PER CURIAM:
The fluctuating workweek ("FWW") method is one way of calculating overtime compensation that satisfies the requirements of the Fair Labor Standards Act ("FLSA"). See 29 C.F.R. § 778.114(a). Saybolt LP, a petroleum products company, used the FWW method to calculate overtime *921compensation for some of its oil and gas inspectors who worked radically varying hours each week. These inspectors also received incentive payments for working less desirable hours during the workweek. A group of these inspectors ("the plaintiffs"), sued Saybolt, alleging that the incentive payments precluded use of the FWW method and placed their employer in violation of the FLSA. The plaintiffs claimed that Saybolt's violation was willful.
The district court held that Saybolt's payment scheme violated the FLSA, but the violation was not willful. The district court adopted the plaintiffs' model for calculating damages after concluding that Saybolt was judicially estopped from challenging this model. The district court also awarded liquidated damages. We affirm the district court's conclusions as to liability and willfulness, reverse the district court's ruling on estoppel and its calculation of damages, vacate the district court's order on liquidated damages, and remand for reconsideration of the liquidated damages award and for reconsideration of its calculation of damages in accordance with this opinion and entry of an appropriate judgment.
BACKGROUND
I. Saybolt's Payment Scheme and the FWW Method
The FLSA requires that nonexempt employees receive an overtime premium of not less than one and one-half times their "regular rate of pay" for each hour worked over 40 hours in a given workweek. 29 U.S.C. § 207(a). Until February 2012, Saybolt used two different methods to pay overtime. Saybolt paid one group of inspectors ("the non-FWW inspectors") using the FLSA's standard time and one-half method. These inspectors earned one and one-half times their "regular rate" for every hour worked over 40. The "regular rate" for salaried employees is simply the salary divided by the number of hours the salary is intended to compensate. 29 C.F.R. § 778.113(a). A non-FWW inspector earning $600 for an intended 40-hour workweek would thus have a "regular rate" of $15.00 per hour (the $600 base salary divided by 40 hours). The non-FWW inspector's "overtime rate" would be one and one-half times the "regular rate"-here, $22.50 per hour (one and one-half times the $15.00 "regular rate"). Thus, in a workweek in which the non-FWW inspector worked 60 hours (instead of the intended 40 hours), the non-FWW inspector would receive the $600 base salary plus a $450 overtime premium (20 overtime hours times the $22.50 "overtime rate") for a total weekly compensation of $1050.
A second group of Saybolt inspectors ("the FWW inspectors") received overtime compensation under the FWW method. Federal regulations state that this method is appropriate when an employee works hours that fluctuate from week to week and the employee agrees that a fixed weekly salary will constitute straight-time pay (i.e., non-overtime pay) for all the hours worked in a week, however many or few. See id. § 778.114(a). Accordingly, FWW inspectors received the same weekly base salary, regardless whether they worked 60 hours or only 20.
Calculation of overtime premiums under the FWW method is different from the standard FLSA method in several respects. First, the "regular rate" under the FWW method is determined by dividing the weekly base salary by the total number of hours an employee actually works during the week. This is an application of the principle that the "regular rate" equals the weekly salary divided by "the number of hours which the salary is intended to compensate." See id . § 778.113(a). In the FWW context, "the salary is intended to *922compensate" all hours an employee actually works. Because the hours actually worked each week fluctuate, the "regular rate" under the FWW method will fluctuate from week to week as well. See id. § 778.114(a). As the hours worked increase, the "regular rate" will decrease. Therefore, assuming a $600 weekly base salary and 40 hours actually worked during the week, the FWW method would yield a "regular rate" of $15.00 per hour (the $600 base salary divided by 40 hours). But a 60-hour workweek would yield a "regular rate" of $10.00 per hour (the $600 base salary divided by 60 hours).1
Another key difference under the FWW method is that the "overtime rate" is one-half, instead of one and one-half, times the "regular rate." See id. The reason for this is, again, that the fixed weekly salary is meant to compensate all hours worked, including overtime hours. Before receiving an overtime premium, an employee has already agreed to be compensated according to the "regular rate" for every overtime hour worked. See id. The employee need receive only an additional one-half times the "regular rate" to satisfy the FLSA's one and one-half times requirement. See id. In a 60-hour workweek, then, an employee would receive an "overtime rate" of $5.00 per hour (one half times the $10 "regular rate"). The total overtime premium would be $100 (20 overtime hours times the $5.00 "overtime rate").
