. Justice Marshall
delivered the opinion of the Court.
In this case we must decide whether a Mississippi statute imposing a 15% penalty on parties who appeal unsuccessfully from a money judgment violates the Equal Protection Clause.
I
This action grows out of allegations that appellant Bankers Life and Casualty Company refused in bad faith to pay appel-lee Lloyd Crenshaw’s insurance claim for loss of a limb. According to testimony at trial, appellee was injured on January 6, 1979, when a car alternator he was repairing rolled off his workbench and landed on his foot. Three days later, after the injury had not responded to home treatment, appellee went to the emergency room of the local Air Force base hospital. Hospital doctors prescribed a splint, crutches, and pain medication, and told appellee to return in a week. Ap-pellee revisited the hospital three times over the next five days, each time complaining of continuing pain in his foot. By the last visit, appellee’s foot had swollen and begun to turn blue, and the examining doctor recommended a surgery consultation. Appellee was admitted to the hospital, where, on January 17, an Air Force general surgeon determined that a surgical amputation was necessary. The following day, ap-pellee’s leg was amputated below the knee.
At the time of the amputation, appellee was insured under a group policy issued by appellant. The policy provided a $20,000 benefit for loss of limb due to accidental bodily injury. In April 1979, appellee submitted a claim under the policy. Appellant denied the claim. The apparent basis for the denial was an opinion of appellant’s Medical Director, Dr. Nathaniel McParland, that the cause of the amputation was not appellee’s accident but a pre-existing condition of arteriosclerosis, a degenerative vascular disease. Appellee responded to the company’s denial by furnishing a statement signed by three doctors who treated him at the hospital. They stated that appellee’s arteriosclerosis was “ ‘an underlying condition and not the immediate cause of the gangrenous necrosis. The precipating [sic] event must be considered to be the trauma which initially brought him to the Emergency Room on 9 January.’” 483 So. 2d 254, 261 (Miss. 1985). Dr. McParland and a company analyst concluded that this statement was inconsequential, and appellant adhered to its position that the arteriosclerosis was responsible for the loss of limb.
Appellee persisted in his efforts to recover under the policy, eventually hiring an attorney, and appellant persisted in its intransigence. In its correspondence with appellee and his attorney, appellant repeatedly asserted that appellee had not suffered an injury as defined in the policy, that is, a “‘bodily injury, causing the loss while this policy is in force, directly and independently of all other causes and effected solely through an accidental bodily injury to the insured person.’” Id., at 262, quoting letter of Apr. 8, 1980, from Wm. Herzau to appellee. In contemporaneous internal memoranda, however, appellant noted that notwithstanding the policy language, appellee was entitled to recovery under Mississippi law if his injury had “‘“aggravate^], rendered] active, or set in motion a latent or dormant pre-existing physical condition or disease.”’” Id., at 262, 263. The memo-randa also demonstrated that appellant knew its flies were incomplete yet never attempted to obtain appellee’s medical records, most notably his emergency room report, even though Mississippi law and internal company procedures required such efforts.
After appellant again denied the claim on the ground that there was no evidence that appellee’s “ ‘injury caused this loss “directly and independently of all other causes,””’ see id., at 263, appellee brought this suit in Mississippi state court. His complaint requested $20,000 in actual damages, and, as amended, $1,635,000 in punitive damages for the tort of bad-faith refusal to pay an insurance claim. The jury awarded appellee the $20,000 provided by the policy and punitive damages of $1.6 million.
