After the City of Two Rivers decided that all of its firefighters must be certified as paramedics, the City and the firefighters' union agreed that one third of any necessary training would occur during normal work hours, one third would be treated as overtime at the contractual overtime rate, and the remaining third would be treated as "donated" time. When the City learned that, by virtue of the Fair Labor Standards Act, time required of an employee may not be treated as "donated," it decided to compensate the firefighters at half of their regular hourly rate. Christopher Heder's regular rate in 1997, when his training occurred, was $11.16 per hour, so he received $5.58 per hour for the "donated" time. The deal between the City and the union included a 3% increase in the wages of firefighters who held certifications, plus an undertaking that any firefighter leaving the City's employ within the next three years would reimburse the City for the cost of the training, which would give each firefighter a portable credential. Two and a half years after beginning his training, Heder quit. Two Rivers withheld all of Heder's pay from his last two pay periods. Heder filed suit under the FLSA, and the City counterclaimed for the remainder of the money that it believes Heder owes under its memorandum of agreement with the union.

The district judge held that the FLSA requires the City to pay time and a half for the "donated" hours and forbids recoupment by setting terminal wages to zero. Although the court held that the union's agreement with the City is not vitiated by the fact that Heder commenced his training before the details were ironed out, this conclusion (the only aspect of the decision adverse to Heder) turned out not to matter given the court's next rulings: that, under Wisconsin law, an employer must reduce any reimbursement obligation as time passes, so that someone such as Heder, who quit 5/6 of the way into the reimbursement period, cannot be required to repay more than 1/6 of the training expense. Because the collective bargaining agreement did not reduce the obligation as time passed, the judge deemed the repayment obligation completely invalid and directed the City to pay Heder his full wages for the last two pay periods, plus whatever extra is required to raise his compensation for "donated" time to the statutory overtime rate. 149 F. Supp. 2d 677 (E.D.Wis.2001). On appeal Heder seeks to defend his judgment by renewing his argument that the agreement is impermissibly retroactive, but we agree with the district court's rejection of this submission and thus turn to the City's contentions.

Although Two Rivers argued in the district court that it was entitled to reimbursement for all of the wages paid at the overtime and "donated" time rates, it now concedes that Heder is entitled to keep any compensation that the FLSA specifies as a statutory floor below which no contract may go. That means, in particular, that Heder was entitled to at least the statutory minimum wage for his final two pay periods (leaving the City to collect any residue as an ordinary creditor), see 29 U.S.C. § 206(a)(1), and that Heder is entitled to time and a half for any overtime hours for which the FLSA requires that premium. But the parties do not agree on what this means in practice, because the firefighters do not work an ordinary 40-hour week. Instead the City has prescribed a longer base period over which time is calculated—216 hours on the job over a span of 27 days. This is a lawful arrangement for firefighters' work. See 29 U.S.C. § 207(a), (k); 29 C.F.R. § 553.230. The collective bargaining agreement specifies that the first 204 hours are paid at the regular rate and any excess is overtime. The statutory minimum rate for overtime hours depends on whether the firefighters work a "fluctuating workweek." If they do, then their standard compensation covers any number of hours, so that the only statutorily required payment is the 50% premium for overtime. See 29 C.F.R. § 778.114. That's where the $5.58 figure came from: it was half of Heder's regular hourly rate at the time.

Under the FLSA an employee who works a "fluctuating workweek" may be paid 50% of the regular wage for overtime on the theory that the base wage covers any number of hours at straight time. But a person working a "variable workweek"— which is to say, a schedule that may call for more or less time at work—must be paid at least 150% for overtime hours. Two Rivers insists that its firefighters work a "fluctuating workweek" because the 216 hours over a 27-day period are distributed unevenly under what the parties call the California Plan. Each firefighter works three 24-hour shifts during a nine-day window. Three nine-day cycles form the 27-day pay block. The number of hours at work in any given week fluctuates widely. Like the district court, however, we think that Two Rivers has applied a lay understanding of "fluctuating workweek" to what is under the FLSA and its regulations a term with a technical meaning.

The paradigm of an employee working a "fluctuating workweek" is one who receives a fixed salary no matter how many hours the work requires that week. Consider an employee paid $400 per week for however many hours worked. That employee may work 30 hours one week and 50 hours the next. The salary is not diminished even if the number of hours falls below 40, nor is the employee expected to make them up in the future. The possibility of a higher hourly rate in one week justifies a reduction in overtime compensation if, in future weeks, hours rise above 40. Numerically it works like this. In the 30-hour week, the $400 salary produces a straight-time compensation of $13.33 per hour ($400/30), all of which the employee keeps. In the 50-hour week, the straight-time rate is $8 per hour ($400/50); 10 of these 50 hours are overtime, but because the base rate includes $8 for each of these hours, the incremental pay for overtime is only $4 per hour more, and the total wages for the week are $440. This includes time and a half for the 10 overtime hours, giving the employer credit for the $8 base rate spread over 50 hours. See 29 C.F.R. § 778.114(b).

