
669 F.3d 225 (2012)
James LINDQUIST; Sandra Lindquist, Plaintiffs-Appellants,
v.
The CITY OF PASADENA TEXAS, Defendant-Appellee.
No. 09-20683.
United States Court of Appeals, Fifth Circuit.
January 25, 2012.
*227 David Alfred Kahne (argued), Law Office of David A. Kahne, Houston, TX, for Plaintiffs-Appellants.
William S. Helfand (argued), Charles Teilhard Jeremiah, Chamberlain, Hrdlicka, White, Williams & Aughtry, Houston, TX, for Defendant-Appellee.
Deborah J. La Fetra, Timothy Mason Sandefur, Pacific Legal Foundation, Sacramento, CA, for Amicus Curiae.
Before DENNIS, OWEN and SOUTHWICK, Circuit Judges.
OWEN, Circuit Judge:
James and Sandra Lindquist filed suit against the City of Pasadena, Texas (the City or Pasadena) alleging that the City violated their constitutional rights under the Texas and United States constitutions by exercising unbridled discretion in connection with the denial of an application for a waiver of city zoning ordinances. The present appeal comes to us following a remand as a result of a prior appeal in which this court reversed the district court's order of dismissal.[1] On remand, the district court granted summary judgment in favor of the City. We affirm.

I
For many years the Lindquists have operated a used-car dealership known as "Professional Auto" on a location at 2602 Preston Road in Pasadena. There are many other used-car dealerships in the Citymore than eighty as of 2003and in 2003 the Pasadena City Council enacted an ordinance adopting licensing standards for used-car dealers. The ordinance criminalizes the sale of used cars without a license and imposes a number of requirements that dealers must meet as a condition of receiving a license.
Two of the ordinance's requirements are relevant to this appeal. First, a requirement that we will refer to as the 1000' Rule provides: "Each new license location is required to be a minimum of one thousand (1000) feet from any existing license location as measured from nearest property line to nearest property line." In addition to distancing dealerships from one other, the ordinance distances the dealerships from residential areas. A second provision, which we will call the 150' Rule provides: "There shall not be issued a new license for the operation of a used car lot within one hundred fifty (150) feet of the lot lines of a residential area or subdivision." The ordinance also contains a grandfather clause permitting a license to issue even if the dealership does not meet the 150' Rule or the 1000' Rule. In order to come within the grandfather clause, among other conditions, a dealership must have been operating at the same location and continuously licensed for a certain period of time, with no more than a sixty-day interruption of sales activity.
In order to obtain a license under the ordinance, a used-car dealer must first submit an application to a building official for the City. The building official then *228 forwards the application to the City's chief of police, who must conduct an investigation regarding certain facts pertaining to the background of the applicants, none of which are at issue in this appeal.
The chief of police must also investigate the location of the proposed dealership. After completing the investigation, the chief of police is to forward his or her findings to the building official with a recommendation of either approval or denial. The building official then considers the application, reviews the chief of police's investigation, and determines whether the applicant has complied with the terms of the ordinance and other applicable laws and regulations. If the building official denies an application, the applicant has the right to appeal to the City Council. The appeal provision provides:
The hearing before the council shall be de novo and the applicant shall have the burden of proving that he is entitled to the license. At such hearing, the council shall have the right and authority to consider the information obtained by the chief of police or his duly authorized representative when investigating the applicant and also any report or statement of facts prepared by the city building official in connection with the matter.... After such hearing, the council shall decide, by motion, whether or not the license applied for shall be granted or refused. In the event the council grants such license, the applicant shall be entitled to the issuance thereof in the same manner as other licenses are issued under this article.
After this ordinance was enacted, the Lindquists considered purchasing two lots in Pasadena to expand their used car dealership. One was located at 4545 Spencer Highway, and the other was located at 4646 Spencer Highway. When the Lindquists consulted city officials responsible for issuance of the necessary license, the officials told them that neither lot qualified for a license. Specifically, the officials told the Lindquists that the 4545 Spencer Highway location violated both the 1000' Rule and the 150' Rule and the 4646 Spencer Highway location violated the 1000' Rule. The Lindquists nevertheless purchased the lot at 4646 Spencer Highway, which had previously been used as a gas station, and applied for a used-car-dealer license. City officials denied the Lindquists' application, but, after consultation with city officials, the Lindquists applied for and received a license to sell "Boats, Motorcycles, Travel Trailers, Golf carts, ATVs, Classic Cars, and Classic Trucks."
The Lindquists subsequently discovered that their competitors Keith and Tammy Nielsen had purchased the lot located at 4545 Spencer Highway and applied for a license to operate a used-car dealership there. City officials denied the Nielsens' license application because 4545 Spencer Highway violated the 1000' Rule. Although city officials had informed the Lindquists that the 4545 Spencer Highway lot also violated the 150' Rule, that rule was not a basis for the denial of the Nielsens' license application.
The Nielsens appealed the denial of their license application to the City Council. At the beginning of the hearing pertaining to that appeal, the City's planning director, Tim Tietjens, made the following statement:
Now, it's important to note, this is not a variance. This is not a variance request in which someone's coming forward and seeking administrative relief around an ordinance. It is a section in the ordinance that's allowed those who have made such application. It is of public record and everyone that gets *229 rejected is able to make the same appeal.
