WINTER, Circuit Judge:
This is the second appeal in this matter. In the first appeal, we held that New York’s lag-payroll law, Act of May 25, 1990, ch. 190, § 375(b), 1990 N.Y.Laws 587, violated the Contract Clause, U.S. Const, art. I, § 10, and remanded to the district court with instructions to order restitution. See Association of Surrogates v. New York, 940 F.2d 766 (2d Cir.1991), cert. denied, - U.S. -, 112 S.Ct. 936, 117 L.Ed.2d 107 (1992), familiarity with which is assumed. This appeal is from Judge Patterson’s decision after remand ordering appellants to make restitution to affected [77]*77employees from 1990-91 fiscal year (“FY”) appropriations, specifically from, a surplus in the judiciary budget for FY 1990-91. Association of Surrogates v. New York, 772 F.Supp. 1412 (S.D.N.Y.1991).
We conclude that the State’s liability occurred in FY 1991-92, because, at the time the judgment was entered, August 29, 1991, the only wages withheld pursuant to the lag-payroll law were for the immediately preceding two-week pay period. We also believe that the district court’s order is based on unfounded assumptions. There being no compelling reason to intrude on the State’s budget-making processes, we vacate that part of the judgment that orders that restitution be paid from the surplus in the judiciary budget for FY 1990-91.
BACKGROUND
In an effort to limit cuts to the judiciary’s budget request for FY 1990-91, the New York State Legislature enacted a “lag-payroll plan” affecting certain non-judicial employees of the Unified Court System. See Act of May 25, 1990, ch. 190, § 375(b). This measure, with estimated savings of $7 million and actual savings of $9.2 million, was adopted to fund current operations of the court system and to finance the hiring of 308 additional judicial and non-judicial employees.
The statute mandated the withholding of salaries of affected employees for two weeks as of the final bi-weekly payroll period ending on or before March 17, 1991. Because the employees were paid on a biweekly basis for the preceding ten workdays, a total of ten days of salary had to be withheld prior to the commencement of the lag. The lag was not to begin until almost ten months after the statute was passed, and the State Comptroller adopted a procedure designed to introduce the lag gradually and to avoid skipping an entire pay period. Under this procedure, the employees were paid for nine days of work, instead of ten, for each bi-weekly pay period beginning November 7, 1990. The salary received at the end of the first of these pay periods was thus for the first nine days worked, the tenth day being withheld until the next pay period. The salary received at the end of the second pay period was for eight days of work from the preceding ten days, and for the one day withheld from the first pay period. And so on through the tenth pay period ending on March 13, 1991. When the two-week payroll lag began on March 14, 1991, therefore, ten days of salary had been withheld from the affected employees, as statutorily required. Thus, when the last paycheck of FY 1990-91 was received on March 27, 1991, the affected employees had been paid for 50 weeks of work instead of 52. The first two paychecks of FY 1991-92, received on April 10 and April 24, 1991, then compensated the employees for the remaining unpaid workdays of FY 1990-91.1
The instant action was filed in the Southern District on October 4, 1990. Judge Patterson granted summary judgment for the defendants. Relying on his interpretation of New York Civil Service Law Section 204-a(l), he concluded, inter alia, that the plaintiffs’ contractual right to compensation had not been impaired. See Association of Surrogates v. New York, 749 F.Supp. 97, 100-101 (S.D.N.Y.1990).
Plaintiffs appealed. After certifying a question concerning the proper interpretation of New York Civil Service Law Section 204-a(l) to the New York Court of Appeals, we concluded that the lag-payroll scheme violated the Contract Clause as an impairment of the employees’ collective bargaining agreement that was not “reasonable and necessary.” Association of Surrogates, 940 F.2d at 772-74. We remanded to the district court with instructions to: (1) enter a declaratory judgment regarding the unconstitutionality of the lag-payroll' statute; (2) enjoin the further implementation and effects of the lag-payroll plan; and (3) order restitution of the [78]*78deferred wages to the affected employees. Id. at 775.
Subsequently, defendant-appellee Matthew T. Crosson, the Chief Administrator of the Unified Court System, requested that the district court order that the withheld salaries, totalling approximately $9.2 million, be paid out of the FY 1990-91 appropriation. In his affidavit, he explained that a $15.8 million surplus remained from the judiciary’s FY 1990-91 appropriation that would lapse by statute on September 15, 1991. The surplus existed because “the court system was required to implement cost containment measures ... amounting to [savings of] $15.8 million.” He also opined that the FY 1991-92 budget of the Unified Court System, already in “crisis situation,” was severely underfunded and could not endure further cuts resulting from the restitution of lagged wages. Contending that current low funding levels will already mean “the loss of hundreds of court employee jobs through attrition and layoffs” along with “the closing down of civil parts of court,” Crosson claimed that any more cuts will be “devastating” since “[h]undreds of more employees would lose their jobs and even more court parts would close.”