Two Rivers does not fit the model, because its firefighters never work fewer than 216 hours in a 27-day period. There is no shortfall of time (and correspondingly higher hourly rate) in one pay period that might make up for longer work in another. Every hour is accountable. A firefighter who does not put in 216 hours in a 27-day period is docked unless he has sick or vacation hours to use. In any event, Two Rivers could not use the "fluctuating workweek" option even if it fit that model, for only a "clear mutual understanding" that the base rate constitutes straight time for any overtime worked enables the employer to calculate pay under the fluctuating workweek plan. See 29 C.F.R. § 778.114(a). The collective bargaining agreement does not express a "clear mutual understanding"; to the contrary, it calls for overtime pay at time and a half, or more, for hours in excess of 204 per 27-day period. Every extra hour is calculated and paid for. That is incompatible with treating the base wage as covering any number of hours at straight time. See Condo v. Sysco Corp., 1 F.3d 599 (7th Cir.1993) (an agreement fixing overtime at 50% of straight time displays the required "clear mutual understanding"). So the FLSA required the City to pay—and entitles Heder to retain, despite the union's agreement —time and a half for all hours over 204 per 27-day period, even if some of those hours were devoted to paramedic training. As the district judge held, Heder has a good FLSA claim for extra compensation (the City does not contend that his suit is untimely). Next we must decide whether the City has a good claim for reimbursement of at least some outlays.

Heder depicts a repayment obligation as a covenant not to compete that is invalid under Wis. Stat. § 103.465. The district judge adopted this characterization; we do not, because in Wisconsin (as in other states) a covenant not to compete must be linked to competition. An agreement to repay Two Rivers if a firefighter goes to work for a rival fire department would be treated as a covenant not to compete. See Union Central Life Insurance Co. v. Balistrieri, 19 Wis. 2d 265, 120 N.W.2d 126 (1963). But the agreement between Two Rivers and the firefighters' union does not restrict Heder's ability to compete against the City after leaving its employ. The obligation is unconditional: a firefighter departing before three years have expired must repay training costs even if he goes back to school, changes occupation, or retires. Competition has nothing to do with the matter.

According to Heder, Wisconsin would act as if this were a covenant not to compete, on the ground that repayment induces "involuntary servitude" that is more onerous than the agreements explicitly regulated under § 103.465. Yet this is not what the Supreme Court of Wisconsin said in Balistrieri: there it limited application of § 103.465 to agreements that condition repayment on going to work for the exemployer's rival. True enough, as the district judge emphasized, Two Rivers' repayment obligation shares with genuine restrictive covenants the feature that it makes changing jobs costly. But that is not enough to throw a contract out the window. Employers offer their workers many incentives to stay, so that they can reap the benefit of training and other productivity enhancers that depend on employees' tenure with the firm. Pay that increases with longevity is one common device; an employee who leaves must start elsewhere at the bottom rung. Firm-specific training (the value of which is lost if the employee changes jobs) likewise penalizes departures. See Daniel Parent, Wages and Mobility: The Impact of Employer-Provided Training, 17 J. Labor Econ. 298 (1999). Seniority systems that link duration of service to better assignments, protection against layoffs, and so on, have a similar effect; to quit is to give up accumulated seniority. Private employers give employees profit-sharing plans and stock options that vest later (if the person remains employed) and bonuses that accrue after extra years have been served. Defined-benefit pension systems usually are back-loaded, so that the last years of work before retirement add more to the monthly pension benefit than do earlier years. See Jones v. UOP, 16 F.3d 141 (7th Cir.1994). The common formula that starts with multiplying the final salary by the number of years served produces this effect automatically because salaries tend to rise with inflation and years of service. Yet no one believes that this powerful financial incentive to stick with one's employer until retirement is unlawful, even though it is much larger than the amount Heder must repay Two Rivers for paramedic training. The parties do not cite, and we could not find, any Wisconsin decision that characterizes the kind of incentives mentioned above as restrictive covenants regulated by Wis. Stat. § 103.465. Instead, Wisconsin applies Wis. Stat. § 103.465 only to the extent that a consequence is linked on working for a competitor. See Zimmermann v. Brennan, 78 Wis. 2d 510, 254 N.W.2d 719 (1977); Holsen v. Marshall & Ilsley Bank, 52 Wis. 2d 281, 190 N.W.2d 189 (1971).

Nor can we see any reason why Wisconsin would want to extend its precedents to block reimbursement agreements such as the one Two Rivers made with its union. Employees received considerable benefits as a result: paramedic training that will be useful for years to come, a 3% increase in compensation starting in 1998 (rising to 3.5% in 1999) for those who are certified paramedics, and extra compensation (at overtime rates) for the training time. Residents of Two Rivers received the benefit of a fire department more likely to save lives. Cities fearing that employees would take their new skills elsewhere would be less likely to provide these benefits. Or they might use other ways to acquire a workforce with better skills. They could, for example, require the employees to undergo and underwrite their own training, with none of the time compensated. This is what law firms do when they limit hiring to persons who already have law degrees, what school systems do when hiring only teachers who hold state certificates. The employer must pay indirectly, through a higher salary, but no court would dream of calling this system (under which employees finance their own training) "involuntary servitude." If an employer may require employees to pay up front, why can't the employer bear the expense but require reimbursement if an early departure deprives the employer of the benefit of its bargain? A middle ground also would be feasible (and lawful): The employer could require the worker to pay for his own training but lend the worker the money and forgive repayment if he sticks around. See Milwaukee Area Joint Apprenticeship Training Committee v. Howell, 67 F.3d 1333 (7th Cir.1995). A worker who left before the loan had been forgiven would have to come up with the funds from his own sources, just as Heder must do. If that system is lawful, as it is, then the economically equivalent system that Two Rivers adopted must be lawful. The cost of training equates to the loan, repayment of which is forgiven after three years.