Each appeal stands on its own merits. Council has discretion to grant or refuse as you deem appropriate.
Tietjens then presented the council with a number of findings of fact. He stated that the previous owner of 4545 Spencer Highway was issued a used-car-dealer license in 1999, but that at some undetermined time the previous owners stopped sales operations. Mail was returned from the address as of September 29, 2003 and, according to Tietjens, the sixty-day window for the grandfather clause began to run as of that date. Tietjens observed that the application was rejected because the grandfather clause was forfeited as to 4545 Spencer Highway because more than sixty days had elapsed with no sales activity and the 1000' Rule thus applied to the lot.
The Nielsens then addressed the council. They contended that the 4545 Spencer Highway location did qualify for an exemption from the 1000' Rule under the grandfather clause because the location still maintained an active used-car-dealer license. They also pointed out that the location had been designed and built as a car dealership and would remain vacant unless it was used as a car dealership.
After the Nielsens' presentation, the council inquired of a city attorney whether the lot qualified for an exemption under the grandfather clause. The city attorney reiterated the position that the lot did not qualify because the sixty-day window began to run when mail was returned from that address. Tietjens, also, observed that, although the location still had an active license, he had not seen proof that there was any sales activity in the relevant sixty-day window.
The council then discussed the application, with some members observing that the lot had been vacant for quite some time. Councilman Welch, for example, observed: "[T]hose of us who have lived in Pasadena very long know that there's been no activity at the Gulf Coast Truck lot for several years. It's been dark. Their lights have been turned off. So we know they've been doing no business for sometime." Councilman Isbell also noted that "there's no dispute that it's been vacant for quite a long time" and that he would "probably say it's probably close to a year since they've actually had activity at that facility." One council member, Councilwoman Philibert, even observed that the lot had been specifically discussed at meetings addressing passage of the city ordinance:
But we were specifically told, because the truck center came up, that that unit would not be reopened as a used auto lot. I mean, it was a conversation piece that came up in the meeting. I have made numerous contacts with both Tim and several with our permit department, our legal department in regards to this issue, and have been assured relatively along the way that this permit was going to be denied.
Other members noted that the lot was built as a dealership, conformed with every applicable ordinance other than the 1000' Rule, and could be put to good use as a car dealership. Mayor Pro Tem Barker, for example, stated: "I remember when that lot was built.... It met all the qualifications we had at that time.... Now as far as I can see ... there's not much use for that lot the way it is other than as a car dealership." Councilman Welch, also, observed that it would "def[y] common sense to say that this property is suitable for any other purpose than a used car lot." And, even though he had previously observed that there had been no activity at the lot for several years, Councilman Welch stated: "we do have the argument of the 60-day *230 shutdown.... It's questionable." Another member of the council, Councilman Harrison, stated his belief that the sixty-day requirement was unconstitutional.
In response to the council's observations, the Nielsens emphasized that the ordinance does not define what constitutes sales activity for purposes of the grandfather clause. They claimed to have submitted evidence of sales by the previous owner of the lot in the prior year. Finally, they asserted that theirs was a unique situation. The council ultimately granted the Nielsens a license, by a vote of five to three.
The following day, the Lindquists applied for a license to operate a used car dealership at 4646 Spencer Highway. Their application was denied, and they appealed. As with the Nielsens' appeal, Tim Tietjens made the following statement at the beginning of the appeals hearing: "This appeal has been requested in accordance with Chapter 22-29(b) of the Pasadena Code of Ordinances. This is an actual appeal of a rejection to Council. It's not a variance, as such. Each appeal stands on its own merits. Council has discretion to grant or refuse." Tietjens then stated that the Lindquists' application was denied because the 4646 Spencer Highway lot violated the 1000' Rule.
Sandra Lindquist then addressed the council. She argued that the 1000' Rule should be implemented by measuring from "side lot line to side lot line." She also contended that the 4646 Spencer Highway location "has been meant for the sole purpose of cars being on it." She stated that the Lindquists could comply with all of the other applicable city rules and regulations except the 1000' Rule and that they were already selling classic cars and other recreational vehicles on the site. She emphasized that it was the Lindquists' dream to open a lot on Spencer Highway and that they bought the property with the intent to sell automobiles.
The council then discussed the application. Councilman Douglass began by observing that he was against granting the license to the Lindquists, but that he had also been against granting a license to the Nielsens. He asserted: "By allowing Keith Nielson to violate our Used Car Dealer Ordinance and turning around and not allowing the Lindquists the same courtesy sounds like favoritism." His comments were later echoed by Councilwoman Philibert: "And I agree with Council Member Jack Douglass in regards to denial on one and acceptance on another in essentially the same exact circumstances from the standpoint of documentation and wherewithal for the facility does speak of favoritism." Councilman Isbell also stated that he voted against granting the Nielsens' application because the ordinance was "cut and dried" and that his feelings had not changed.