Under Saybolt's payment scheme, FWW inspectors were purportedly paid overtime under the FWW method. But the company also paid incentive payments for working on a scheduled day off ("day-off pay"), working at sea ("offshore pay"), and working on a scheduled holiday ("holiday pay"). Non-FWW inspectors were ineligible for these incentives. When calculating the "regular rate," Saybolt added weekly incentive payments to the weekly base salary. Therefore, if a FWW inspector had a weekly base salary of $600, earned $150 in incentive payments, and worked a 60-hour workweek, the "regular rate" for that week would be $12.50 per hour ($600 base salary plus incentive payments of $150 for a total of $750 divided by the 60 hours worked). The "overtime rate" would be $6.25 per hour (one half times the $12.50 "regular rate"), resulting in an overtime premium of $125 (20 overtime hours times the $6.25 "overtime rate"). The FWW inspector's total compensation for the 60-hour week would be $875 ($600 base salary plus $150 incentive pay plus $125 overtime premium).2
II. Saybolt's Legal Advice
Saybolt communicated with outside counsel to assess whether the FWW method allowed for additional incentive payments. In May 2009, Saybolt contacted attorney Robert Ivey. Ivey counseled Saybolt that combining incentive payments with the FWW method was a "potential issue." Ivey explained that several district courts and the First Circuit had concluded that paying hours-based premiums in addition to a weekly salary precluded the use of the FWW method. But Ivey also explained that the Fifth Circuit had not addressed the question and that the Department *923of Labor ("DOL") had issued proposed regulations in 2008 that would allow the payment of incentives under the FWW method.
Saybolt contacted Joseph Maddaloni, another outside attorney, in January 2010. Saybolt forwarded Ivey's recommendation to Maddaloni and said that it was "seeking a final opinion and recommendation in order to bring closure to this pay practice." Maddaloni said he disagreed with the court decisions rejecting the use of incentive payments under the FWW method. But Maddaloni conceded that the judges involved were well respected and that a New Jersey district court would likely find their reasoning persuasive. Maddaloni concluded that "while I have always taken the position that Saybolt's use and application of the FWW was defensible, I am concerned that under the present state of the law and the facts that may no longer hold true." Maddaloni later testified that he had considered the law on this issue to be unsettled.
III. Proceedings in the District Court
In January 2010, Joseph Dacar, on behalf of Saybolt inspectors paid under the FWW method, filed a collective action complaint in the Eastern District of North Carolina. A year later, the case was transferred to the Southern District of Texas, and the plaintiffs filed an amended complaint, alleging that (1) Saybolt did not comply with the requirements for using the FWW method and (2) Saybolt willfully violated the FLSA. The complaint also substituted Lyle Deroche and Felton Ravia as named plaintiffs in place of Dacar. The district court conditionally certified a collective action in June 2011, and a total of 112 employees and former employees opted into the case.
In January 2013, the parties filed cross-motions for summary judgment. Saybolt moved for partial summary judgment on the issue of willfulness; the plaintiffs moved for summary judgment on willfulness, liability, damage calculation, and liquidated damages. In August 2014, the district court granted Saybolt's motion and held that Saybolt's violation, if any, was not willful. The plaintiffs moved for reconsideration.
In December 2015, the district court denied the plaintiffs' motion for reconsideration but granted, in part, their motion for summary judgment. The district court held that Saybolt had violated the FWW method because the plaintiffs were not paid a "fixed salary," that liquidated damages were appropriate, and that damages should not be offset by the incentive payments the plaintiffs already received.
In December 2016, the district court held a hearing on damages. The district court asked the parties to brief any remaining issues related to the damages calculation. Saybolt's brief contended that the "regular rate" for calculating overtime damages should be based on the plaintiffs' hours actually worked-not on a 40-hour workweek-and that overtime hours should be multiplied by one half-not one and one-half-times that "regular rate." The district court held that Saybolt was judicially estopped from contesting the appropriate damages model and ordered damages of $3,020,813.21 plus an equal amount in liquidated damages.
The plaintiffs timely appealed the district court's partial grant of summary judgment on Saybolt's willfulness. Saybolt cross-appealed the district court's summary judgment on liability and damages.
STANDARDS OF REVIEW
A district court's grant or denial of summary judgment is reviewed de novo, applying the same standards as the district *924court. Castellanos-Contreras v. Decatur Hotels, LLC , 622 F.3d 393, 397 (5th Cir. 2010) (en banc). The court views all evidence in the light most favorable to the non-moving party. Matsushita Elec. Indus. Co. v. Zenith Radio Corp. , 475 U.S. 574, 587, 106 S.Ct. 1348, 1356, 89 L.Ed.2d 538 (1986). Summary judgment is appropriate only where there is no genuine issue of material fact and the moving party is entitled to judgment as a matter of law. Bolton v. City of Dallas , 472 F.3d 261, 263 (5th Cir. 2006).