Appellants responded with affidavits indicating that the $15.8 million surplus for FY 1990-91 is not a cash fund in the judiciary budget available for distribution to plaintiffs but is essentially a bookkeeping mirage. Because the surplus was the anticipated result of required cost containment measures, cash for the $15.8 million surplus was never available for use by the court system during FY 1990-91, the appropriation being no more than a legal limit on the judiciary’s spending authority. As a practical matter, therefore, ordering restitution from the FY 1990-91 appropriation would force the state to raise $9.2 million through cuts in non-judicial programs or the raising of new revenues during FY 1991-92.
On August 29, 1991, Judge Patterson issued the declaratory judgment pursuant to our remand and granted Crosson’s motion mandating the FY 1990-91 appropriation as the source of funds for restitution. On September 3, 1991, he issued an opinion explaining the reasons for this judgment. See Association of Surrogates, 772 F.Supp. 1412. The district court held that directing the judgment to be paid out of FY 1990-91 funds was within its broad equitable powers to remedy constitutional violations. Id. at 1415-16. The court rejected the State’s claim that the restitution order violated New York State Finance Law Section 40(2)(a). That section states that funds appropriated for a specific fiscal year may not be used after the end of the fiscal year “except as to liabilities already incurred thereunder.” N.Y.State Fin.Law § 40(2)(a) (McKinney 1989). Under Section 40(3), funds remain available for such liabilities until the September 15th after the close of that fiscal year. N.Y.State Fin. Law § 40(3).
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WINTER, Circuit Judge:
This is the second appeal in this matter. In the first appeal, we held that New York’s lag-payroll law, Act of May 25, 1990, ch. 190, § 375(b), 1990 N.Y.Laws 587, violated the Contract Clause, U.S. Const, art. I, § 10, and remanded to the district court with instructions to order restitution. See Association of Surrogates v. New York, 940 F.2d 766 (2d Cir.1991), cert. denied, - U.S. -, 112 S.Ct. 936, 117 L.Ed.2d 107 (1992), familiarity with which is assumed. This appeal is from Judge Patterson’s decision after remand ordering appellants to make restitution to affected [77]*77employees from 1990-91 fiscal year (“FY”) appropriations, specifically from, a surplus in the judiciary budget for FY 1990-91. Association of Surrogates v. New York, 772 F.Supp. 1412 (S.D.N.Y.1991).
We conclude that the State’s liability occurred in FY 1991-92, because, at the time the judgment was entered, August 29, 1991, the only wages withheld pursuant to the lag-payroll law were for the immediately preceding two-week pay period. We also believe that the district court’s order is based on unfounded assumptions. There being no compelling reason to intrude on the State’s budget-making processes, we vacate that part of the judgment that orders that restitution be paid from the surplus in the judiciary budget for FY 1990-91.
BACKGROUND
In an effort to limit cuts to the judiciary’s budget request for FY 1990-91, the New York State Legislature enacted a “lag-payroll plan” affecting certain non-judicial employees of the Unified Court System. See Act of May 25, 1990, ch. 190, § 375(b). This measure, with estimated savings of $7 million and actual savings of $9.2 million, was adopted to fund current operations of the court system and to finance the hiring of 308 additional judicial and non-judicial employees.
The statute mandated the withholding of salaries of affected employees for two weeks as of the final bi-weekly payroll period ending on or before March 17, 1991. Because the employees were paid on a biweekly basis for the preceding ten workdays, a total of ten days of salary had to be withheld prior to the commencement of the lag. The lag was not to begin until almost ten months after the statute was passed, and the State Comptroller adopted a procedure designed to introduce the lag gradually and to avoid skipping an entire pay period. Under this procedure, the employees were paid for nine days of work, instead of ten, for each bi-weekly pay period beginning November 7, 1990. The salary received at the end of the first of these pay periods was thus for the first nine days worked, the tenth day being withheld until the next pay period. The salary received at the end of the second pay period was for eight days of work from the preceding ten days, and for the one day withheld from the first pay period. And so on through the tenth pay period ending on March 13, 1991. When the two-week payroll lag began on March 14, 1991, therefore, ten days of salary had been withheld from the affected employees, as statutorily required. Thus, when the last paycheck of FY 1990-91 was received on March 27, 1991, the affected employees had been paid for 50 weeks of work instead of 52. The first two paychecks of FY 1991-92, received on April 10 and April 24, 1991, then compensated the employees for the remaining unpaid workdays of FY 1990-91.1
The instant action was filed in the Southern District on October 4, 1990. Judge Patterson granted summary judgment for the defendants. Relying on his interpretation of New York Civil Service Law Section 204-a(l), he concluded, inter alia, that the plaintiffs’ contractual right to compensation had not been impaired. See Association of Surrogates v. New York, 749 F.Supp. 97, 100-101 (S.D.N.Y.1990).