Other members of the council responded to Councilman Douglass's suggestion of favoritism. Councilman Harrison stated that he had voted in favor of the Nielsens because "I didn't agree with the 60-day rule. I believe it's unconstitutional." Harrison further observed that the Lindquists presented a "unique and a different situation, complete different situation from last time." Councilman Barker also observed that the Lindquists' and Nielsens' situations presented different circumstances: "On the other situation where the dealership had been made strictly for a car dealership and a million dollars spent to develop that and the license in effect, I voted to override the appeal. I don't see the same circumstances for this appeal, so I'll be voting against it." Councilman Welch agreed: "I, too, feel that this is a creation of another parking lot from a *231 situation of property that was not previously designed as a parking lotor as a car lot. So, therefore, I see it as a totally different situation than the other." The council unanimously denied the Lindquists' appeal.
Two years later, in 2006, the City Council addressed another appeal by an individual attempting to obtain a used-car-dealer license. Joe Chambers purchased a lot located at 2801 Preston Road in 2005. He applied for a used-car-dealer license in 2006, but his application was denied because the lot violated the 150' Rule. Like the Lindquists and the Nielsens, he appealed.
The City Council first addressed Chambers's appeal on July 25, 2006. Tietjens again started the appeals hearing by explaining the appeals process to the council: "You can appeal a rejection if it's not a variance, as such. Each appeal stands on its own merits. Council does have the discretion to grant or refuse, as you deem appropriate." He then explained that the Preston Road property violated the 150' Rule and that, even though the property was previously used as a used-car dealership, it had since been converted to a check cashing business and that no car sales had occurred within the sixty-day period relevant to the ordinance's grandfather clause.
Before Chambers made his presentation to the council, a former councilman who was attending the hearing stated that Chambers was "a very respectable businessman in the community." He further claimed that Chambers had been told by a city employee that he could reopen the property as a used-car dealership. The former councilman stated that Chambers would not have purchased the property "if he couldn't reopen it." Chambers reiterated this story in his own presentation to the council. He stated that he was told by a city official that he would be able to use the lot to sell used cars. He further argued that he was now stuck with a piece of property that had previously served as a car lot and he was unable to sell it.
In response to Chambers's argument, at least one City Council member expressed a concern that the City might face liability if Chambers had purchased his property in reliance on the representations of a City employee. Councilman Isbell stated: "My struggle is, the ordinance is black and white, but I'm not sure the City doesn't have some liability if we don't allow this, based on the actions of the employees." Other council members, observing that Chambers's property only ran afoul of the requirement that a used-car dealer be at least 150' from a residential area, suggested that it might be helpful to hear from the residents near the property. Councilman Barker stated: "If I'd heard from the neighbors on this property that they had no objection to this being a car lot there, it would certainly help me to determine whether I would go along with the variance or not." Mayor Manlove, also, stated: "If we had maybe letters from some of the residents that lived around that car lot that said they just absolutely wouldn't mind, then we as a city, as a governing body, do have the ability to allow a variance." Councilman Harrison, too, stated: "[I]f you can get the letter from the seven different property owners that they have no objection, I would seriously consider it." And, Councilman Guthrie stated: "I'll go on record, if all of the residential owners within the required number of feet of this property in writing state that they have no objection to a used car lot going in there and knowing that this property would have to meet all of the existing city code, I'd probably lobby that for you."
The City Council met again on August 15, 2006. At this hearing, Chambers submitted *232 letters from the residents near his property stating that they did not oppose having a car dealership on the property. The City Council voted unanimously to grant Chambers a license.
In 2006, the Lindquists filed suit in federal court. The Lindquists' amended complaint raised three distinct claims: (1) that the existence of unbridled discretion for the City to approve or deny licenses violates the Due Process Clause and the Equal Protection Clause of the United States Constitution, as well as the Texas Constitution; (2) that the City grants used-car-dealer licenses to similarly situated dealers with no rational basis to treat the Lindquists differently, in violation of the right to equal protection in the United States and Texas constitutions; and (3) that the City's denial of the Lindquists' license application violated due process. The City filed a motion to dismiss, which the district court granted.[2]
On appeal, we reversed the district court's determination that the Lindquists' equal protection claim failed to state a claim for relief.[3] The district court had dismissed the Lindquists' equal protection claim after determining that it sounded in selective enforcement and was therefore deficient in the absence of an allegation that the City acted with "illegitimate animus or ill-will." We reversed based on our interpretation and application of prior circuit precedent, which "compel[led] our holding that the Lindquists' equal protection claim does not sound in selective enforcement and does not require a showing that the city acted with illegitimate animus or ill will."[4] We affirmed the district court's treatment of the Lindquists' due process claims, however, and further observed that the Lindquists' unbridled discretion claim overlapped with their due process and equal protection claims.[5] We concluded that, to the extent the Lindquists' unbridled discretion claim could be interpreted as an attack on the validity of the ordinance, "[t]he district court's holding that the ordinance is not facially invalid was ... correct."[6]
On remand, the parties engaged in discovery and ultimately filed cross-motions for summary judgment. In their own motion for partial summary judgment, the Lindquists reasserted their claim that the City unconstitutionally exercised unbridled discretion in considering appeals from denials of used-car-dealer licenses. The district court granted summary judgment to the City after determining that the Lindquists had failed to create a genuine issue of fact with respect to their equal protection claim.[7] The district court also addressed the Lindquists' renewed unbridled discretion claim by concluding that the renewed claim was "not a distinct claim from the class-of-one equal protection claim remanded to this court."[8] The Lindquists now appeal.