A district court's determination of judicial estoppel is reviewed for abuse of discretion. See Love v. Tyson Foods, Inc. , 677 F.3d 258, 262 (5th Cir. 2012). A court's imposition of liquidated damages is likewise reviewed for abuse of discretion. See Singer v. City of Waco , 324 F.3d 813, 823 (5th Cir. 2003). The correct methodology for calculating the amount of overtime pay due is a question of law, which is reviewed de novo. Black v. SettlePou, P.C. , 732 F.3d 492, 496 (5th Cir. 2013).
DISCUSSION
I. Liability
As explained above, the FLSA generally requires that employees be paid an overtime premium of one and one-half times the "regular rate of pay" for all hours worked in excess of the 40-hour workweek. 29 U.S.C. § 207(a)(1). Although an employer may satisfy this requirement by using the FWW method, courts require four prerequisites for its use:
(1) the employee's hours must fluctuate from week to week;
(2) the employee must receive a fixed salary that does not vary with the number of hours worked during the week (excluding overtime premiums);
(3) the fixed amount must provide compensation every week at a regular rate at least equal to the minimum wage; and
(4) the employer and employee must share a clear mutual understanding that the employer will pay the fixed salary regardless of the number of hours worked.
Brantley v. Inspectorate Am. Corp. , 821 F.Supp.2d 879, 888 (S.D. Tex. 2011) (citing 29 C.F.R. § 778.114(a), (c) ; O'Brien v. Town of Agawam , 350 F.3d 279, 288 (1st Cir. 2003) ). The plaintiffs have the burden of proving noncompliance. See Samson v. Apollo Resources, Inc., 242 F.3d 629, 636 (5th Cir. 2001). The district court held that Saybolt did not meet the second requirement-that is, Saybolt failed to pay a "fixed salary" because it paid additional incentives for day-off, offshore, and holiday hours worked each week.3 We agree with the district court that Saybolt's incentive payments disqualified it from using the FWW method.4
The case against Saybolt is simple: the FWW method requires a fixed weekly salary that does not vary by the number of hours worked, and Saybolt's incentive payments caused weekly variance in the FWW
*925inspectors' straight-time pay.5 Saybolt argues that nothing in the federal regulations detailing the FWW method's requirements, see 29 C.F.R. § 778.114, expressly prohibits an employer from paying additional sums on top of a fixed salary-especially when those payments are included in the "regular rate" and thus increased the overtime premium.
In O'Brien v. Town of Agawam , the First Circuit squarely addressed this issue and found that payment of "additional compensation" for nighttime shifts in addition to a fixed weekly base salary failed to comply with the FWW method. 350 F.3d at 288-90.6 Regarding the FWW regulations, the O'Brien court noted that "by the plain text of § 778.114, it is not enough that the officers receive a fixed minimum sum each week." See id. at 288 (emphasis in original). The regulations refer to a "fixed amount" and a "fixed salary," not a minimum or base salary. See 29 C.F.R. § 778.114(a). Because Saybolt's incentive payments depend on the types of hours FWW inspectors worked each week, their weekly straight-time compensation was not "fixed."
Indeed, despite the proposed regulations that Saybolt relied on, the DOL ultimately decided against the amendment in 2011 and issued a final rule stating that incentive payments are "incompatible with the fluctuating workweek method" and that it would not "be appropriate to expand the use of this method of computing overtime pay beyond the scope of the current regulation." See Updating Regulations Issued Under the Fair Labor Standards Act, 76 Fed. Reg. 18832, 18848-50 (April 5, 2011). The final rule noted that changing the regulations could cause "employers to pay a greatly reduced fixed salary and shift a large portion of employees' compensation into bonus and premium payments, potentially resulting in wide disparities in employees' weekly pay." See 76 Fed. Reg. at 18850. As noted, such disparities in weekly straight-time pay are incompatible with the "fixed salary" requirement.
Saybolt relies on two decisions to support its payment scheme. Both cases are readily distinguishable. First, Saybolt notes that in Aiken v. County of Hampton , a district court affirmed the compatibility of the FWW method with additional "holiday pay" bonuses. 977 F.Supp. 390, 397 (D.S.C. 1997), aff'd , 172 F.3d 43 (4th Cir. 1998). But the "holiday pay" in Aiken was a "fringe benefit" paid whether or not an employee actually worked the "holiday hours." 977 F.Supp. at 397. Thus, though the Aiken employees' total compensation included the "holiday pay," their salaries did not increase or decrease because of the hours they worked.