The Mississippi Supreme Court affirmed the jury verdict without modification. It concluded that the punitive damages award was not excessive in light of appellant’s financial worth and the degree of its wrongdoing. See id., at 279. Because the money judgment was affirmed without modification, a penalty of $243,000, or 15% of the judgment, was assessed against appellant and added to appellee’s recovery in accordance with Mississippi’s penalty statute. See Miss. Code Ann. § 11-3-23 (Supp. 1987). In its appeal to the Mississippi Supreme Court, appellant did not raise a federal constitutional challenge to the size of the punitive damages award. Following the affirmance of the jury verdict, appellant filed a petition for rehearing. Appellant argued in the petition that “[t]he punitive damage verdict was clearly excessive, not reasonably related to any legitimate purpose, constitutes excessive fine, and violates constitutional principles.” App. to Juris. Statement 139a. An accompanying brief asserted that the punitive damages award violated “due process, equal protection, and other constitutional standards.” Id., at 151a. Appellant also filed a Motion to Correct Judgment in which it alleged that the 15% penalty under § 11-3-23 “violated] the rights of equal protection and due process of Bankers Life” guaranteed in the Federal and State Constitutions. App. to Juris. Statement 106a-107a. The Mississippi Supreme Court, without opinion, denied the petition for rehearing and overruled the Motion to Correct Judgment.
II
Appellant focuses most of its efforts in this appeal to challenging the punitive damages award of $1.6 million. It contends foremost that the award violates the Eighth Amendment’s guarantee that “excessive fines [shall not be] imposed.” Appellant argues first, that the Excessive Fines Clause applies to punitive damages awards rendered in civil cases, and second, that the particular award in this case was constitutionally excessive. In addition to its excessive fines claim, appellant challenges the punitive damages award in this case on the grounds that it violates the Due Process Clause and the Contract Clause. Although we noted probable jurisdiction as to all of the questions presented in appellant’s jurisdictional statement, appellant’s challenges to the size of the punitive damages award do not fall within our appellate jurisdiction. See 28 U. S. C. §1257(2). We therefore treat them as if contained in a petition-for a writ of cer-tiorari, and our unrestricted notation of probable jurisdiction of the appeal is to be understood as a grant of the writ as to these claims. See Mishkin v. New York, 383 U. S. 502, 512 (1966). We conclude, however, that these claims were not raised and passed upon in state court, and we decline to reach them here. See ibid. (“The issue thus remains within our certiorari jurisdiction, and we may, for good reason, even at this stage, decline to decide the merits of the issue, much as we would dismiss a writ of certiorari as improvidently granted”).
Appellant maintains that it raised its various challenges to the size of the punitive damages award in its petition for rehearing before the Mississippi Supreme Court. In urging us to entertain the claims, appellant relies on our decision in Hathorn v. Lovorn, 457 U. S. 255, 262-265 (1982), in which we accepted certiorari jurisdiction of claims that were raised, but not passed upon, in the Mississippi Supreme Court on petition for rehearing. Hathom would be apposite were we to conclude that appellant had adequately raised its claims on rehearing. But appellant’s petition for rehearing alleged only that the punitive damages award “was clearly excessive, not reasonably related to any legitimate purpose, constitutes excessive fine, and violates constitutional principles.” App. to Juris. Statement 139a. The vague appeal to constitutional principles does not preserve appellant’s Contract Clause or due process claims. A party may not preserve a constitutional challenge by generally invoking the Constitution in state court and awaiting review in this Court to specify the constitutional provision it is relying upon. Cf. Taylor v. Illinois, 484 U. S. 400, 407, n. 9 (1988) (“A generic reference to the Fourteenth Amendment is not sufficient to preserve a constitutional claim based on an unidentified provision of the Bill of Rights . . .”).