II
We review the district court's grant of summary judgment de novo, applying the same standards as the district court.[9]*233 "Summary judgment is appropriate when the record discloses that no genuine issue of material fact exists and that the movant is entitled to judgment as a matter of law."[10] "When assessing whether a dispute to any material fact exists, we consider all of the evidence in the record but refrain from making credibility determinations or weighing the evidence."[11] We also "consider all evidence in a light most favorable to the non-moving party and draw all reasonable inferences in favor of the non-moving party."[12]

III
We first address the Lindquists' equal protection claim. The Lindquists allege a violation of their equal protection rights under both the United States and Texas constitutions. Because "the federal analytical approach applies to equal protection challenges under the Texas Constitution,"[13] we do not address separately the Lindquists' claim under the Texas Constitution.[14]
The Lindquists argue that the city treated them differently than others similarly situated in violation of their constitutional right to equal protection as a "class of one." We review such claims under a two-prong test: the plaintiff must show that (1) he or she was intentionally treated differently from others similarly situated and (2) there was no rational basis for the difference in treatment.[15] Here, we conclude the Lindquists have failed to create a genuine issue of fact with respect to either of these two prongs.

A
We begin with the question of whether the Lindquists have presented evidence that they were treated differently from other "similarly situated" individuals. The Lindquists point to the competing auto dealerships owned by Chambers and the Nielsens as similarly situated comparators for purposes of satisfying their burden on this question. The Lindquists note that, like themselves, both Chambers and the Nielsens initially failed to obtain used-car-dealer licenses because of a failure to comply with the used-car-dealer ordinance's distance requirements and both appealed the denial to the City Council.
The legal requirement that a class-of-one plaintiff's comparators be "similarly situated" is not a requirement susceptible to rigid, mechanical application"[t]here is no precise formula to determine whether an individual is similarly situated to comparators."[16] Several of our sister circuits, confronting this issue, have stated that, in order to be similarly situated, comparators must be prima facie identical in all relevant *234 aspects.[17] But this statement simply raises new questions. What aspects of a particular case are relevant? What is relevant in one case might not be relevant in another, for example, and "the degree to which others are viewed as similarly situated" necessarily will depend "substantially on the facts and context of the case."[18] In short, the inquiry is case-specific and requires us to consider "the full variety of factors that an objectively reasonable ... decisionmaker would have found relevant in making the challenged decision."[19]
The Lindquists have not satisfied their burden of pointing to similarly situated comparators. In a case like this one, which involves the application of an ordinance or statute, the plaintiff's and comparators' relationships with the ordinance at issue will generally be a relevant characteristic for purposes of the similarly-situated analysis. For example, in Beeler v. Rounsavall,[20] we rejected an equal protection claim by a convenience store operator who claimed that a city "applied ... municipal ordinances, including the distance requirements established by Ordinance 1939, unreasonably in his case by frustrating his application for a permit based on a failure to comply with those ordinances."[21] We did so because the ordinance at issue "clearly distinguishe[d] between applications for new permits and applications to renew existing permits,"[22] and the plaintiff, who was applying for a new permit, only pointed to individuals who were applying to renew existing permits as similarly situated comparators. We held that "the relevant question [was] whether the two stores were similarly situated under the Code," and we observed that "[t]he Code's differential treatment of businesses applying for their first permit and businesses applying to renew their permits indicates that Beeler and the Rodriguezes were not similarly situated."[23] Similar disparities exist between the Lindquists and their proposed comparators: the Nielsens and Chambers.
First, the ordinance requirement the Lindquists failed to satisfythe 1000' Rulewas not at issue in Chambers's appeal. Chambers appealed to the City Council because the 2801 Preston Road address failed to satisfy the 150' Rule. Moreover, Chambers presented letters from the affected residents indicating that they did not object to the dealership, and the City Council appears to have considered these letters to be extremely relevant *235 to its decision to grant Chambers's appeal. Thus, not only did Chambers's appeal implicate a different requirement in the City's ordinance than the Lindquists' appeal, but Chambers's presentation to the City Council also differed significantly from the Lindquists' presentation insofar as Chambers established that the residentsthe purported beneficiaries of the 150' Rulesupported his appeal.
Second, we note that the Nielsens' property, unlike the Lindquists' property, had previously served as the location for a used-car dealership. Indeed, the location still had an active used-car-dealer license at the time of the Nielsens' appeal. Thus, when the Nielsens appealed the denial of their license application, they argued that their property qualified for an exemption from the 1000' Rule pursuant to the ordinance's grandfather clause. The Lindquists did not argue that their property qualified for an exemption under that clause. In short, the Nielsens argued that their property satisfied the City's requirements for a license pursuant to a section of the ordinance that was not an issue in the Lindquists' appeal. Under these circumstances, it is difficult to see how this case differs significantly from the circumstances we confronted in Beeler. We conclude the Lindquists, the Nielsens, and Chambers are not similarly situated.