Second, Saybolt contends that the First Circuit's recent decision in Lalli v. General Nutrition Centers, Inc. , undermines O'Brien by holding that the payment of *926additional commissions is compatible with the FWW method. 814 F.3d 1, 4-10 (1st Cir. 2016). In Lalli , however, the First Circuit reaffirmed O'Brien , and held that the "time-based bonuses" addressed in O'Brien are distinct from "performance-based bonuses" like commissions. See id. at 8. Time-based bonuses, unlike performance-based commissions, run afoul of the FWW regulations because they make weekly pay dependent on the type of hours worked. Saybolt's incentives are "time-based bonuses" because they depend on the kind and number of hours worked-i.e. day-off hours, off-shore hours, or holiday hours. Under Lalli , as under O'Brien , Saybolt's payment scheme is incompatible with the FWW requirements.
In sum, we hold that Saybolt failed to comply with the FWW method, and, therefore, its use of that method to calculate the FWW inspectors' overtime premiums was erroneous.
II. Willfulness
If a plaintiff can demonstrate that a defendant's violation of the FLSA was willful, then the limitations period is extended from two to three years. See 29 U.S.C. § 255(a). A willful violation occurs when the "employer either knew or showed reckless disregard for the matter of whether its conduct was prohibited." McLaughlin v. Richland Shoe Co. , 486 U.S. 128, 133, 108 S.Ct. 1677, 1681, 100 L.Ed.2d 115 (1988). Plaintiffs bear the burden of establishing a defendant's willfulness. Ikossi-Anastasiou v. Bd. of Supervisors of La. State Univ. , 579 F.3d 546, 552 (5th Cir. 2009). The district court held that there was no evidence that Saybolt violated the FLSA intentionally or recklessly. Viewing the facts in the light most favorable to the plaintiffs, we agree.
Evidence that a defendant was merely negligent regarding FLSA requirements is insufficient to show willfulness. See Steele v. Leasing Enters.,Ltd. , 826 F.3d 237, 248 (5th Cir. 2016). Here, it is not even clear that Saybolt's conduct was negligent: (1) Saybolt twice sought the advice of legal counsel to ensure compliance with the FLSA; (2) Saybolt knew from these communications that the relevant legal issue was unsettled and had not been addressed in the Fifth Circuit; and (3) Saybolt knew that the DOL had issued proposed regulations that would vindicate its application of the FWW method. Ultimately, of course, Saybolt's view of the law, though not irrational, was rejected. After the plaintiffs filed this lawsuit in January 2011, more district courts held that incentive payments were incompatible with the FWW regulations. See, e.g. , Brumley v. Camin Cargo Control, Inc. , No. 08-1798 (JLL), 2010 WL 1644066 (D.N.J. April 22, 2010). Then, in 2011, the DOL's final rule affirmed this position and a district court in this circuit held accordingly. See Brantley, 821 F.Supp.2d at 889-90. At this point, Saybolt transitioned away from paying inspectors under the challenged method. Even subject to hindsight bias, these facts do not suggest an intentional or reckless violation.
The plaintiffs contend that the legal opinions of Ivey and Maddaloni cast doubt on the continuing viability of Saybolt's payment procedure. But both attorneys also communicated that the legal landscape was unsettled even if courts within the First Circuit would likely rule against Saybolt's payment method. The plaintiffs also cite the existence of a 2009 lawsuit in New York regarding the legality of Saybolt's pay practices. See Lauer v. Saybolt LP , No. 09-CV-3442, 2010 WL 1992008 (E.D.N.Y. May 17, 2010). This lawsuit settled without a final ruling on the merits to resolve the legality of the payment scheme.
*927In sum, the plaintiffs offer no evidence from which a court could infer that Saybolt willfully violated the FLSA. This conclusion does not mean that an absence of controlling authority or reliance on advice of counsel or the existence of proposed regulations necessarily preclude a willfulness determination. But in this case, all three countervailing considerations are present, and the plaintiffs have not created an issue of disputed fact regarding Saybolt's willfulness.
III. Judicial Estoppel
The district court held that Saybolt was judicially estopped from challenging the methodology used to calculate overtime damages. The doctrine of judicial estoppel is appropriate when (1) a party has asserted a position that is plainly inconsistent with a previously asserted position, (2) the earlier position was accepted by the court, and (3) the party did not act inadvertently. Reed v. City of Arlington , 650 F.3d 571, 574 (5th Cir. 2011) (en banc). Under this standard, the district court was mistaken about the nature of Saybolt's arguments and erred in applying judicial estoppel.
Before the district court entered summary judgment, Saybolt suggested that damages, if any, should be based on what the plaintiffs would have earned under a non-FWW payment scheme. Saybolt's own non-FWW inspectors would serve as comparators. Because non-FWW inspectors were not eligible for incentive payments, Saybolt argued that any incentives the plaintiffs earned should offset the damages or, at least, should not be included in the "regular rate" used to calculate damages.
