1994-1996 CBA, the firefighters' arguments are naturally different for these two time periods. With respect to the 1987-1993 period, they argue first that the language of the CBA unambiguously required the City to pay the full 18 hours of overtime for the last 12 hours of the shift (205-216). Even if, as the district court found, the language was ambiguous, they claim that extrinsic evidence supported their position on the true intent of the parties. In that connection, they claim that the court erred when it found that Fed.R.Evid. 408 required the exclusion of evidence related to the settlement agreements. Finally, for the 1994-1996 period, they object strenuously to the sentence of the paragraph from the CBA quoted above that proclaims adherence to the FLSA, which they see as a blatant attempt to circumvent the law. Pointing out that the 1994-1996 CBA also claims that it carries forward past practice, they argue that this means they are entitled to the full 18 hours of overtime compensation for the last 12 hours of the shift under that agreement as well.

A. 1987-1993 Agreements

The first question we must consider, which we review de novo, is whether the 1987 CBA (as well as those that copied it) was unambiguous. If the firefighters are right, then under well established principles of contract law, as applied to the interpretation of a collective bargaining agreement, the court should not resort to extrinsic evidence to interpret the agreement. Illinois Conf. of Teamsters Welfare Fund v. Mrowicki, 44 F.3d 451, 459 (7th Cir. 1994); Hickey v. A.E. Staley Manufacturing, 995 F.2d 1385, 1389 (7th Cir. 1993). A collective bargaining agreement that lends itself to only one reasonable interpretation is considered to be unambiguous. Murphy v. Keystone Steel Wire Co., 61 F.3d 560, 565 (7th Cir. 1995). This means, among other things, that the court should be able to ascertain how the contract applies to a particular set of circumstances without resort to facts external to the contract. If there is some doubt about the sense or meaning of a contract, the court may consult evidence about its formation or the parties' course of dealing to throw light on the question. See Railway Labor Executives Ass'n v. Norfolk Western Ry. Co., 833 F.2d 700, 705 n. 4 (7th Cir. 1987).

The firefighters see no ambiguity in the 1987 language, because on its face it contains no exception to the rule that pay for time above the FLSA maximum must be in the form of compensatory time off, "as allowed by the FLSA." The FLSA maximum for them is 204 hours; they worked 216 hours on their shift; therefore they were entitled to 18 hours of time off for the additional 12 hours of work. The district court found that this language was not as clear as the plaintiffs argued, because the contract nowhere specified the number of days in a work period, the number of hours to be worked per work period, or what hours of work were to be compensated by the listed salaries. If the work period had been less than seven days, instead of 27 days as it was, the FLSA regulation ( 29 C.F.R. § 553.230(c)) would not even have applied. A second ambiguity arises over the amount of compensation these firefighters were already receiving. The FLSA does not require the payment of two and one-half times regular salary for overtime, but if the City was already paying straight time monetary compensation for the last 12 hours, then the addition of 18 hours of compensatory time off would amount to exactly that. Finally, the last clause of the provision allows compensatory time off "as allowed by the FLSA." When one consults the FLSA, one sees that sec. 207(o) permits, but does not require, states and municipalities to meet their overtime obligations with compensatory time off. Thus, to handle overtime "as allowed by the FLSA" may just give the City the option of using compensatory time for all of the extra hours; it does not necessarily compel that result.

We agree with the district court that all of this is enough to show that the language of the 1987 agreement was not unambiguous. We review the district court's findings about the parties' past practice only for clear error. See Railway Labor Executives Ass'n, 833 F.2d at 705-06. The district court found that the overall compensation the firefighters received was intended to cover the full 216-hour tour of duty, as it had done for at least 27 years by the time of the trial. The court also commented that "after twenty-two years of compensating firefighters for twenty-seven (27) day, two hundred sixteen (216) hour tours of duty, it is not reasonable to accept an argument that the City would make such a change [in the 1987 CBA and following ones based on it] without express provision." It also referred to testimony from a City negotiator that the contested language in the 1987 agreement was inserted to give the City "an option in satisfying federal labor law overtime requirements in either compensatory time or cash." Based on this additional information, the court concluded that the word "overtime" in the 1987 CBA meant the premium to be paid over and above the straight time compensation the firefighters were already receiving for their 216-hour tour of duty.

The firefighters point to three additional factors which, they argue, show that the district court clearly erred in its interpretation of the extrinsic evidence. First, they point out that the City began crediting firefighters with 18 hours of compensatory time after Hertli wrote her letter demanding such a change. Second, they argue that the district court abused its discretion in refusing to consider the settlement agreement between the City and the other firefighters, which they claim would have shown that their reading was the correct one. Finally, they note that the City made no effort to change the troublesome clause when it negotiated the 1991-1993 CBA, even though by then it was quite clear that the firefighters at least thought that the old language entitled them to the full 18 hours of compensatory time.

Although these arguments might have carried some weight with the district court, we cannot say that it clearly erred when it ultimately concluded that they did not carry the day. The City's decision to acquiesce, for a period of time, to the demands of the DOL conveyed through Hertli throws little if any light on its understanding of the meaning of the CBA. At oral argument, counsel for the City informed the court that the City had essentially taken this action under protest. Furthermore, the record shows that the City changed its method of computing overtime a number of times following its meeting with Hertli and again during the time period after the settlement agreements with other firefighters were concluded. The district court reasonably could have concluded that this kind of flip-flopping was of little use in interpreting the language of the 1987 agreement.