Appellant’s reference to the excessiveness of the punitive damages award more colorably raises a cognizable constitutional challenge to the size of the award, one based on the Excessive Fines Clause of the Eighth Amendment. But this language as well is too oblique to allow us to conclude that appellant raised before the Mississippi Supreme Court the federal claim it now urges us to resolve. As this Court stated in Webb v. Webb, 451 U. S. 493, 501 (1981), “[a]t the minimum. . . there should be no doubt from the record that a claim under & federal statute or the Federal Constitution was presented in the state courts and that those courts were apprised of the nature or substance of the federal claim at the time and in the manner required by the state law.” Although the petition for rehearing alleges that the fine is excessive, it does not indicate that the fine is excessive as a constitutional matter, be it state or federal. It certainly does not identify the Excessive Fines Clause of the Eighth Amendment to the Federal Constitution as the source of appellant’s claim. Indeed, the crucial language from appellant’s petition contains no reference whatsoever to the Eighth Amendment, the Federal Constitution, or federal law. This failure to invoke the Federal Constitution is especially problematic in this case because the Mississippi Constitution contains its own Excessive Fines Clause. Miss. Const., Art. 3, §28. Thus, even if the Mississippi Supreme Court understood appellant to be offering a constitutional challenge, it may very well have taken that challenge to be anchored in the State Constitution. Cf. Webb, 451 U. S., at 496-498 (finding that party’s reference to “full faith and credit” in state-court proceedings had failed to raise a federal constitutional claim even though the State Constitution contained no full faith and credit clause); id., at 502-503 (Marshall, J., dissenting). We therefore conclude that appellant’s Eighth Amendment challenge, like its other challenges to the size of the punitive damages award, was not properly raised below.
Whether appellant’s failure to raise these claims in the Mississippi courts deprives us of all power to review them under our certiorari jurisdiction is an unsettled question. As then Justice Rehnquist wrote for the Court in Illinois v. Gates, 462 U. S. 213 (1983), the cases have been somewhat inconsistent in their characterization of the “not pressed or passed upon below” rule. Early opinions seemed to treat the requirement as jurisdictional, whereas more recent cases clearly view the rule as merely a prudential restriction that does not pose an insuperable bar to our review. See id., at 218-219 (discussing cases). We are not called on today to conclusively characterize the “not pressed or passed upon below” rule, however, because assuming that the rule is merely prudential, we believe that the more prudent course in this case is to decline to review appellant’s claims.
In determining whether to exercise jurisdiction over ques-. tions not properly raised below, the Court has focused on the policies that animate the “not pressed or passed upon below” rule. These policies are first, comity to the States, and second, a constellation of practical considerations, chief among which is our own need for a properly developed record on appeal. See Webb v. Webb, supra, at 500-501. Because the chief issue appellant would have us resolve — whether the Eighth Amendment’s Excessive Fines Clause serves to limit punitive damages in state civil cases — is a question of some moment and difficulty, these policies apply with special force. See Illinois v. Gates, supra, at 224 (“Where difficult issues of great public importance are involved, there are strong reasons to adhere scrupulously to the customary limitations on our discretion”); Mishkin v. New York, 383 U. S., at 512-513 (“The far-reaching and important questions tendered by this claim are not presented by the record with sufficient clarity to require or justify their decision”). Our review of appellant’s claim now would short-circuit a number of less intrusive, and possibly more appropriate, resolutions: the Mississippi State Legislature might choose to enact legislation addressing punitive damages awards for bad-faith refusal to pay insurance claims; failing that,' the Mississippi state courts may choose to resolve the issue by relying on the State Constitution or on some other adequate and independent non-federal ground; and failing that, the Mississippi Supreme Court will have its opportunity to decide the question of federal law in the first instance, while any ultimate review of the question that we might undertake will gain the benefit of a well-developed record and a reasoned opinion on the merits. We think it unwise to foreclose these possibilities, and therefore decline to address appellant’s challenges to the size of the punitive damages award.
Ill
There remains appellant’s challenge to Mississippi’s “penalty statute,” which requires unsuccessful appellants from money judgments, as well as from several other categories of judgments whose value may readily be determined, to pay an additional assessment of 15% of the judgment. Appellant argues that the penalty statute violates the Equal Protection Clause of the Fourteenth Amendment because it singles out appellants from money judgments, and because it penalizes all such appellants who are unsuccessful, regardless of the merit of their appeal. This claim is properly before us under our appellate jurisdiction because the Mississippi Supreme Court, in denying appellant’s Motion to Correct Judgment, upheld the validity of § 11-3-23 against appellant’s federal constitutional claim. See 28 U. S. C. § 1257(2).