At summary judgment, the district court rejected the non-FWW comparator model by holding that incentive payments must be included in the "regular rate" calculation and could not offset damages. The court did not otherwise determine how damages would be calculated. Almost a year later, the district court held its hearing on damages and asked for final briefing on the issue. Saybolt's brief argued that the FWW method should be used to calculate damages. That is, the "regular rate" should be calculated by dividing total compensation (base salary plus incentives) by all the hours actually worked by the plaintiffs and that the "overtime rate" for calculating damages should be one-half times the "regular rate." The district court held that Saybolt was judicially estopped from making these arguments because Saybolt had previously argued that the "regular rate" for damage calculation could be based on a 40-hour workweek and that the plaintiffs could receive an "overtime rate" of one and one-half times that "regular rate." We disagree.
Saybolt's initial position-that damages should be calculated using non-FWW inspectors as comparators-was not plainly inconsistent with its subsequent argument that damages should be calculated under the FWW method. Cf. Hall v. GE Plastic Pac. PTE Ltd. , 327 F.3d 391, 398 (5th Cir. 2003) (party estopped from arguing defective product manufactured by company A because it initially argued that company B manufactured the product); Love , 677 F.3d at 262-63 (debtor estopped from pursuing damages claim because he had told bankruptcy court he possessed no potential claims). In arguing for the comparator model, Saybolt never conceded that the FWW plaintiffs were paid based on a 40-hour workweek or were owed overtime at one and one-half times the "regular rate." There was thus no inconsistency.
Nor did the district court accept Saybolt's initial position as is required for judicial estoppel. Indeed, the court rejected the comparator model by requiring that incentive payments be included in the *928"regular rate" calculation. This is why Saybolt fell back on the alternative argument that, since incentive payments must be included, the FWW method should be used to calculate the plaintiffs' damages. Accordingly, the district court erred in holding that Saybolt was judicially estopped from challenging the plaintiffs' damages model.7
IV. Damages
An employer who violates the FLSA's overtime requirements is "liable to the employee or employees affected in the amount of ... their unpaid overtime compensation." 29 U.S.C. § 216. The district court adopted the plaintiffs' damages model, under which the "regular rate" for calculating overtime is based on a 40-hour workweek and the "overtime rate" equals one and one-half times the "regular rate." The plaintiffs' model leaves them with significantly more overtime compensation than they originally earned under Saybolt's application of the FWW method. This is because their model employs a hypothetical 40-hour divisor, which augments the "regular rate."8
Because judicial estoppel does not prevent Saybolt from challenging the plaintiffs' model, we may consider the alternative models that Saybolt has proposed. To begin with, we note that this is a difficult case in which to estimate the plaintiffs' "unpaid overtime compensation." It is not a misclassification case in which the plaintiffs were never paid overtime at all. See, e.g., Hills v. Entergy Operations, Inc. , 866 F.3d 610, 613 (5th Cir. 2017). The plaintiffs have already received an overtime premium under the FWW method. Nor is this a case in which incentive payments were erroneously omitted from the "regular rate" calculation, thereby diminishing overtime premiums. See O'Brien , 350 F.3d at 295. Saybolt added the incentive payments to the base salary, thereby increasing the "regular rate," the "overtime rate," and the resulting overtime premiums.
Saybolt proposes that the Court assess damages by looking to its non-FWW comparator inspectors. However, Saybolt has not thoroughly argued this method of damages on appeal or explained how the non-FWW comparators provide a sufficient empirical basis to make the damages model feasible.9
Saybolt's fallback damages methodology contains two separable elements: (1) the "regular rate" should be calculated using a denominator of all hours actually worked and not a hypothetical 40-hour denominator and (2) the plaintiffs should receive only one-half times this "regular rate" instead *929of the one and one-half times awarded by the district court.
DOL regulations and relevant case law establish that the "regular rate" should be calculated based on the number of hours the plaintiffs' salary was intended to compensate. There is no 40-hour "default" for calculating the "regular rate," as the plaintiffs suggest. To the contrary, DOL regulations state that the "regular rate" is "determined by dividing [an employee's] total remuneration for employment ... in any workweek by the total number of hours actually worked by him in that workweek for which such compensation was paid ." 29 C.F.R. § 778.109 (emphasis added). Likewise, the regulation pertaining to salaried employees specifies that the "regular rate" should be computed by "dividing the salary by the number of hours which the salary is intended to compensate." Id . § 778.113. These regulations reflect the Supreme Court's holding in Overnight Motor Transportation Company v. Missel that "[w]age divided by hours equals regular rate," and the "regular rate" formula is no different when a salary is intended to compensate hours that fluctuate from week to week. 316 U.S. 572, 580 n.16, 62 S.Ct. 1216, 1221 n.16, 86 L.Ed. 1682 (1942). These authorities establish that it would be improper to calculate the "regular rate" using a 40-hour divisor unless the plaintiffs' salary was intended to compensate 40 hours each week.
