This matter is before us on the Petitioner National Labor Relations Board’s (“NLRB”) application for enforcement of its order against Respondent Velocity Express Inc., f/k/a Corporate Express Delivery Systems (“Velocity”). Velocity contests the calculation of backpay for wrongfully terminated employees. We exercise jurisdiction pursuant to 29 U.S.C. § 160(e), and enforce the order.
Background
Velocity is a company that provides same-day delivery and related services. Edwin and Hildegard Kirk were both Velocity drivers. They owned the vehicles they used for their delivery routes. They were paid flat salaries. From those salaries, Velocity deducted amounts for vehicle insurance and pager service. The Kirks were responsible for payment of any vehicle operating expenses they might incur. Velocity discharged the Kirks in 1999 and each obtained interim employment. Edwin Kirk was self-employed and subsequently obtained a job that paid an hourly wage. Hildegard Kirk was employed during the interim period and received an hourly wage. The NLRB determined that Velocity wrongfully discharged the Kirks in retaliation for their union activities and ordered their reinstatement. Corporate Express Delivery Systems, 332 NLRB 1522, 1532-33 (2000). The NLRB also ordered Velocity to make the Kirks “whole” for any loss of earnings. Id.
In 2002, the D.C. Circuit enforced the NLRB’s order and denied Velocity’s petition for review. Corporate Express Delivery Sys. v. NLRB, 292 F.3d 777 (D.C.Cir.2002). In doing so, the court held that the Kirks were employees, rather than independent contractors. A supplemental compliance proceeding was initiated to determine the amount of backpay that Velocity owed the Kirks. The NLRB’s regional director issued a compliance specification. In it, the regional director calculated each Kirk’s gross backpay, with deductions for *1201vehicle insurance and pager services, estimated vehicle operating expenses, severance pay, and interim earnings. The specification calculated Edwin Kirk’s interim earnings by subtracting his business expenses from gross receipts. It based Hildegard’s gross backpay on her average base pay for 1999.
All parties objected to the specification. Specifically, the Union, the charging party before the NLRB, argued that the specification should not have reduced gross backpay by the operating expenses the Kirks presumably would have incurred, had they continued to be employed at Velocity. Velocity contested (1) the backpay formula’s determination of operating expenses, (2) the calculation of Edwin’s interim earnings, and (3) the use of average pay rate to determine Hildegard’s back-pay. A hearing was held on July 22, 2003 before an Administrative Law Judge (“ALJ”). The ALJ issued a supplemental decision and recommended order, dated September 30, 2003. The ALJ determined that the Kirks’ gross backpay should be calculated without deduction for vehicle operating expenses but found that the compliance specification was otherwise appropriate. Velocity filed exceptions to the ALJ’s recommended order, which the NLRB considered and overruled. In a split decision, the NLRB adopted the ALJ’s recommended order on August 31, 2004. It directed Velocity to,pay Edwin $136,818.13 and Hildegard $12,000.27 plus interest, less appropriate tax withholdings.
Velocity contends that enforcement of the NLRB’s order should be denied because (1) the NLRB’s backpay formula was arbitrary and unreasonable and does not approximate what the Kirks would have earned absent discharge, (2) the most accurate backpay calculation is based upon the Kirks’ tax returns, (3) the ALJ’s rulings at the hearing regarding the appropriate backpay formula and subsequent reversal of those rulings denied Velocity the opportunity to present evidence, and (4) the rate of pay the ALJ used to calculate Hildegard’s gross backpay is without support in the evidence.
