The City of Chicago shut down Como’s Pizza for three days during May 1994 based on health violations. The owner of *1288Como’s, Dave Clark, along with some of Como’s employees brought this suit challenging the constitutionality of the City’s action. The inspection and closing of the restaurant occurred after neighborhood group leaders, who apparently harbored some animus against Mexicans, complained to their alderman about Como’s, which had Mexican employees and customers. The plaintiffs alleged that this animus and unusual circumstances surrounding the shutdown suggest violations of the Constitution actionable under 42 U.S.C. § 1983 as well as violations of state and municipal law. The District Court granted summary judgment for the defendants on the federal constitutional claims and declined to exercise supplemental jurisdiction over the remaining state law claims. Contreras v. City of Chicago, 920 F.Supp. 1370 (N.D.Ill.1996). The District Court also declined to award costs to the prevailing parties and ordered each side to pay its own costs. The plaintiffs now appeal the- grant of summary judgment, and the defendants cross-appeal the denial of an award of costs. As we explain in detail below, we affirm with respect to the grant of summary judgment but remand with respect to the award of costs.
I. History
Because the District Court’s opinion recounts the facts of this case in exhaustive detail, see Contreras, 920 F.Supp. at 1377-86, we will summarize only the evidence most relevant to the issues raised on appeal. In 1988, plaintiff Dave Clark opened Como’s Pizza in the Ravenswood neighborhood of Chicago. From the start, Clark had problems with two women who lived across the street from Como’s — Victoria and Suzanne Khamis. The Khamises were active neighborhood citizens, and Victoria was the president of the Uptown Ravenswood Charitable Trust (UPRAVE), a community organization that monitors neighborhood activities and issues. Over approximately the past 20 years, the Khamises have taken numerous complaints to their alderman — defendant Schulter — and to other city officials. They have complained, for example, about the disrepair of the neighborhood YMCA building, building code violations at a grocery store, garbage from an apartment building next to Como’s, and the cleanliness of the area around the pizza place that preceded Como’s at its location.
The Khamises’ problems with Como’s and Clark started before Como’s was even open. Victoria Khamis apparently threatened Clark back in the late 1980s that she could and would go to the City to hinder Como’s operation. During subsequent years, the Khamises and UPRAVE continued to complain about Como’s. At a 1991 UPRAVE meeting attended by city officials, for example, problems related to Como’s — such as noise from delivery trucks, double-parked trucks, problems with an exhaust fan, a grease pit in the alley, and rodent control — were key topics of discussion.
Clark employed numerous individuals of Mexican descent at Como’s, including plaintiffs Amalia Gloria, Antonio Contreras, and Raul Contreras. Mobile food truck drivers, who were often Mexican, would also be at Como’s when purchasing pizza for their trucks. The Khamises, meanwhile, made numerous discriminatory comments toward Mexicans over the years. On one occasion, one of the Khamises told Gloria that there was “so much garbage outside all the time because these Mexican people over here are so dirty.” She also told Gloria — who was born in the United States but of Mexican descent — that Mexicans born in this country were different. The Khamises also complained about Mexican employees who they thought looked like gang-bangers. At an UPRAVE meeting, Victoria Khamis stated she was “sick of seeing” Mexican tenants at the apartment building next to Como’s in “their funny hats and boots.” And at a meeting with Como’s manager and defendant Schulter, Suzanne Khamis made repeated references to “Mexican gang-bangers” and “blacks from Uptown.” Schulter apparently made no effort to distance himself from these remarks.
On May 13, 1994, Schulter organized a meeting at City Hall to discuss Como’s Pizza. Present during part or all of the meeting were Schulter and one of his staff members; *1289defendant Shoenberger as Commissioner of the Department of Consumer Services (DCS); two officials from the Department of Revenue; an official from the Department of Zoning; and the Khamises. At the meeting, the Khamises discussed problems associated with Como’s catering trucks, garbage, and grease. Schulter asked Shoenberger to form a task force to investigate Como’s. Schulter’s notes from the meeting indicate that departments other than DCS, such as the Department of Health, were to be included on the task force.