B
We now address whether, if the Lindquists could show that they are similarly situated to the Nielsens and Chambers, they have established "that a genuine issue of material fact exists as to whether any rational basis could exist for the [City's] action."[24] On appeal, the Lindquists argue the City Council's grants of the appeals of Chambers and the Nielsens served no legitimate state interest, and were thus irrational, because they involved exercises of "unbridled discretion" by the council. In their reply brief, for example, the Lindquists argue: "The City's repeated admissions confirm its intent to use unbridled discretion to ignore terms in the ordinance, with no requirement for findings, or even an explanation, in writing. This intent means the City lacks `a legitimate state interest' and precludes finding a rational basis as a matter of law." The Lindquists thus appear to argue that the City Council's decisions to deny their appeal and to grant the appeals of Chambers and the Nielsens cannot be rational because the City Council's actions conflicted with the requirements of the used-car-dealer ordinance.
As the district court correctly observed, however, the fact that a government actor's actions might be illegal under state or local law does not mean that they are irrational for purposes of the Equal Protection Clause.[25] We have explained this point in the past and reiterate it today. In Stern v. Tarrant County Hospital District, for example, we observed:
The guarantees of the fourteenth amendment, its requirement that state *236 laws be applied in the same way to those entitled to equal treatment and its promise of protection from arbitrary or irrational state action, are guarantees that turn on federal constitutional standards of equality and rationality rather than on state standards. Converting alleged violations of state law into federal equal protection and due process claims improperly bootstraps state law into the Constitution. In doing so, this novel approach would expand the scope of the fourteenth amendment, would render its meaning less certain, and would serve no legitimate policy.
....
... When a legislature has a choice of means, each rationally related to its legislative purpose, it may constitutionally choose any of them. Its choice of one does not render the others irrational. It follows that acts violative of the chosen means, although by definition contrary to state law, are not ipso facto contrary to the fourteenth amendment. The constitutional test for rationality of a legislative classification, whether the classes be distinguished in the text of the law or in its administration, is whether any rational decisionmaker could have so classified.[26]
Thus, the relevant question for purposes of the Lindquists' equal protection claim is not whether the City Council's actions conflicted with the terms of the used-car-dealer ordinance. The question is whether a rational decisionmaker could have drafted that ordinance in a way that would have allowed used-car-dealer licenses to the Nielsens and Chambers while denying the Lindquists a license.
We answer this question in the affirmative. A rational decisionmaker certainly could have drafted the grandfather clause in the City's ordinance to exempt from the City's distance requirements every property, including the Nielsens' property, that had previously served as the location of a used-car dealership. Such a decisionmaker might conclude that, rather than immediately prohibit every dealership that violated the distance requirements, it would be more appropriate to prevent only new dealerships from further exacerbating the problems the distance requirement seeks to alleviate.[27]
The district court identified a number of other rationale bases on which the City could have treated the Lindquists differently from the Chambers and the Nielsens.[28] We will not lengthen this opinion by repeating that analysis. In short, the reality of this case is that the differences between the Lindquists, Chambers, and the Nielsens provided the City Council with rational bases for making the decisions that it did. Chambers's property violated the 150' Rule, not the 1000' Rule, and he obtained the consent of all the affected residents. The Nielsens' property was developed for and had been used as a car dealership, and they argued that the property satisfied the ordinance's grandfather clause. The Lindquists' property was *237 constructed for and was previously operated as a gas station, and the Lindquists made no similar arguments about their property. Given these and other facts identified by the district court, the Lindquists cannot show that the City Council acted irrationally when it denied their appeal.

IV
Finally, we address the Lindquists' "unbridled discretion" claim. Because the contours of this claim, and the issues that it presents in this appeal, are initially difficult to decipher, we begin with an overview of the claim's history in this litigation.
In their response to the City's original motion to dismiss, the Lindquists described the claim as an argument that the City's used-car-dealer licensing ordinance granted the City Council "unbridled discretion to license used car dealers notwithstanding the 1000' Rule and other rules." The Lindquists claimed that this unbridled discretion violated due process pursuant to Texas Supreme Court holdings in Spann v. City of Dallas[29] and related cases.