Discussion
Our standard of review over a NLRB order is well-settled: “We will grant enforcement of an NLRB order when the agency has correctly applied the law and its findings are supported by substantial evidence in the record as a whole.” NLRB v. Interstate Builders, Inc., 351 F.3d 1020, 1027 (10th Cir.2003) (quoting Miera v. NLRB, 982 F.2d 441, 444 (10th Cir.1992)); see also 29 U.S.C. § 160(e); Universal Camera Corp. v. NLRB, 340 U.S. 474, 488-90, 71 S.Ct. 456, 95 L.Ed. 456 (1951). Our scope of review is a limited one and an NLRB decision will not be overturned just because an appellate panel may have decided the matter differently. Interstate Builders, 351 F.3d at 1028; Ready Mixed Concrete Co. v. NLRB, 81 F.3d 1546, 1551 (10th Cir.1996) (review is “quite narrow”). We do not re-weigh the evidence or second guess the NLRB’s factual inferences. Interior Alterations, Inc. v. NLRB, 738 F.2d 373, 376 (10th Cir.1984); see also Universal Camera, 340 U.S. at 488, 71 S.Ct. 456. Rather, we review only to ensure the NLRB acted within reasonable bounds and substantial evidence supports the order. Interstate Builders, 351 F.3d at 1028 (quoting Ready Mixed Concrete Co., 81 F.3d at 1551). “Substantial evidence is defined as such relevant evidence as a reasonable mind might accept as adequate to support a conclusion.” Id. at 1027-28; see also Dickinson v. Zurko, 527 U.S. 150, 162, 119 S.Ct. 1816, 144 L.Ed.2d 143 (1999); Allentown Mack Sales and Servs., Inc. v. NLRB, 522 U.S. 359, 366-67, 118 S.Ct. 818, 139 L.Ed.2d 797 (1998).
*1202We must give “special respect” to the NLRB’s choice when we review a remedy imposed for violation of the National Labor Relations Act (NLRA). Monfort v. NLRB, 965 F.2d 1538, 1546 (10th Cir.1992) (citing NLRB v. Gissel Packing Co., 395 U.S. 575, 612 n. 32, 89 S.Ct. 1918, 23 L.Ed.2d 547 (1969)). The NLRB’s power to order backpay is “a broad, discretionary one, subject to limited judicial review.” Fibreboard Corp. v. NLRB, 379 U.S. 203, 216, 85 S.Ct. 398, 13 L.Ed.2d 233 (1964); Monfort, 965 F.2d at 1546; Angle v. NLRB, 683 F.2d 1296, 1301 (10th Cir.1982). It is a “power for the [NLRB], not this court, to wield.” Angle, 683 F.2d at 1301 (citing NLRB v. Seven-Up Bottling Co., 344 U.S. 344, 346, 73 S.Ct. 287, 97 L.Ed. 377 (1953)). This deference, however, ends when the order “is a patent attempt to achieve ends other than those which can fairly be said to effectuate the policies of the [NLRA].” Monfort, 965 F.2d at 1546 (quoting Virginia Elec. & Power Co. v. NLRB, 319 U.S. 533, 540, 63 S.Ct. 1214, 87 L.Ed. 1568 (1943)).
It is against this deferential backdrop that we turn to Velocity’s arguments against enforcement. We hold that the NLRB’s decision not to deduct presumed operating expenses from gross backpay was reasonable. A backpay award is “only an approximation” and the NLRB “has considerable discretion in selecting a method reasonably designed to approximate the amount of pay a wrongfully discharged employee” is entitled to. Angle, 683 F.2d at 1302. Our sister circuits have appropriately described this wide discretion, overturning a backpay order only when' the award is “arbitrary or unreasonable.” See NLRB v. International Ass’n of Bridge, Structural & Reinforced Iron Wkrs., Local 378, 532 F.2d 1241, 1242-43 (9th Cir.1976); Woodline Motor Freight, Inc. v. NLRB, 972 F.2d 222, 225 (8th Cir.1992).
The NLRB applied its standard formula in calculating the Kirks’ backpay — it took the amount of gross pay each would have earned absent wrongful discharge, then subtracted interim earnings and regular withholdings. As noted above, Edwin was paid a flat salary and vehicle operating expenses were not regularly withheld. Nevertheless, Velocity argues that the NLRB also should have deducted vehicle operating expenses the Kirks would have incurred, had they been employed by Velocity. Rejecting this argument, the NLRB relied on settled law that it does not “deduct from the gross backpay those expenses that employees would have incurred had they not been unlawfully discharged.” Supplemental D & O at 2 (citing Laborers Local 38 (Hancock-Northwest), 268 NLRB 167 (1983), enf'd. in relevant part, 748 F.2d 1001 (5th Cir.1984) (declining to deduct expenses for transportation, lodging and meals that the discriminatees would have incurred had they been employed during the back-pay period); Myerstown Hosiery Mills, 99 NLRB 630, 631 (1952)).