Here, the record is unequivocal that the plaintiffs' hours varied from week to week and that they received the same base salary (plus incentives) regardless whether they worked 25 or 65 hours. Under these circumstances, it does not matter that the FWW regulations are inapplicable. For instance, in Singer , the firefighter plaintiffs worked 120 hours in one 14-day pay period and 96 hours in the next. 324 F.3d at 824. As in this case, the plaintiffs argued that the divisor for calculating the "regular rate" should include only non-overtime hours. See id. This court acknowledged that the FWW method was inapplicable, but nevertheless held that the "regular rate" for calculating overtime damages should "include[ ] both non-overtime and overtime hours in the divisor." Id. at 824-25 & n.4. Following Singer , a number of district courts in this circuit have affirmed that the "regular rate" divisor should include all hours actually worked even when the FWW method has been violated. See, e.g , Brantley , 821 F.Supp.2d at 894 ("[T]he fact that Plaintiffs' hours frequently did not correspond to a 40 hour work week, weigh[s] against calculating Plaintiffs' regular hourly rate based on a 40 hour work week.").
The plaintiffs cite several cases to support the district court's use of a hypothetical 40-hour divisor, but these are distinguishable or unpersuasive. See Yourman v. Dinkins , 865 F.Supp. 154 (S.D.N.Y. 1994), aff'd , 84 F.3d 655 (2d Cir. 1996), vacated on other grounds , 519 U.S. 1145, 117 S.Ct. 1078, 137 L.Ed.2d 213 (1997) ; Ayers v. SGS Control Services, Inc. , No. 03 Civ. 9077 RMB, 2007 WL 646326 (S.D.N.Y. Feb. 27, 2007) ; Brumley , 2010 WL 1644066. In Yourman , the district court relied on a 35-hour divisor for some plaintiffs and a 40-hour divisor for others because "those were ... the hours reflected on plaintiffs' paystubs." 865 F.Supp. at 165. Here, of course, the plaintiffs' paystubs reflect hours that fluctuate significantly, so the reliance on a fixed number of weekly hours would be inappropriate. In Ayers and Brumley , the district courts simply did not analyze the "regular rate" divisor as a separate issue. Ayers , 2007 WL 646326, at *3 ; Brumley , 2010 WL 1644066, at *7. As explained above, it is incorrect to assume that a violation of the FWW regulations requires the court to *930resort to a hypothetical 40-hour divisor. Under Missel , Singer , and the plain language of the relevant regulations, the district court erred in failing to include all hours intended to be compensated in the "regular rate" divisor.
We agree with the district court's conclusion that plaintiffs are entitled to an award of one and one-half times the "regular rate" instead of using the one-half multiplier that Saybolt claims is appropriate. Use of the one-half multiplier depends on whether the employer establishes that the FWW method of compensation is appropriate under the regulation. See 29 C.F.R. § 778.114(a). The DOL's April 2011 final rule makes it clear that the payment of bonuses and premium payments are "incompatible with the FWW method of computing overtime." Updating Regulations, 76 Fed. Reg. at 18848-18850. And the applicable regulation plainly provides that if an employer does not meet the conditions necessary to employ the FWW method, it may not reap the benefit afforded by it: namely, the deviation from the normal practice of using the one and one-half multiplier of the regular rate to calculate overtime. See 29 C.F.R. § 778.114(a) ; Flood v. New Hanover Cty. , 125 F.3d 249, 252 (4th Cir. 1997) ("The language of section 778.114 suggests that an employer must meet the following requirement[ ] before it can pay an employee pursuant to the fluctuating workweek method ... the employee must receive a fixed weekly salary that remains the same regardless of the number of hours that the employee works during the week....").
In Singer , we held that the FWW method did not apply because the employer failed to establish one of the four requirements for its application. Singer , 324 F.3d at 825 n.4. In concluding that the regular overtime rate of one and one-half times the regular rate of pay applied, we stated:
The fire fighters correctly observe that the fluctuating method would be inappropriate in this case. An employer can use this method only if the employer and employee have a "clear mutual understanding" that the method applies. 29 C.F.R. 778.114(a) ; Heder v. City of Two Rivers, Wisconsin , 295 F.3d 777, 780 ; Valerio v. Putnam Assoc. Inc. , 173 F.3d 35, 39 (1st Cir.1999). In this case, neither party has presented evidence of such a "clear mutual understanding."
However, the fire fighters are incorrect to say that the district court applied the fluctuating method in this case. The district court did not calculate the fire fighters' damages by multiplying their overtime hours by one-half of their regular rate of pay. Instead, the district court multiplied the fire fighters' overtime hours (i.e., the hours exceeding 106 in a 14-day work period) by one-and-one half of their regular rate of pay. The district court thus used the usual method of calculating overtime pay, not the less common fluctuating method. See 29 C.F.R. § 778.107 ("The general overtime pay standard ... requires that overtime must be compensated at a rate not less than one and one-half times the regular rate at which the employee is actually employed[.]").