This claim was, essentially, a void-for-vagueness claim. In Spann, the Supreme Court of Texas addressed the constitutionality of an ordinance prohibiting "the construction of any business house within what the ordinance denominates a residence district of the City, except with the consent of three-fourths of the property owners of the district, and on the building inspector's approval of the design of the proposed structure."[30] One of the reasons the court gave for holding the ordinance "clearly unconstitutional and void" was the ordinance's grant of "unbridled discretion" to the building inspector to disapprove the design of the proposed structure. The court observed:
No rule or standard is given [t]o govern the applica[n]t in fashioning the design of his building or to govern the inspector in approving or rejecting it.... This leaves the right to construct the building subject to the arbitrary discretion of the inspector, and of itself renders the ordinance void. The very essence of American constitutions is that the material rights of no man shall be subject to the mere will of another.[31]
This principle embodies the void-for-vagueness doctrine.[32] For example, in Women's Medical Center of Northwest Houston v. Bell, we held that a law "is unconstitutionally vague if it ... is so indefinite that it allows arbitrary and discriminatory enforcement."[33] Moreover, our sister circuits treat claims that zoning ordinance procedures permit the exercise of unbridled discretion as void-for-vagueness *238 challenges.[34] Accordingly, when the Lindquists claimed in Lindquist I that the City's used-car-dealer ordinance was unconstitutional under Spann, they were in effect arguing that the ordinance was void for vagueness and thus violated the due process protections of both the federal and Texas constitutions.[35] We rejected that argument when we held that "[t]o the extent the Lindquists argue that the licensing ordinance is facially invalid because it does not provide adequate standards to guide the city's discretion, they are incorrect for the reasons stated in the district court's opinion."[36]
After we remanded the case to the district court, the Lindquists again raised an unbridled discretion claim under Spann. Specifically, they argued that our decision in Lindquist I only addressed the facial constitutionality of the City's licensing ordinance and thus did not address the constitutionality of the City's actual implementation of the ordinance. They argued the city council had an established policy or custom of failing to follow the ordinance's constitutionally adequate standards for determining entitlement to a used-car-dealer license, and thus exercised unbridled discretion in deciding appeals for used-car-dealer licenses. According to the Lindquists, because the City's actual policy or custom involved the exercise of unbridled discretion, the City's actions still violated Spann (regardless of the language of the ordinance). The Lindquists essentially reasserted their unbridled discretion claim, but argued that the district court should focus on the City's actual practice under the ordinance, rather than the ordinance itself, as the relevant policy for purposes of the Spann analysis. The district court granted summary judgment to the City on this claim after determining the Lindquists' "as-applied" unbridled discretion claim was "not a distinct claim from the class-of-one equal protection claim remanded to this court."[37]

A
The City argues that the Lindquists' unbridled discretion claim is barred by the law-of-the case doctrine. "The law-of-the-case doctrine `posits that when a court decides upon a rule of law, that decision should continue to govern the same issue in subsequent stages in the same case.'"[38] The doctrine generally bars the district court on remand, or the appellate court on a subsequent appeal, from reexamining an issue of law decided on appeal.[39] Importantly, "the law of the *239 case doctrine applies only to issues that were actually decided, rather than all questions in the case that might have been decided, but were not."[40] The City argues that the law-of-the-case doctrine applies to the Lindquists' unbridled discretion claim because, in Lindquist I, we affirmed the district court's dismissal of the claim.
We do not believe the Lindquists' current unbridled discretion claim implicates the law-of-the-case doctrine, however. In Lindquist I, the Lindquists claimed that the used-car-dealer ordinance itself granted the City Council unbridled discretion in evaluating appeals under the ordinance. In other words, the Lindquists identified the ordinance as the relevant policy for purposes of the City's liability.
Here, by contrast, the Lindquists argue that, despite the ordinance's facial constitutionality, the City has a custom or practice of exercising unbridled discretion that renders the ordinance irrelevant. "This is the actual policy guiding the City's conduct," they seem to say, "not the ordinance itself." The Lindquists support this argument by relying on the principle "that a plaintiff may be able to prove the existence of a widespread practice that, although not authorized by written law or express municipal policy, is so permanent and well settled as to constitute a custom or usage with the force of law."[41] For example, although "[o]fficial policy is ordinarily contained in duly promulgated policy statements, ordinances or regulations[,] ... a policy may also be evidenced by custom."[42] In this appeal, the Lindquists point to the City Council's actual custom or practice as the alleged relevant policy for purposes of municipal liability, not the ordinance itself. Whether the City Council's alleged "custom or practice" of exercising unbridled discretion is the relevant policy, and whether that custom or practice violates due process, are questions we did not address in Lindquist I. Accordingly, the law-of-the-case doctrine does not apply to the Lindquists' unbridled discretion claim.

B
Despite our holding that the law-of-the-case doctrine does not foreclose the Lindquists' unbridled discretion claim, we conclude that a related doctrine does bar us from considering this claim. Specifically, the Lindquists' current unbridled discretion claim implicates the waiver doctrine. Unlike the law-of-the-case doctrine, which arises "as a consequence of a decision on our part," the waiver doctrine is "a consequence of a party's inaction."[43] The waiver doctrine "holds that an issue that could have been but was not raised on appeal is forfeited and may not be revisited by the district court on remand."[44] The doctrine also prevents us from considering such an issue during a second appeal.[45] The doctrine promotes procedural efficiency and "prevents the bizarre result that a party who has chosen not to argue a point *240 on a first appeal should stand better as regards the law of the case than one who had argued and lost."[46]
The Lindquists' current unbridled discretion claim is an argument the Lindquists could have raised on their initial appeal to this court. The claim rests on public statements by council members and staff made at the various appeal proceedings, indicating their belief that the ordinance did not prevent them from waiving or excepting licensing requirements for any particular applicant on appeal. The subsequent depositions of city employees taken on remand did not produce any substantially different evidence; at best these depositions merely corroborate the statements made during the appeal proceedings.