Like the dissent in the supplemental decision and order, Velocity argues that the vehicle operating expenses in this case are direct expenses associated with the work performed (driving the trucks) and should be treated like the insurance and pager service deductions. See Supplemental D & O at 4 (Battista, Chairman, dissenting). It distinguishes prior cases not allowing a deduction as involving an employee’s personal and domestic expenses (room, board, transportation, or child care), not work-related expenses. The NLRB rejected this distinction as unsupported by its precedent, and found the application of such a principle, at least as to a reduction in gross backpay based upon interim expenses being less than estimated actual expenses, as unsupported by the evidence. Supplemental D & O at 2-3. The dissent would have compared the ex*1203penses in relation to gross pay reported on Edwin’s 1998 tax return and reduced gross backpay for all years by that percentage. Id. at 4 (Battista, J., dissenting). The majority noted that it need not decide whether such reduction could be based upon estimated expenses or whether tax returns (often containing a standard mileage rate) are conclusive as Velocity contends. Id. at 3, n. 8; Resp. Br. 14-20. The majority correctly noted that Velocity had the burden of proof on mitigation of its backpay obligation. Supplemental D & O at 3; see Hansen Bros. Enterprises, 313 NLRB 599, 600 (1993) (respondent has burden of proving all facts to mitigate his backpay liability); Ryder System, 302 NLRB 608 (1991) (same).
The NLRB’s majority decision was reasonable given the aim of liquidating the amounts that the employees would have realized from the employer had they not been discharged wrongfully. Despite the ALJ’s observations that the Kirks were “very much like self-employed individuals,” Tr. 34-35, the D.C. Circuit (affirming the NLRB) has already determined their status as employees, not independent contractors. Corporate Express, 292 F.3d at 780-81. Expenses incurred permitting an employee to work (transportation and child care) seem just as essential as an employee’s vehicle operating expenses. We think the NLRB could permissibly decline to differentiate on this basis, particularly given that the goal of a backpay proceeding is to replicate what the employees would have earned absent the discrimination. We agree with the ALJ that a profit and loss approach to gross backpay (taking receipts less estimated cash expenses) is inconsistent with the complete lack of entrepreneurial opportunity for gain or loss inherent in this arrangement. See Supplemental D & O at 6; see also Corporate Express, 292 F.3d at 780-781.1 And even though the NLRB calculated Edwin’s net interim earnings by subtracting interim expenses from interim gross receipts, it did so when he was seif-employed (not an employee) with identified expenses and consistent with its precedent. See Cliffstar Transportation Co., 311 NLRB 152, 169-70 (1993); A.P.A. Warehouses, Inc., 307 NLRB 838, 841 (1992).
Because we find that the NLRB’s backpay calculation was reasonable on this record, we need not address what the “most accurate formula” is. The NLRB has suggested that given competing formulations of backpay, an ALJ must choose the most accurate formula for Board review. See Regional Import and Export Trucking Co., Inc., 318 NLRB 816, 820 (1995); Woodline Motor Freight, Inc., 305 NLRB 6, n. 4 (1991), enforced, 972 F.2d 222, 226 (8th Cir.1992); American Mfg. Co., 167 NLRB 520 (1967); see also NLRB v. Pepsi Cola Bottling Co., 258 F.3d 305, 314-15 (4th Cir.2001). In this case, the ALJ determined that the method of computing gross backpay ultimately rejected was not reasonable because it was inconsistent with the Kirks’ true status as employees, and the NLRB majority rejected it as inconsistent with precedent. The “most accurate” formula surely does not include formulas based upon an incorrect legal standard. Aneco Inc. v. NLRB, 285 F.3d 326, 336 (4th Cir.2002) (Goodwin, J., concurring in part and dissenting in part). Rather, the NLRB’s formula was sufficient for a “close approximation.” A close approximation, not the “most accurate formula,” is what we require.2 Angle, 683 F.2d at 1302.