Id.
Additionally, in O'Brien , the First Circuit rejected the district court's conclusion that the employer there had properly calculated police overtime in accordance with the FWW. 350 F.3d at 279. The Court reasoned that because the police officers did not receive a "fixed amount" for their labor each week, § 778.114 did not apply. Id. "For obvious reasons," the Court noted, "an employer may not simply elect to pay the lower overtime rate under § 778.114. The regulation requires that [the] four conditions [of the regulation] be *931satisfied before an employer may do so...."10 Id. at 288.
We find nothing in the facts of today's case to warrant a departure from the general rule that the one-half multiplier can be used only in connection with a qualified FWW payment method that meets each of the regulatory requirements. See 29 C.F.R. § 778.114(a). The difference between the majority's approach and the dissent's approach is that the majority enforces the requirement set forth in § 778.114(a) that the employer must pay the employee a "fixed salary." This requirement of a "fixed salary" has existed since § 778.114(a) was adopted in 1968. The final rule issued by the DOL in 2011 did not change the regulation. Instead, the rule concluded that a proposed regulation allowing inclusion of bona fide bonus payments and/or premium payments in the calculation of the regular rate was "incompatible with the fluctuating workweek method of computing overtime under section 778.114." 76 Fed. Reg. at 18850. Therefore, the dissent's contention that the majority is applying the rule retroactively and unfairly is unfounded. Simply put, because the preconditions for application of the FWW method were not satisfied, Saybolt is not entitled to use that method.
Because Saybolt failed to pay its workers a "fixed salary," we must also conclude that one and one-half is the applicable multiplier for calculating the proper amount of overtime pay owed. Accordingly, the district court did not err in using the one and one-half multiplier. Because we determine here that the appropriate denominator for calculating the regular rate includes all hours intended to be compensated, applying the one and one-half multiplier is not a windfall to the plaintiffs. It is merely the ordinary calculation of overtime mandated by the FLSA. See 29 U.S.C. § 207(a).
V. Liquidated Damages
The FLSA provides that liquidated damages be awarded for FLSA violations in an amount equal to the actual damages. 29 U.S.C. § 216(b). A district court may, "in its sound discretion," refuse to award liquidated damages if the employer demonstrates good faith and reasonable grounds for believing it was not in violation. 29 U.S.C. § 260. Whereas the burden is on the plaintiffs to show willfulness, Saybolt bears the "substantial burden" of proving the reasonableness of its conduct. See Ransom v. M. Patel Enters., Inc. , 734 F.3d 377, 387 n.16 (5th Cir. 2013) (citing Singer , 324 F.3d at 823 ). Here, the district court awarded liquidated damages after finding that Saybolt had not met this "substantial burden."
To prove the reasonableness of its conduct, Saybolt repeats the reasons that its conduct was not willful. Saybolt suggests that the district court's willfulness determination precludes the award of liquidated damages. This fails to account for the fact that the evidentiary burden has shifted. Indeed, this court has held that, "[e]ven if the district court determines that the employer's actions were taken in good faith and based on reasonable grounds, the district court still retains the discretion to award liquidated damages." Heidtman v. Cty. of El Paso , 171 F.3d 1038, 1042 (5th Cir. 1999) (citing Lee v. Coahoma Cty. , 937 F.2d 220, 227 (5th Cir. 1991) ). Accordingly, Saybolt has failed to show that the district court abused its discretion.
*932Nevertheless, because the district court erred in adopting the plaintiffs' damages methodology, we must vacate the liquidated damages award and remand for the district court to determine whether liquidated damages remain appropriate.
CONCLUSION
For the foregoing reasons, we: (1) affirm the judgment of the district court on liability and willfulness; (2) reverse the district court's ruling on estoppel and its calculation of damages; (3) vacate the district court's order on liquidated damages; (4) remand for reconsideration of the liquidated damages award; and (5) remand for calculation of damages11 in accordance with this opinion and the entry of an appropriate judgment.
EDITH H. JONES, Circuit Judge, concurring and dissenting:
Although I agree with the per curiam opinion's discussion of liability and willfulness in this FLSA case, and I agree with requiring the use of hours actually worked for purposes of damages, I would reverse the overtime rate calculation on different grounds from those stated by the majority. The majority's proposed formula effects an illegal windfall for the plaintiffs, contrary to the Supreme Court and this court. I would remand for the district court to calculate damages using the FWW weekly wage actually paid by Saybolt, adding one-half times the hourly rate for each hour a plaintiff worked in excess of 40 hours. The majority's formulation, which affords a one-and-a-half hourly multiplier for overtime, overcompensates the plaintiffs. The majority fail to recognize the plaintiffs have already been paid, under the FWW method, a higher rate for weeks in which they worked less than 40 hours.