The district judge objected to the cliff in the repayment system: instead of a slow reduction (equivalent to amortization of a loan), the collective bargaining agreement calls for full repayment before three years and none after. The judge inferred from this that the useful life of paramedic training is three years; as Heder quit with only 1/6 of this time remaining his union could not legally bind him to repay more than 1/6 of these expenses. The inference is unsound: One could as easily infer from the fact that the 3% wage boost is perpetual that paramedic training lasts indefinitely. We know from the record that Heder spent 582 hours undergoing the initial round of training and eight hours to re-certify two years later. This implies that paramedic skills have a useful life that can be extended indefinitely with small recurring investment—and it also implies that the three-year period is generous to workers. Two Rivers could have made the period much longer (say, 10 years). Then even if the debt had been amortized, as the district judge preferred, many workers (all who stayed longer than 3 years but quit or retired before 10) would have been worse off. The actual structure cannot be set aside as onerous—even if Wisconsin had a rule, which it does not, that no onerous term in a collective bargaining agreement is enforceable. The day Heder quit, his paramedic skills were effectively as valuable as the day he received his certification. We do not think that the Supreme Court of Wisconsin is apt to require employers and employees to amortize training costs with precision, to factor in the time value of money (the agreement does not require Heder to pay interest, though it might have done so), or to craft an individual schedule based on the number of years each employee is expected to remain able to work. The collective bargaining agreement is valid under state law, so Heder must repay the full cost of his books and tuition, which came to about $1,400.

What else, if anything, must be repaid? The agreement seems to call for repayment of the overtime compensation, but as we have already observed this violates the FLSA to the extent that it would leave Heder with less than time and a half for all overtime hours. See 29 U.S.C. § 207(a)(1), (k); Martino v. Michigan Window Cleaning Co., 327 U.S. 173, 177-78, 66 S. Ct. 379, 90 L. Ed. 603 (1946); Brooklyn Savings Bank v. O'Neil, 324 U.S. 697, 707, 65 S. Ct. 895, 89 L. Ed. 1296 (1945). The third of the training time that the City and union originally agreed to treat as overtime was paid at $23.09 per hour, more than double Heder's regular hourly rate of $11.16 per hour. The remaining third was paid at $5.58 per hour. Thus for an average overtime hour Heder's compensation was $14.34, about 128% of his regular rate rather than the required 150%. (Note that we have combined hours compensated at more than 150% with hours compensated at less. This is the right method because the accounting unit is the whole week or other pay period, rather than the hour. See 29 U.S.C. § 207(h)(2).) But the district judge expressed some doubt about Heder's regular hourly rate, and we think it best to remand so that any necessary findings may be made and calculations done. (To the extent that the judge assumed that Heder's regular rate must have been 2/3 of the contractual overtime rate, it failed to give effect to 29 U.S.C. § 207(e)(5). But perhaps something else sparked the judge's doubt.) It also is necessary to take into consideration the 3% and 3.5% additions, which the district court held are part of a firefighter's "regular rate." Two Rivers does not contest this conclusion on appeal, so we need not decide whether it is correct. Last, Heder is entitled to the minimum wage for his final two pay periods, see 29 U.S.C. § 206(a)(1); Calderon v. Witvoet, 999 F.2d 1101, 1107 (7th Cir. 1993), and to credit against the reimbursement obligation for the difference between that minimum wage and the total withholding ($2,281.21) that the City effected. We can't tell in whose favor the net judgment runs, but calculation should be a mechanical task in light of our rulings.

One final matter. The district judge suggested that by withholding any amount from the final two pay periods Two Rivers violated Wis. Stat. § 109.03(2), which requires all departing employees to be paid in full. This statute does not prevent employees from striking agreements that reduce what "in full" means, and as we have held that the collective bargaining agreement's repayment proviso is valid there is no problem under § 109.03(2).

By the way, the City's protest that some of the district judge's original calculations and legal theories did not correspond directly to the parties' arguments is not a ground of any additional relief. The City has made to us whatever arguments are available to it, and as appellate review of a decision on summary judgment is plenary it does not matter whether the district judge's decision was based on independent research. See Scaife v. Racine County, 238 F.3d 906 (7th Cir.2001). All of the City's arguments now have been taken into account.

The judgment is vacated, and the case is remanded for further proceedings consistent with this opinion.