Shoenberger delegated the assignment to a DCS deputy commissioner, who included Como’s on the next regularly-scheduled DCS task force. The Department of Health never became involved with this task force, but the two DCS employees who went to inspect Como’s on May 23 were DCS sanitarians who had recently transferred from the Department of Health. The inspectors noted numerous health violations, many of which Clark later admitted in deposition testimony. He admitted, for instance, that a refrigerator was not working, that paint was peeling from the wall, that thermometers were missing from two coolers, and that a window was missing. The inspectors also noted rodent droppings and observed raw meat sitting out at room temperature, but Como’s denied those allegations. The DCS inspectors issued five citations and closed Como’s as an imminent health hazard.
The inspectors notified the Department of Health of the shutdown, and the Department of Health sent out one of its own inspectors to evaluate the situation at Como’s. Although the Health inspector did not conduct a complete inspection, he did find violations. The inspector, however, did not think that the violations warranted closing Como’s.
On May 24, Clark made efforts to correct the alleged health violations, including calling an exterminator. The exterminator found no rodent droppings, but Como’s had been vacuumed before the exterminator arrived. The next day, May 25, two different DCS inspectors went back to Como’s for a re-inspection. The inspectors noted that some problems had been corrected, but the inspectors also made “a judgment call” that Como’s should not re-open. On May 26, however, DCS permitted Como’s to re-open. Around this time, Clark spoke with Kenneth Panerella, the Health Department’s Chief Sanitarian of the Food and Dairy Protection Division, who stated emphatically that the DCS inspectors were neither authorized nor qualified to inspect and close a restaurant like Como’s and that DCS “deserve[d] to have their asses sued.”
The plaintiffs thereafter filed this suit, alleging violations of the First, Fourth, and Fourteenth Amendments of the U.S. Constitution and seeking monetary, declaratory, and injunctive relief. Both sides moved for summary judgment. The District Court granted summary judgment for the defendants on all claims except for the requests for declaratory and injunctive relief, which the District Court dismissed for lack of jurisdiction because they involved only state law issues. The District Court also ordered both sides to pay their own costs. On appeal, the plaintiffs now raise only their Fourth Amendment claims and some of their Fourteenth Amendment claims.1 The defendants challenge the District Court’s ruling only with respect to costs.
II. Analysis
A. Standard of Review
Under Federal Rule of Civil Procedure 56(c), summary judgment is appropriate “if the pleadings, depositions, answers to interrogatories, and admissions on file, together with the affidavits, if any, show that there is no genuine issue as to any material fact and that the moving party is entitled to a judgment as a matter of law.” In determining whether a genuine issue of material fact exists, courts must construe all facts in the light most favorable to the party opposing *1290the motion and draw all justifiable inferences in favor of that party. Anderson v. Liberty Lobby, Inc., 477 U.S. 242, 255, 106 S.Ct. 2505, 2513, 91 L.Ed.2d 202 (1986). However, neither “the mere existence of some alleged factual dispute between the parties,” Anderson, 477 U.S. at 247, 106 S.Ct. at 2509 nor the demonstration of “some metaphysical doubt as to the material facts,” Matsushita Elec. Indus. Co. v. Zenith Radio Corp., 475 U.S. 574, 586, 106 S.Ct. 1348, 1355, 89 L.Ed.2d 538 (1986), will sufficiently demonstrate a genuine issue of material fact. Finally, when we review a grant of summary judgment, we assess the record de novo. Libertarian Party of Ill. v. Rednour, 108 F.3d 768, 772 (7th Cir.1997); Bombard v. Fort Wayne Newspapers, Inc., 92 F.3d 560, 562 (7th Cir.1996).
B. Fourth Amendment Claim
The plaintiffs first argue that the inspection of Como’s by DCS sanitarians violated the Fourth Amendment which, of course, was incorporated against the states by the Fourteenth Amendment’s Due Process Clause. The plaintiffs argue that the inspection failed the test that New York v. Burger, 482 U.S. 691, 107 S.Ct. 2636, 96 L.Ed.2d 601 (1987), established for warrant-less administrative searches pursuant to a regulatory scheme. For such a search to be reasonable, Burger mandates that 1) a substantial government interest must inform the regulatory scheme, 2) the warrantless inspections must be necessary to further the scheme, and 3) the inspection program must provide a constitutionally adequate substitute for a warrant. Id. at 702-03, 107 S.Ct. at 2643-44.