The majority premises this result on DOL's April 2011 final rule and on this court's decision in Singer . Neither rationale holds water. Using the 2011 rule to impose damages on Saybolt before the final rule was promulgated is unfair. Worse, it confuses liability and damages. It is one thing to conclude that the case law did not support Saybolt's methodology before the 2011 rule came into force; it is another to retroactively apply the rule for the purpose of calculating damages.
Under the circumstances of this case, the majority's invocation of time-and-a-half for overtime contravenes the principle that the purpose of actual damages under the FLSA is to compensate employees for unpaid overtime-it is not to punish employers. Even a finding of willfulness does not impose exemplary damages on employers but merely lengthens the limitations period from two years to three. See 29 U.S.C. § 255(a). Courts also have discretion, moreover, to award liquidated damages which are "not penal in [their] nature but *933constitute[ ] compensation for the retention of a workman's pay which might result in damages too obscure and difficult of proof." Brooklyn Sav. Bank v. O'Neil , 324 U.S. 697, 707, 65 S.Ct. 895, 902, 89 L.Ed. 1296 (1945). This court and others have repeatedly emphasized that FLSA damages should reflect the plaintiffs' actual losses and must not represent a windfall. See Johnson v. Martin , 473 F.3d 220, 222 (5th Cir. 2006) ; see also Roman v. Maietta Const., Inc. , 147 F.3d 71, 77 (1st Cir. 1998) (explaining that FLSA plaintiffs are "entitled to be made whole, not to a windfall at the [defendant's] expense") (citations omitted). The best measure of damages will aim to approximate the difference between the overtime premiums that plaintiffs were actually paid and the overtime premiums that they should have been paid.1
When the FLSA's purpose in awarding actual damages is faithfully followed, it is apparent that the one-half multiplier for overtime hours sufficiently compensates the plaintiffs here. The one-half multiplier is more closely tied to Saybolt's attempt to invoke the FWW method. The FWW method's logic is that, where the employees agreed to receive a fixed salary for all hours worked in a pay period, and the actual hours worked varied below and above 40/week, then they have already received straight-time pay for their overtime and should receive only an additional one-half the "regular rate" for each overtime hour. See 29 C.F.R. § 778.114(a). The majority here do not take issue with the fact that these employees understood they were being compensated under the FWW regime for all hours they worked. See, e.g., Hanson v. Camin Cargo Control, 2015 WL 1737394, at *7-8 (S.D.Tx. Apr. 16, 2015). The record also shows that these employees, in receiving FWW-based compensation, were paid more than their straight-time counterparts because Saybolt added monetary incentives for less attractive duty situations. Finally, as explained at the outset, the majority's formula overcompensates the plaintiffs beyond their actual damages.
The majority erroneously rely on two cases in an attempt to support their damage formula. As regards the FWW method, however, the footnote in Singer v. City of Waco, 324 F.3d 813, 825 n.4 (2003), is pure dicta. The employer there did not attempt to justify its wages based on an FWW calculation; the dispute was between a 120-hour and 96-hour workweek for certain kinds of first responders. The firefighters seemed to be contending that the court's overtime damages calculation was erroneously based on the FWW method, but they were simply wrong. All Singer says in this connection is that "the usual method" of calculating overtime, i.e. , time-and-a-half, is appropriate. Id. The court does not say this method is mandatory in every case. Nor do FLSA regulations mandate this damage measure because to do so would contravene the Supreme Court's holding that overtime damages are compensatory, not punitive.
It is also significant that in Singer, the court approves offsetting the time-and-a-half time owed for the firemen's "long" weeks by the amounts they were overcompensated *934for every third "short" week. See Part VII of Singer, 324 F.3d 826-28. In this discussion, the court explains that overpayments in the "short" weeks were in effect partial compensation for the "long weeks." If the majority were applying Singer "as she is writ," the majority would require the offset of time-and-a-half overtime for the Saybolt plaintiffs with the excess hourly wages received by those plaintiffs in their "short" weeks.
Finally, the majority miscite the First Circuit's O'Brien decision as supporting the incorrect damage methodology. O'Brien v. Town of Agawam, 350 F.3d 279 (1st Cir. 2003). O'Brien, to the contrary, discusses only the town's FLSA liability for noncompliance with the FWW method, but the case declines to reach either the damage award or the town's claim for offsets for overtime already paid. See 350 F.3d at 298.
For these reasons, I respectfully dissent from that part of the majority opinion which holds Saybolt liable for the punitive imposition of time-and-a-half compensation under the circumstances of this case.