*1204The dissent suggests that “economic reality” requires that some estimate of operating expenses must be deducted from gross backpay for these employees because such expenses are incurred in the performance of the work itself, and are deductible for tax purposes as business expenses. The dissent distinguishes between personal, incidental expenses such as commuting and child care expenses which it would not require to be deducted from gross backpay. Though recognizing that tax information may be helpful in determining backpay amounts, we do not require that a remedial award follow what might be deductible were the employee an independent contractor. Moreover, the line between personal expenses and ordinary business expenses is not where the dissent places it; after all, unreimbursed employee business expenses are an itemized deduction to the extent they exceed two percent of adjusted gross income, and there is a credit for child care expenses for certain taxpayers. See I.R.C. §§ 21, 67, 162(a), 274(d). And although commuting expenses generally are non-deductible personal expenses, there are exceptions. See I.R.C. § 262(a); Rev. Rul. 99-7; 1999-5 I.R.B. 4; Walker v. Commissioner, 101 T.C. 537, 545, 1993 WL 516197 (1993) (transportation expenses between business locations). In essence, the dissent’s position is that Edwin was in fact an independent contractor (not an employee) and as such, the NLRB should deduct all of his expenses as an independent contractor from gross pay, just as they would be deducted on Schedule C. Given the D.C. Circuit’s decision to the contrary, we think that the ALJ and the NLRB majority had no choice but to reject this position as well as the conceptual difficulty it portends regarding the classification of expenses.
We also decline to hold that Velocity was denied “fundamental fairness” in the proceeding. Resp. Br. at 20-23; Reply Br. at 5-6. Velocity claims it was deprived of an opportunity to present certain evidence because at the hearing the ALJ rejected the standard employee calculation and then later adopted that same formulation. Be that as it may, Velocity was not significantly deprived of the opportunity to argue that issue.
It is clear from the transcript that the ALJ was inclined to utilize a “receipts less expenses” formula, Tr. at 36, but the ALJ’s comments on this could not be fairly characterized as a ruling. Specifically, the ALJ qualified the statements: “I think that’s what we’re doing here;” “That’s my sense of the case. I don’t know, again, without looking at the entire text of [a case cited].” Tr. at 36. In fact, the ALJ specifically laid out that it was Velocity’s burden to show that the operating expenses were deducted by Velocity in the ordinary course of business. Id. at 36-37. It is clear that they were not. After reading the record, we do not find that the ALJ’s statements constituted a ruling, nor do we find that those statements denied Velocity the opportunity to present any evidence it desired.
Velocity argues that the NLRB’s calculation of Hildegard Kirk’s rate of pay was unreasonable because there was insufficient evidence to base the rate of pay on her average weekly salary rather than her salary on her last day of employment. Resp. Br. at 24-27. This argument is unpersuasive in light of our deferential standard of review. We must credit the NLRB’s factual inferences and credibility determinations. Interior Alterations, Inc., *1205738 F.2d at 376-77. We will only disturb the NLRB’s order if no reasonable mind could accept the NLRB’s conclusion. See Interstate Builders, 351 F.3d at 1027-28.
Here, the NLRB’s calculation was reasonable because Hildegard’s own testimony supported the finding. She testified that Velocity cut her route, and therefore her earnings, approximately one week before her discharge. Hildegard testified without contradiction that the office manager “said it would not be a problem” to adjust her route such that her earnings would be consistent with what they had originally been. Tr. 88-89,94. Based on this testimony, the NLRB concluded “it is reasonable to assume [that] Hildegard Kirk would have earned [her previous average] if she had not been unlawfully terminated.” Supplemental D & O at 6. The NLRB’s decision to utilize averaging to determine Hildegard’s rate of pay is supported by precedent, Bridgeway Oldsmobile, 294 NLRB 858, 861-62 (1989), and the NLRB’s decision to credit her testimony was reasonable and provides sufficient support for its conclusions.
ORDER ENFORCED.
. Moreover, it is inconsistent with what actually would have occurred in this case because the only deductions Velocity took were for insurance, pager expenses, uniforms, drug tests and physical exams. Supplemental D & O at 6.
. In NLRB v. Pepsi Cola Bottling Co., 258 F.3d 305, 314-15 (4th Cir.2001), the ALJ re*1204jected the General Counsel's approach to backpay, but the NLRB reversed without rejecting any of the underlying factual determinations of the ALJ. The Fourth Circuit noted that NLRB did not address accuracy of the respective methods. We do not read this case as altering our standard of review of NLRB orders.