The plaintiffs sensibly do not contest the first prong of the Burger standard. The safety of the food provided in Chicago is an obvious “substantial governmental interest” that informs the City’s food sanitation regulatory scheme. The plaintiffs do contest the second prong, but their argument is weak. They argue that DCS inspections are unnecessary to further the regulatory scheme because the Health Department enforcement is entirely adequate. The plaintiffs misunderstand this element of the Burger test, however, which requires only that warrantless searches in general must be necessary to further the regulatory scheme. See id. This prong does not give courts the task of evaluating the necessity of each particular aspect of a regulatory scheme. As the District Court put it, “[T]he pertinent inquiry is whether the City’s objectives would be frustrated by requiring a warrant or notice.” Contreras, 920 F.Supp. at 1390. Because the plaintiffs do not contend that warrantless searches are generally unnecessary, we consider Burger’s second prong satisfied.
The plaintiffs’ strongest argument concerns Burger's third prong, which requires “certainty and regularity” in the application of any regulatory scheme that uses warrant-less searches. See Burger, 482 U.S. at 703, 107 S.Ct. at 2644. The plaintiffs contend that the very irregularity of the inspection of Como’s shows a violation of the Fourth Amendment. More specifically, the plaintiffs argue that the “undisputed fact that DCS was not authorized or qualified to search and regulate Como’s ... leads to the conclusion that this warrantless search was unreasonable.” Appellants’ Reply Br. at 12 (emphasis omitted). It is hardly undisputed, however, that DCS was unauthorized and unqualified to inspect Como’s, and we furthermore disagree with the plaintiffs’ conclusion that the inspection was unreasonable under the Fourth Amendment.
Burger's third prong requires that the regulatory statutes that authorize warrant-less searches must perform two of the functions that warrants do: 1) an owner of a searched premises must be advised that the search is pursuant to the law and has a properly-defined scope, and 2) the discretion of the inspecting officers must be limited. See Burger, 482 U.S. at 703, 107 S.Ct. at 2644. Regarding the first of these, the plaintiffs present strong evidence that this case was the only time DCS has ever inspected and shut down a food dispenser. Apparently, DCS sanitarians typically focus on “food-purveyor establishments” like grocery stores and leave the inspection of “food-dispensing establishments” like restaurants to the Health Department. Indeed, Chicago’s food sanitation ordinances (found in chapter 4-8 of *1291the Chicago Municipal Code) generally refer to inspections by the Health Department rather than by DCS. The Municipal Code, for example, requires all food establishment owners “to permit a representative of the department of health, after proper identification, to enter at any reasonable time and make inspections of the facilities, equipment and vehicles for determining compliance with the requirements of this Municipal Code relating to health and sanitation____” Municipal Code of Chicago § 4-8-050(a) (1993) (emphasis added); see also id. § 4-8-060(a); id. § 4-9-030.
Another section of the Municipal Code, however, provides that “[a]ny food sanitarian employed by the city of Chicago shall be empowered to enforce applicable provisions” of chapter 4-8 and that the mayor “may designate one or more departments to supervise the activities of food sanitarians.” Id. § 4-8-075 (emphasis added). The plain language of this section authorizes sanitarians from departments other than Health to enforce chapter 4-8 and, more importantly, gives owners of food establishments notice of this fact. Section 4-8-075 thus plainly advises owners that inspections by sanitarians of any department are “pursuant to the law.” Although the inspection by DCS may well have been unusual, Burger’s, protection is triggered not by peculiar searches but by searches that are unrestrained by law.
Regarding the second function of the warrant requirement discussed by Burger, the plaintiffs argue that even if DCS inspections are authorized by law, the discretion of DCS inspectors is too broad. The plaintiffs assert that DCS inspectors were subject to neither state regulations nor the Health Department’s internal rules, one of which, for example, required a trained and qualified supervisor to personally inspect an establishment before closing it. This argument, however, misunderstands what Burger meant when it referred to the discretion of inspecting officers. The Fourth Amendment protects against the intrusion of unreasonable searches, not against what authorities might do after they have conducted a reasonable search. Burger says that inspectors’ discretion must be “carefully limited in time, place, and scope.” Burger, 482 U.S. at 703, 107 S.Ct. at 2644 (quoting United States v. Biswell, 406 U.S. 311, 315, 92 S.Ct. 1593, 1596, 32 L.Ed.2d 87 (1972)). Inspectors, in other words, cannot barge into an establishment any time they want and inspect the place however they please. As stated above, DCS inspectors were authorized to inspect Como’s, and Clark does not contend that the search itself was unreasonable in time, place, or scope. The inspectors’ discretion to close down Como’s after the inspection may be challengeable under other provisions of the Constitution, but it does not implicate the Fourth Amendment protection against unreasonable searches. We therefore find as a matter of law that the Burger test was satisfied and that the defendants are entitled to judgment on the plaintiffs’ Fourth Amendment claim.