Plaintiffs appealed. After certifying a question concerning the proper interpretation of New York Civil Service Law Section 204-a(l) to the New York Court of Appeals, we concluded that the lag-payroll scheme violated the Contract Clause as an impairment of the employees’ collective bargaining agreement that was not “reasonable and necessary.” Association of Surrogates, 940 F.2d at 772-74. We remanded to the district court with instructions to: (1) enter a declaratory judgment regarding the unconstitutionality of the lag-payroll' statute; (2) enjoin the further implementation and effects of the lag-payroll plan; and (3) order restitution of the [78]*78deferred wages to the affected employees. Id. at 775.
Subsequently, defendant-appellee Matthew T. Crosson, the Chief Administrator of the Unified Court System, requested that the district court order that the withheld salaries, totalling approximately $9.2 million, be paid out of the FY 1990-91 appropriation. In his affidavit, he explained that a $15.8 million surplus remained from the judiciary’s FY 1990-91 appropriation that would lapse by statute on September 15, 1991. The surplus existed because “the court system was required to implement cost containment measures ... amounting to [savings of] $15.8 million.” He also opined that the FY 1991-92 budget of the Unified Court System, already in “crisis situation,” was severely underfunded and could not endure further cuts resulting from the restitution of lagged wages. Contending that current low funding levels will already mean “the loss of hundreds of court employee jobs through attrition and layoffs” along with “the closing down of civil parts of court,” Crosson claimed that any more cuts will be “devastating” since “[h]undreds of more employees would lose their jobs and even more court parts would close.”
Appellants responded with affidavits indicating that the $15.8 million surplus for FY 1990-91 is not a cash fund in the judiciary budget available for distribution to plaintiffs but is essentially a bookkeeping mirage. Because the surplus was the anticipated result of required cost containment measures, cash for the $15.8 million surplus was never available for use by the court system during FY 1990-91, the appropriation being no more than a legal limit on the judiciary’s spending authority. As a practical matter, therefore, ordering restitution from the FY 1990-91 appropriation would force the state to raise $9.2 million through cuts in non-judicial programs or the raising of new revenues during FY 1991-92.
On August 29, 1991, Judge Patterson issued the declaratory judgment pursuant to our remand and granted Crosson’s motion mandating the FY 1990-91 appropriation as the source of funds for restitution. On September 3, 1991, he issued an opinion explaining the reasons for this judgment. See Association of Surrogates, 772 F.Supp. 1412. The district court held that directing the judgment to be paid out of FY 1990-91 funds was within its broad equitable powers to remedy constitutional violations. Id. at 1415-16. The court rejected the State’s claim that the restitution order violated New York State Finance Law Section 40(2)(a). That section states that funds appropriated for a specific fiscal year may not be used after the end of the fiscal year “except as to liabilities already incurred thereunder.” N.Y.State Fin.Law § 40(2)(a) (McKinney 1989). Under Section 40(3), funds remain available for such liabilities until the September 15th after the close of that fiscal year. N.Y.State Fin. Law § 40(3). The district court held that the State’s liability was fixed, not at the time of the court’s judgment, but during FY 1990-91 when the State was obligated by contract to pay the affected workers their full salary. Id. at 1416-17. Judge Patterson noted that the restitution was fashioned in a manner to avoid the “inevitable consequence” of “causing the affected employees of the Unified Court System to finance the court-ordered relief.” Id. at 1417. He projected that the employees previously affected by the lag-payroll statute would likely be the same employees who would be laid off in a budgetary cutback resulting from payment of the restitution from FY 1991-92. Id.
This appeal followed.
DISCUSSION
We disagree with the district court’s conclusion that the State’s liability occurred in FY 1990-91. Because of the very nature of a lag-payroll scheme, the monies owed to affected employees at the time the judgment was entered were for the two weeks preceding that judgment, weeks that are within FY 1991-92. After November 7, 1990, when the gradual phase-in period of the lag began, the affected employees were paid nine days’ salary for ten days worked in each successive bi-weekly pay period. [79]*79As a result, at the close of FY 1990-91 on March 31, 1991, workers subject to the lag-payroll statute had received all salary due except for the two-week pay period ending on March 27 and the first three days of the next pay period — March 27, 28 and 29, 1991. The shortfall of FY 1990-91 was then paid to the employees in the first two pay periods of the new fiscal year. See supra, note 1. Succeeding lags were for salaries due in FY 1991-92. Therefore, the only shortfall in pay — or “liability” in the words of State Finance Law Section 40(2)(a) — that existed at the time of judgment was for FY 1991-92 salaries, specifically for salaries that were earned during the pay period immediately preceding the entry of judgment on August 29, 1991. Thus, in fashioning its remedy, the district court erred by ruling that the State’s liability from FY 1990-91 still existed. State Finance Law Section 40(2)(a), therefore, directs that the restitution be from FY 1991-92 appropriations, while State Finance Law Section 40(3) directs that the FY 1990-91 surplus go to the General Fund.