The Lindquists did not argue in Lindquist I, however, that the relevant policy for purposes of their unbridled discretion claim was the City's actual custom or practice of exercising discretion. Indeed, we have reviewed the Lindquists' briefs from that appeal, and, although the Lindquists' did point to the "words and deeds of the Mayor, City Council, and other City officials," they did so as a way of demonstrating the legislative intent behind the appeal clause in the ordinance. They argued that, because "City Council made clear its legislative intent and purpose," the district court could not construe the ordinance to avoid constitutional questions.[47] Finally, the Lindquists did state in a footnote "that the City, as a matter of policy and practice, exercises unfettered discretion to disregard the written rules," but this statement alone does not suffice to preserve the argument.[48]
In short, nothing prevented the Lindquists, in their appeal in Lindquist I, from arguing that the City Council's actual practice in implementing the used-car-dealer ordinance, and not the ordinance itself, was the relevant policy for purposes of their unbridled discretion claim. They did not do so, and the claim was thus waived. This waiver precluded the Lindquists from asserting their new unbridled discretion claim on remand and precludes them from raising the claim to us in a subsequent appeal.

* * *
For the above reasons, the judgment of the district court is AFFIRMED.
NOTES
[1]  Lindquist v. City of Pasadena, Tex. (Lindquist I), 525 F.3d 383 (5th Cir.2008).
[2]  Lindquist v. City of Pasadena, Tex., No. H-06-1975, 2006 WL 3499527 (S.D.Tex. Dec. 5, 2006).
[3]  Lindquist I, 525 F.3d 383 (5th Cir.2008).
[4]  Id. at 387.
[5]  Id. at 387-88.
[6]  Id. at 388.
[7]  Lindquist v. City of Pasadena, Tex., 656 F.Supp.2d 662, 680-707 (S.D.Tex.2009).
[8]  Id. at 679.
[9]  Travelers Lloyds Ins. Co. v. Pac. Emp'rs Ins. Co., 602 F.3d 677, 681 (5th Cir.2010).
[10]  Id.
[11]  Delta & Pine Land Co. v. Nationwide Agribusiness Ins. Co., 530 F.3d 395, 398-99 (5th Cir.2008).
[12]  Frakes v. Crete Carrier Corp., 579 F.3d 426, 429-30 (5th Cir.2009) (internal quotation marks and citation omitted).
[13]  Bell v. Low Income Women of Tex., 95 S.W.3d 253, 266 (Tex.2002).
[14]  See Lindquist I, 525 F.3d 383, 386 n. 1 (5th Cir.2008).
[15]  Vill. of Willowbrook v. Olech, 528 U.S. 562, 564, 120 S.Ct. 1073, 145 L.Ed.2d 1060 (2000); see also Stotter v. Univ. of Tex. at San Antonio, 508 F.3d 812, 824 (5th Cir.2007) ("To establish such a [`class of one'] claim, the plaintiff must show that (1) he or she was treated differently from others similarly situated and (2) there was no rational basis for the disparate treatment.") (citing Olech, 528 U.S. at 564, 120 S.Ct. 1073).
[16]  McDonald v. Vill. of Winnetka, 371 F.3d 992, 1002 (7th Cir.2004).
[17]  See Grider v. City of Auburn, Ala., 618 F.3d 1240, 1264 (11th Cir.2010) ("To be similarly situated, the comparators must be prima facie identical in all relevant respects." (internal quotation marks and citations omitted)); Jicarilla Apache Nation v. Rio Arriba Cnty., 440 F.3d 1202, 1212 (10th Cir.2006) ("In [class-of-one] cases, courts have insisted that plaintiffs demonstrate similarity in all material respects."); Neilson v. D'Angelis, 409 F.3d 100, 104 (2d Cir.2005), overruled on other grounds by Appel v. Spiridon, 531 F.3d 138 (2d Cir. 2008) ("`In order to succeed, the plaintiffs must demonstrate that they were treated differently than someone who is prima facie identical in all relevant respects.'") (quoting Purze v. Vill. of Winthrop Harbor, 286 F.3d 452, 455 (7th Cir.2002)); Racine Charter One, Inc. v. Racine Unified Sch. Dist., 424 F.3d 677, 680 (7th Cir.2005) ("To be considered similarly situated, comparators must be prima facie identical in all relevant respects or directly comparable to plaintiff in all material respects." (internal quotation marks, brackets, and citations omitted)).
[18]  Jennings v. City of Stillwater, 383 F.3d 1199, 1214 (10th Cir.2004).
[19]  Griffin Indus., Inc. v. Irvin, 496 F.3d 1189, 1203 (11th Cir.2007).
[20]  328 F.3d 813 (5th Cir.2003).
[21]  Id. at 816.
[22]  Id. at 817.
[23]  Id.
[24]  Whiting v. Univ. of S. Miss., 451 F.3d 339, 349 (5th Cir.2006).
[25]  See, e.g., Jeneski v. City of Worcester, 476 F.3d 14, 17 (1st Cir.2007) ("[A] violation of state law is not by itself a constitutional violation."); Sylvia Dev. Corp. v. Calvert Cnty., Md., 48 F.3d 810, 825 (4th Cir.1995) ("While an equal protection claim must be rooted in an allegation of unequal treatment for similarly situated individuals, a showing of such disparate treatment, even if the product of erroneous or illegal state action, is not enough by itself to state a constitutional claim."); Smith v. City of Picayune, 795 F.2d 482, 487 (5th Cir. 1986) ("Although the City did not conform to state law in zoning the property, that violation of state law does not per se constitute denial of the federal constitutional right to equal protection of law.").