C. Equal Protection Claim
The plaintiffs next argue that the inspection and shutdown of Como’s violated the Equal Protection Clause of the Fourteenth Amendment. The plaintiffs argue that the actions of the City and defendants Schulter and Shoenberger unconstitutionally effectuated or furthered the Khamises racial animosity towards Mexicans.
The Equal Protection Clause plainly prohibits state actors from intentionally discriminating based on race or national origin. See Village of Arlington Heights v. Metropolitan Hous. Dev. Corp., 429 U.S. 252, 265, 97 S.Ct. 555, 563, 50 L.Ed.2d 450 (1977). This ease, however, presents the difficult situation where the direct evidence of racial animus pertains not to state actors but to private citizens asking state actors for assistance. As the District Court noted, the record clearly contains enough evidence to create a genuine issue of fact regarding whether the Khamises were bigoted. To survive summary judgment, however, a party must show a genuine issue of material fact, meaning that the factual dispute must be outcome-determinative under governing law. Wainwright Bank & Trust Co. v. Railroadmens Fed. Sav. & Loan Ass’n of Indianapolis, 806 F.2d 146, 149 (7th Cir.1986); Egger v. Phillips, 710 F.2d 292, 296 (7th Cir.1983) (en *1292banc). “[F]aets not outcome-determinative under the applicable law, though in dispute, may still permit the entry of summary judgment.” Wainwright, 806 F.2d at 149. We are not convinced that the record contains enough evidence to create a genuine issue regarding the ultimate question here, namely whether the defendants inspected and shut down Como’s with a racially-discriminatory purpose.
To evaluate the plaintiffs claim, the District Court used a modified version of a test used by at least two other district courts to decide claims that the government improperly effectuated the racial animus of constituents. The test in its original form required a plaintiff to show “[1] the decision-making body acted for the sole purpose of effectuating the desires of private citizens, [2] that racial considerations were a motivating factor behind those desires, and [3] that members of the decision-making body were aware of the motivations of the private eitizen[s].” United States v. City of Birmingham, Mich., 538 F.Supp. 819, 828 (E.D.Mich.1982), aff'd. as modified, 727 F.2d 560 (6th Cir.1984). The District Court, of course, was not bound by this extra circuit precedent and therefore modified the first prong of the test to read, “the decision-making body acted in whole or in part with the purpose of effectuating the discriminatory desires of private citizens.” Contreras, 920 F.Supp. at 1399 n. 19. The District Court made the change because of language in Personnel Administrator of Massachusetts v. Feeney, 442 U.S. 256, 99 S.Ct. 2282, 60 L.Ed.2d 870 (1979), stating that a showing of discriminatory purpose “implies that the decisionmaker ... selected or reaffirmed a particular course of action at least in part ‘because of,’ not merely ‘in spite of,’ its adverse effects upon an identifiable group,” id. at 279, 99 S.Ct. at 2295. The District Court worried that the original formulation of the test “leaves open the possibility that an Equal Protection violation will be found where an elected official has acted only ‘in spite of his or her constituent’s racial animus not ‘because of that animus,” Contreras, 920 F.Supp. at 1399 n. 19. Cf. Bachman v. St. Monica’s Congregation, 902 F.2d 1259, 1262-63 (7th Cir.1990) (stating that constitutional tort requires racial prejudice to be but-for cause of harm).
We agree with the District Court that the first prong of the test needed to be changed. With the District Court’s modification, however, the first prong of the test becomes so broad and all-encompassing that it in effect subsumes the other prongs. In fact, the District Court’s first prong is general enough that it alone presents the ultimate standard by which this type of case should be judged. Arlington Heights requires that our overall focus remain on the general question of what motivated the government officials to take the challenged action. See Arlington Heights, 429 U.S. at 265-66, 97 S.Ct. at 563-64. A formulaic three-part test like that employed in City of Birmingham may sidetrack us from this ultimate question. Indeed, the Sixth Circuit itself ignored the three-part test in favor of a more general inquiry when it affirmed the trial court ruling in that ease. See City of Birmingham, 727 F.2d at 565.