The firefighters concede that we must review the district court's decision whether to admit the evidence of the settlement agreements under Fed.R.Evid. 408 only for abuse of discretion. Winchester Packaging, Inc. v. Mobil Chemical Corp., 14 F.3d 316, 320 (7th Cir. 1994). That rule does not permit the admission of evidence of settlement or compromise to prove liability for a claim or its amount, but it does allow such evidence if it is offered for another purpose, "such as proving bias or prejudice of a witness, negativing a contention of undue delay, or proving an effort to obstruct a criminal investigation or prosecution." Fed.R.Evid. 408. See United States v. Hauert, 40 F.3d 197, 200 (7th Cir. 1994) (upholding admission of a settlement-related letter to show tax evasion defendant's knowledge of the law and of his duty thereunder); Cates v. Morgan Portable Building Corp., 780 F.2d 683, 691 (7th Cir. 1985) (upholding use of a negotiated stipulation to fix liability for consequential damages incurred after the parties entered into the stipulation). The firefighters argue that in this case they were not offering the settlement agreement to prove liability on the City's part, but instead they were just trying to demonstrate the City's own interpretation of the 1987 agreement. But the purpose of trying to demonstrate the City's own interpretation of the agreement was, quite simply, to show that the City was liable for the extra overtime hours — precisely the issue at stake here. The district court did not abuse its discretion when it concluded that the proffered use either fell within the literal terms of Rule 408's prohibition, or at least came so close to the line that exclusion was appropriate.

Perhaps the best evidence the firefighters have is the City's failure to try to renegotiate the clause in 1991, once it was fully aware of the contours of this dispute. If the City had thought that Hertli's interpretation of the 1987 CBA did not reflect the true intent of the parties, it is hard to see why it did not try to correct the phrasing of the clause when it had the chance to do so. On the other hand, it is possible that the City might have feared that a change of language in the midst of the litigation would have been seen as an implicit concession that the earlier contracts did mean what the firefighters said they did. Furthermore, since it is hard to be sure what lay behind the choice to stay with the status quo, this evidence alone does not demonstrate a clear past practice or understanding on the City's part that 18 hours of overtime compensatory hours were to be credited for 12 hours of work above 204. Again, at the very least we cannot say the district court clearly erred in viewing the evidence this way.

B. 1994-1996 Agreement

Although the district court granted summary judgment for the City on the claims pertaining to this agreement, and our review is therefore de novo, little need be said about it. The district court summarized its reasoning as follows:

Summary judgment is appropriate in this case because, in short, the 1994-1996 CBA succeeded where others failed. That is to say, the '94-'96 CBA unambiguously expresses what this Court found to be the parties' intent in the earlier CBAs. Significantly, the earlier CBAs were ambiguous and proper construction required significant analysis and extrinsic evidence. The intent found, the only question is whether the intent is legal, i.e., have the Firefighters improperly forsaken their FLSA rights. On August 25, 1995, this Court said no. It is proper and lawful for the parties to agree to a scheme whereby overtime compensation can be paid in compensatory hours.

We agree that the compensatory scheme described in the 1994-1996 CBA unambiguously provides that (1) the firefighters will be paid straight-time monetary compensation for 216 hours of work, (2) they will receive, in addition, a premium of 50% for each hour worked in excess of the 204, up to and including 216, and (3) for all overtime worked above 216, they will be compensated at a rate of one and one-half their regular rate. The agreement also gives the City the option of awarding any or all overtime compensation in the form of time off. This is all crystal clear and consistent with the FLSA. We therefore agree with the district court that there was no need to resort to extrinsic evidence. The mere fact that the parties added a self-serving (and meaningless) sentence at the end of the clause proclaiming their own compliance with the FLSA and announcing that their new arrangement was consistent with past intent and practices does not change this conclusion. Neither we nor the district court relied on that sentence to interpret the 1987-1993 practice, and the clause taken as a whole is clear with respect to the 1994-1996 period.

C. Local 357

Local 357 argues that the firefighters failed to perfect any appeal from the district court's grant of summary judgment against them with respect to the claims against the Association. Although normally a notice of appeal from a final judgment would bring up all claims against all parties, the notice filed here specified precisely which parts of the district court's judgment the firefighters wished to appeal:

Plaintiffs appeal the following portions of the district court's judgment: judgment for the defendant on the issue of overtime compensation owed for hours worked between two hundred four (204) and two hundred sixteen (216); judgment for the defendant on the issue of liquidated damages; summary judgment for the defendant on Count III and IV of the complaint.

There is a certain ambiguity in this notice, since there were two defendants for Count IV, the City and Local 357. In context, however, it appears that the firefighters intended to limit their appeal to issues relating to the City. They are entitled to do so under Fed.R.App.P. 3(c). We therefore agree with Local 357 that no properly perfected appeal exists with respect to it.

Even if we construed the last part of the notice as including the claims against Local 357, however, we would affirm the district court's judgment. The firefighters have said not a word about Local 357's role in the arrangement in their brief. This means that they have waived the right to contest the district court's summary judgment in Local 357's favor. Hartford Accident and Indemnity Co. v. Sullivan, 846 F.2d 377, 385 (7th Cir. 1988). We therefore AFFIRM the district court's judgment for the City of Evansville and we DISMISS the appeal insofar as it relates to the International Association of Professional Fire Fighters, Local 357. Each side will bear its own costs on appeal.