[26]  Stern v. Tarrant Cnty. Hosp. Dist., 778 F.2d 1052, 1056 (5th Cir.1985) (en banc); see also Snowden v. Hughes, 321 U.S. 1, 8, 64 S.Ct. 397, 88 L.Ed. 497 (1944) ("[N]ot every denial of a right conferred by state law involves a denial of the equal protection of the laws, even though the denial of the right to one person may operate to confer it on another.").
[27]  Cf. City of New Orleans v. Dukes, 427 U.S. 297, 305-06, 96 S.Ct. 2513, 49 L.Ed.2d 511 (1976) (per curiam) (upholding against an equal protection challenge a grandfather clause in an ordinance banning pushcart food vendors from the French Quarter in New Orleans).
[28]  Lindquist v. City of Pasadena, Tex., 656 F.Supp.2d 662, 686-87 (S.D.Tex.2009).
[29]  111 Tex. 350, 235 S.W. 513 (1921).
[30]  Id. at 513.
[31]  Id. at 517.
[32]  See Women's Med. Ctr. of Nw. Houston v. Bell, 248 F.3d 411, 421 (5th Cir.2001) ("The Fourteenth Amendment's guarantee of Due Process proscribes laws so vague that persons of common intelligence must necessarily guess at their meaning and differ as to their application.") (internal quotations and citations omitted).
[33]  248 F.3d at 421. Cf. City of Houston v. Freedman, 293 S.W.2d 515, 520-21 (Tex.Civ. App.1956) ("[T]he City's position that each member of the Council without regard to any rule of action established by ordinance is free arbitrarily to exercise his personal discretion from time to time as applications are filed to determine [validity] ... cannot be squared with the due process and due course of the law of the land provisions of the Federal and state Constitutions, respectively.") (citing Crossman v. City of Galveston, 112 Tex. 303, 247 S.W. 810 (1923)).
[34]  See, e.g., White Oak Prop. Dev., LLC v. Wash. Twp., Ohio, 606 F.3d 842, 847-50 (6th Cir.2010); Henry v. Jefferson Cnty. Planning Comm'n, No. 99-2122, 2000 WL 742188, at *4-7 (4th Cir. June 9, 2000); see also Leib v. Hillsborough Cnty. Pub. Transp. Comm'n, 558 F.3d 1301, 1309 (11th Cir.2009) ("[I]t is difficult to distinguish Leib's `unbridled discretion' claim from his void-for-vagueness claim.").
[35]  The protections afforded by the Texas Constitution's Due Course of Law Clause and the United States Constitution's Due Process Clause are generally the same. Tex. Worker's Comp. Comm'n v. Patient Advocates of Tex., 136 S.W.3d 643, 658 (Tex.2004) ("Texas's due course of law clause and the federal due process clause are textually different, but we generally construe the due course clause in the same way as its federal counterpart.").
[36]  Lindquist I, 525 F.3d 383, 388 (5th Cir. 2008).
[37]  Lindquist v. City of Pasadena, Tex., 656 F.Supp.2d 662, 679 (S.D.Tex.2009).
[38]  United States v. Castillo, 179 F.3d 321, 326 (5th Cir. 1999), rev'd on other grounds, 530 U.S. 120, 120 S.Ct. 2090, 147 L.Ed.2d 94 (2000) (quoting Arizona v. California, 460 U.S. 605, 618, 103 S.Ct. 1382, 75 L.Ed.2d 318 (1983)).
[39]  See United States v. Lee, 358 F.3d 315, 320 (5th Cir.2004).
[40]  Alpha/Omega Ins. Servs., Inc. v. Prudential Ins. Co. of Am., 272 F.3d 276, 279 (5th Cir. 2001).
[41]  City of St. Louis v. Praprotnik, 485 U.S. 112, 127, 108 S.Ct. 915, 99 L.Ed.2d 107 (1988) (internal quotation marks and citation omitted).
[42]  Piotrowski v. City of Houston, 237 F.3d 567, 579 (5th Cir.2001).
[43]  Castillo, 179 F.3d at 326.
[44]  Med. Ctr. Pharm. v. Holder, 634 F.3d 830, 834 (5th Cir.2011).
[45]  See Nw. Ind. Tel. Co. v. FCC, 872 F.2d 465, 470 (D.C.Cir.1989) ("It is elementary that where an argument could have been raised on an initial appeal, it is inappropriate to consider that argument on a second appeal following remand.").
[46]  Id. (internal quotation marks omitted).
[47]  See Commodity Futures Trading Comm'n v. Schor, 478 U.S. 833, 841, 106 S.Ct. 3245, 92 L.Ed.2d 675 (1986) (observing that the canon of constitutional avoidance "does not give a court the prerogative to ignore the legislative will in order to avoid constitutional adjudication").
[48]  See Bridas S.A.P.I.C. v. Gov't of Turkmenistan, 345 F.3d 347, 356 n. 7 (5th Cir.2003) ("Arguments that are insufficiently addressed in the body of the brief, however, are waived.").