Of course, private citizens’ motivations and government officials’ knowledge of these motivations may be quite relevant to the ultimate issue of the government officials’ purposes. If a government official, for instance, did not know of the private citizens’ animus, it would be hard to impute that animus as a cause of the government action. Arlington Heights, however, tells us that our examination of the evidence must be broad — we should consider, inter alia, 1) the racial impact of an official action; 2) the historical background of the decision; 3) the specific sequence of events leading up to the challenged decision, including departures from normal procedures and substantive norms; and 4) the legislative or administrative history of the decision. Arlington Heights, 429 U.S. at 266-67, 97 S.Ct. at 563-64. The standard embodied in the District Court’s first prong appropriately keeps our focus at this broad level.
With these considerations in mind, we may now turn to the specifics of this case. Like the District Court, we think that the evidence clearly creates a genuine issue of fact regarding whether the Khamises were bigoted. The evidence also suggests that *1293defendant Sehulter might have been aware of this racial animosity because he was present at meetings where the Khamises allegedly made stereotypical and even racist statements.
The evidence is less clear, however, regarding whether the Khamises’ complaints about Como’s were racially motivated. The Khamises had, after all, complained in the past to the City about neighborhood businesses with no clear connection to any disfavored minority. Even assuming that the Khamises’ complaints about Como’s were racially motivated, the evidence is shaky that Sehulter knew about any racial motivation behind these particular complaints. The only evidence the plaintiffs put forward to suggest Schulter’s knowledge are two meetings where the Khamises allegedly made discriminatory remarks in the presence of Sehulter while complaining about Como’s. The probative value of these incidents is limited, however, by the fact that one of the meetings occurred back in 1990 or 1991 and by the fact that the plaintiffs are not even sure Sehulter attended the other meeting.
So by the time we get to the May 13,1994 meeting with Sehulter, Shoenberger, and the other city officials, the causal chain extending from the Khamises’ racial animosity to the shutdown of Como’s is already strained by some tenuous inferential links. The chain is weakened further, however, by the lack of any evidence that race was mentioned or even implicitly considered at the May 13 meeting. Sehulter called in Commissioner Shoenberger and handed off the investigation of Como’s to her, but here again there is no evidence that she knew of the Khamises before the meeting, let alone their racial biases or even the ethnicity of Como’s employees and customers. Indeed, in her notes from the meeting, Shoenberger mistakenly wrote down “Connie’s Pizza,” apparently referring to a pizza chain on the near south side of Chicago. Moreover, any racial connection to the investigation would hardly have become obvious to Commissioner Shoenberger because the most obvious victim of such an investigation (i.e., Como’s owner Dave Clark) was not of Mexican ancestry. Shoenberger, meanwhile, handed off the investigation to a deputy commissioner within DCS, who also does not appear from anything in the record to have had any knowledge of the Khamises or of the fact that Mexicans were involved with Como’s.
But perhaps this unawareness by Shoenberger and other DCS employees is a distraction from what was really going on. Perhaps the DCS officials were entirely innocent of any racial influence but still operated under a racially-motivated directive from Schulter. What motivated the DCS officials, in other words, would be irrelevant because they were merely implementing Schulter’s orders to shut Como’s down posthaste. To conclude that the DCS investigation was such an entire sham, however, requires numerous inferential leaps. Although the plaintiffs repeatedly point to the uncustomary involvement of DCS in closing the restaurant, the evidence that Sehulter did (or even could) order DCS to shut down Como’s is extremely thin. Schulter’s notes from the May 13 meeting specify that the Health Department was to be included on the task force, and Shoenberger’s memo to her deputy regarding the investigation also specifies that Health was to be involved. The exclusion of the Health Department, according to the only evidence on the record, came about at the suggestion of Shoenberger’s deputy who knew that DCS had sanitarians who had transferred from Health. Moreover, the DCS inspectors did find health violations, many of which the plaintiffs acknowledge. Admittedly, whether the Health Department would have suspended Como’s license for these violations is unclear from the record, and Health officials seem to have been upset at DCS’s unprecedented restaurant inspection. Questions about the propriety of the DCS inspection, however, are a far cry from showing that the government officials involved were racially motivated. Pure polities rather than race may have been behind the investigation of Como’s, and the reaction of Health Department officials may be nothing more than bureaucrats trying to protect their investigatorial turf.