Of course, state budgetary processes may not trump court-ordered measures necessary to undo a federal constitutional violation, and federal courts have broad discretion in fashioning equitable remedies for such constitutional violations. See Todaro v. Ward, 565 F.2d 48, 54 n. 7 (2d Cir.1977). However, the equitable relief must be “commensurate with the scope of the constitutional infraction.” Id. Discretion to frame equitable relief is limited by considerations of federalism, and remedies that intrude unnecessarily on a state’s governance of its own affairs should be avoided. See Milliken v. Bradley, 433 U.S. 267, 280-81, 97 S.Ct. 2749, 2756-57, 53 L.Ed.2d 745 (1977); see also Rizzo v. Goode, 423 U.S. 362, 379, 96 S.Ct. 598, 607, 46 L.Ed.2d 561 (1976) (“appropriate consideration must be given to principles of federalism in determining the availability and scope of equitable relief”). Federal courts must take care to exercise “a proper respect for the integrity and function of local government institutions,” Missouri v. Jenkins, 495 U.S. 33, 50, 110 S.Ct. 1651, 1662, 109 L.Ed.2d 31 (1990), and recognize the strong “need of a State to administer its own fiscal operations.” Tully v. Griffin, Inc., 429 U.S. 68, 73, 97 S.Ct. 219, 222, 50 L.Ed.2d 227 (1976).
In the instant case, the order mandating restitution from the FY 1990-91 budget was an intrusion into New York’s fiscal affairs not commensurate with the scope of the constitutional violation. Todaro, 565 F.2d at 54 n. 7. The theory of the district court was that if restitution were to be made from the judiciary’s FY 1991-92 budget, the affected employees would have to finance the remedy for the constitutional violation that resulted in their delayed receipt of two-weeks pay. If so, restitution from the FY 1990-91 surplus is necessary to restore the affected employees to the same position they would have enjoyed had the lag-payroll scheme not been enacted. We disagree.
Even if it is assumed for present purposes that restitution from the judiciary’s FY 1991-92 appropriations will have the “devastating” effects outlined in Crosson’s' affidavit and will cause some of the plaintiffs to be laid off, the district court’s order is based on flawed assumptions. One such assumption is that the only pertinent impact of the lag-payroll scheme was to delay the plaintiffs’ receipt of two-weeks pay. However, the lag-payroll scheme provided additional money to the Unified Court System’s FY 1990-91 budget and avoided in that year the very harsh consequences predicted for this year by Crosson's affidavit. As Crosson stated in an earlier affidavit, the lag-payroll legislation was enacted “in lieu of requiring even further cuts in Judiciary programs.” He also stated that the proceeds were used both to fund operations “deemed vital to the system” and to hire new employees. If Crosson is correct that the $9.2 million payment from the judiciary’s FY 1991-92 budget will have “devastating” effects, then a similar conclusion can be reached as to the consequences that would have occurred if the monies generated by the lag-payroll scheme had not been available during FY 1990-91.
[80]*80Moreover, because the measures leading to the $15.8 million surplus were required as part of an overall deficit reduction plan and cash was never available to the judiciary in that amount, there is no basis for an assumption that the surplus would have been available to replace the $9.2 million in expenditures made possible by the lag-payroll system. The $9.2 million would either have to have been found elsewhere or would not have been available. We surely cannot assume that the Governor and State Legislature would have taken steps to provide it.
Thus, even if we were willing to disregard New York’s budgetary processes, we would not direct the State to fund the restitution from a particular FY’s appropriation. The record indicates that, had the lag-payroll statute not been enacted, the affected employees would have encountered the very layoffs (or, in some cases, would not have even been hired) predicted by Crosson. The order directing restitution from the judiciary’s FY 1990-91 budget thus does not restore the affected employees to the position they would have enjoyed had the lag-payroll scheme not been enacted. Instead, it shifts the consequences of the loss of the revenues resulting from the lag-payroll scheme to other parts of the State budget. The remedy selected by the district court is thus based on assumptions without sufficient foundation to support the highly intrusive order before us.
We therefore vacate that portion of the district court’s judgment directing restitution to be paid from the surplus in the judiciary budget for FY 1990-91.