On the ultimate issue of whether the inspection and suspension were racially motivated, the plaintiffs’ primary evidence is the *1294Khamises’ alleged racial animosity. Without any further evidence on the record to suggest racial bias on the part of Schulter or Shoenberger, we must agree with the District Court that no genuine issue of material fact has been created regarding whether these government officials acted out of racial animosity. Like the District Court, we realize that proving a claim of intentional discrimination is difficult and that circumstantial evidence is often the best evidence plaintiffs can come by. “Municipal officials acting in their official capacities seldom, if ever, announce on the record that they are pursuing a particular course of action because of their desire to discriminate against a racial minority.” Contreras, 920 F.Supp. at 1399 (quoting Smith v. Town of Clarkton, 682 F.2d 1055, 1064 (4th Cir.1982)). Nonetheless, “even this Nation’s racists are entitled to political representation and the assistance of their elected officials with respect to their otherwise legitimate concerns.” Id. at 1398. We cannot allow mere speculation about the motivation of government officials to force those officials and their municipalities to trial whenever they have responded to the complaints of bigots. The plaintiffs’ attempt to bootstrap the Khamises’ alleged racial animosity into proof that the DCS inspection — no matter how unusual — was racially motivated is simply too much of a stretch.
D. Substantive Due Process Claim
The plaintiffs’ final claim derives from the Due Process Clause of the Fourteenth Amendment. In the District Court, the plaintiffs raised both procedural and substantive due process arguments, but on appeal they raise only the substantive due process claim. The issue we must consider, therefore, is not whether the City’s decisionmaking process lacked adequate procedural protections such as notice and an opportunity to be heard, but rather whether the inspection and shutdown of Como’s was “fundamentally flawed” in the sense of being arbitrary and irrational. See Polenz v. Parrott, 883 F.2d 551, 557 (7th Cir.1989).
We would first note that much of the plaintiffs’ argument reflects a confusion between what constitutes a constitutional violation and what makes a municipality liable for constitutional violations. Both in the District Court and here on appeal, the plaintiffs invoked “failure to train” and “deliberate indifference” theories as the basis for the substantive due process claim. The plaintiffs spend much of this section of their appellate brief, for example, attempting to show “the lack of training of DCS consumer investigators and ‘sanitarians.’ ” Appellants’ Br. at 44. Notions of “deliberate indifference” and “failure to train,” however, are derived from municipal liability cases such as Monell v. Department of Social Services of City of New York, 436 U.S. 658, 98 S.Ct. 2018, 56 L.Ed.2d 611 (1978), Canton v. Harris, 489 U.S. 378, 109 S.Ct. 1197, 103 L.Ed.2d 412 (1989), and most recently, Board of County Comm’rs of Bryan County, Okla. v. Brown, — U.S.-, 117 S.Ct. 1382, 137 L.Ed.2d 626 (1997). Those cases presume that a constitutional violation has occurred (typically by a municipal employee) and then ask whether the municipality itself may be liable for the violations. Indeed, the Supreme Court has “emphasize[d] the separate character of the inquiry into the question of municipal responsibility and the question whether a constitutional violation occurred.” Collins v. City of Harker Heights, Tex., 503 U.S. 115, 122, 112 S.Ct. 1061, 1066, 117 L.Ed.2d 261 (1992). The liability of the City of Chicago for any deliberate indifference or for failing to train DCS inspectors is therefore secondary to the basic issue of whether a constitutional guarantee has been violated.
Turning therefore to the plaintiffs’ actual constitutional claim, the Due Process Clause of the Fourteenth Amendment provides, “[N]or shall any State deprive any person of life, liberty, or property, without due process of law.” U.S. Const, amend XIV, § 1. The ease law defining what procedures constitute due process of law is well-developed, but we have less guidance regarding what substantive protections the Due Process Clause affords. This court has repeatedly noted the lack of instruction from the U.S. Supreme Court in this area, particularly regarding cases where plaintiffs have alleged deprivations of state-created property interests. See, e.g., Doherty v. City of *1295Chicago, 75 F.3d 318, 325 (7th Cir.1996); Holstein v. City of Chicago, 29 F.3d 1145, 1148-49 (7th Cir.1994); Polenz, 883 F.2d at 557-58 (collecting cases); Kauth v. Hartford Ins. Co. of Ill, 852 F.2d 951, 956-58 (7th Cir.1988). Because we are reluctant to “undermine established Supreme Court precedent requiring plaintiffs complaining of arbitrary deprivations of their property to seek redress through state remedies,” Kauth, 852 F.2d at 957, we have insisted on a “disciplined jurisprudence” for such claims, Doherty, 75 F.3d at 325. Thus, a plaintiff bringing a substantive due process claim predicated on a deprived property interest must show 1) that the state’s decision was arbitrary and irrational, and 2) that the state committed a separate constitutional violation or that state law remedies are inadequate. Id.; Kauth, 852 F.2d at 958.
Assuming that Clark’s license to operate Como’s was a protectable property interest for Fourteenth Amendment purposes, and assuming that the temporary suspension of that property interest by the City was arbitrary and irrational, we still do not see how the plaintiffs’ substantive due process claim can succeed under this circuit’s case law. As we have discussed in the preceding sections, the plaintiffs have not shown an independent constitutional violation. And the plaintiffs have attempted neither in the District Court, see Contreras, 920 F.Supp. at 1395, nor here on appeal to show that state law remedies are inadequate. We therefore find as a matter of law that the plaintiffs’ substantive due process claim must fail.
E. Costs
Federal Rule of Civil Procedure 54(d)(1) provides in part that “costs other than attorneys’ fees shall be allowed as of course to the prevailing party unless the court otherwise directs.” In this case, the District Court ordered both sides to bear their own costs despite the fact that it had granted summary judgment for the defendants on all of the plaintiffs’ federal claims. The defendants now appeal this ruling.
Although a district court has discretion when awarding costs, M.T. Bonk Co. v. Milton Bradley Co., 945 F.2d 1404, 1409 (7th Cir.1991), the discretion is “narrowly confined” because of the strong presumption created by Rule 54(d)(1) that the prevailing party will recover costs, Congregation of the Passion, Holy Cross Province v. Touche, Ross & Co., 854 F.2d 219, 221-22 (7th Cir.1988). “Generally, only misconduct by the prevailing party worthy of a penalty ... or the losing party’s inability to pay will suffice to justify denying costs.” Id. at 222.
The only indication we have of the District Court’s reason for denying costs to the defendants is a statement made in open court during consideration of the defendants’ motion for attorneys’ fees in addition to costs. The trial judge stated, “I am concerned about issuing attorneys’ fees or allowing attorneys’ fees and costs in this ease and sending what is, in effect, a chilling effect on plaintiffs’ attorneys who believe that they have a bona fide civil rights case.” The trial judge also noted that plaintiffs still had a chance to proceed with their claims in state court.
We cannot uphold the District Court’s decision regarding costs. Based on the foregoing statement, it could be that the District Court determined that it had to award either attorneys’ fees and costs or neither. If that was the case, the District Court was in error. See 42 U.S.C. § 1988(b). The statement in open court could also indicate that the District Court concluded that civil rights plaintiffs require different treatment. We know of no authority, however, to support such an exception to Rule 54(d)(1), and the plaintiffs have given us no argument why we should create such an exception. On the other hand, the District Court may have concluded that the defendants deserved to be penalized or that the plaintiffs were indigent-both viable reasons under appropriate circumstances. The District Court, however, did not explain the basis for its decision. See York Ctr. Park Dist. v. Krilich, 40 F.3d 205, 209 (7th Cir.1994) (“Legal rules committing decisions to judicial discretion suppose that the court will have, and give, sound reasons for proceeding one way rather than the other.”). Because there is no readily-apparent reason to overcome Rule 54(d)(l)’s presumption, we must vacate the District Court’s decision regarding *1296costs and remand the case for reconsideration in light of the exceptions to Rule 54(d)(1) that our case law has recognized.
We therefore Affirm the District Court’s grant of summary judgment but Vacate its order denying costs to the defendants. This ease is Remanded with instructions to make an award of costs appropriate under Rule 54(d)(1).
. The District Court dismissed the plaintiffs' official capacity claims against Schulter and Shoenberger as redundant because the plaintiffs also raised the same claims against the City. See Contreras, 920 F.Supp. at 1376. On appeal, the plaintiffs challenge neither this ruling nor the District Court’s grant of summary judgment for the defendants on the plaintiffs’ First Amendment and procedural due process claims.