Under this Court’s equal protection jurisprudence, Mississippi’s statute is “presumed to be valid and will be sustained if the classification ... is rationally related to a legitimate state interest.” Cleburne v. Cleburne Living Center, Inc., 473 U. S. 432, 440 (1985). The state interests assertedly served by the Mississippi statute were detailed by the Mississippi Supreme Court in Walters v. Inexco Oil Co., 440 So. 2d 268 (1983). The penalty statute, some version of which has been part of Mississippi law since 1857, “expresses the state’s interest in discouraging frivolous appeals. It likewise expresses a bona fide interest in providing a measure of compensation for the successful appellee, compensation for his having endured the slings and arrows of successful appellate litigation.” Id., at 274-275. In a similar vein, the statute protects the integrity of judgments by discouraging appellant-defendants from prolonging the litigation merely to “squeeze a favorable settlement out of an impecunious” appellee. Id., at 275. Also, the penalty statute “tells the litigants that the trial itself is a momentous event, the centerpiece of the litigation, not just a first step weighing station en route to endless rehearings and reconsiderations.” Ibid. Finally, in part because it serves these other goals, the penalty statute furthers the State’s interest in conserving judicial resources. Ibid.
The legitimacy of these state interests cannot seriously be doubted, and this Court has upheld statutes that serve similar interests. See, e. g., Life & Casualty Ins. Co. v. McCray, 291 U. S. 566 (1934) (upholding additional assessment on insurance companies that wrongfully refuse to pay policy benefits); see also, Louisville & Nashville R. Co. v. Stewart, 241 U. S. 261, 263 (1916) (State may make appeal “costly in cases where ultimately the judgment is upheld”) (Holmes, J.). Cf. Lindsey v. Normet, 405 U. S. 56, 78 (1972) (“We do not question here reasonable procedural provisions to safeguard litigated property ... or to discourage patently insubstantial appeals”) (citation omitted). The statute therefore offends the Equal Protection Clause only if the legislative means that Mississippi has chosen are not rationally related to these legitimate interests.
In arguing that § 11-3-23 violates equal protection, appellant seeks to draw support from the Court’s opinion in Lindsey v. Normet, supra. Lindsey addressed the constitutionality of an Oregon statute that required tenants challenging eviction proceedings to post a bond of twice the amount of rent expected to accrue pending appellate review. The bond was forfeited to the landlord if the lower court decision was affirmed. We agreed with the appellants that the double-bond requirement violated the Equal Protection Clause. We noted that the requirement was “unrelated to actual rent accrued or to specific damage sustained by the landlord.” 405 U. S., at 77. Moreover, the requirement, which burdened only tenants, including tenants whose appeals were nonfrivolous, erected “a substantial barrier to appeal faced by no other civil litigant in Oregon.” Id., at 79. We therefore concluded that the requirement bore “no reasonable relationship to any valid state objective” and that it discriminated against the class of tenants appealing from adverse decisions in wrongful-detainer actions in an “arbitrary and irrational” fashion. Id., at 76-77, 79.
As Lindsey demonstrates, arbitrary and, irrational discrimination violates the Equal Protection Clause under even our most deferential standard of review. Unlike the statute in Lindsey, however, Mississippi’s penalty statute does not single out a class of appellants in an arbitrary and irrational fashion. First, whereas the statute in Lindsey singled out the narrow class of defendant-tenants for discriminatory treatment, the sweep of § 11-3-23 is far broader: the penalty applies both to plaintiffs and defendants, and it also applies to all money judgments as well as to a long list of judgments whose money value may readily be determined. See n. 6, infra. Second, and more generally, there is a rational connection between the statute’s objective and Mississippi’s choice to impose a penalty only on appellants from money judgments or judgments the money value of which can readily be determined. If Mississippi wanted similarly to deter frivolous appeals from other kinds of judgments, it either would have to erect a fixed bond that bore no relation to the value of the underlying suit, or else it would have to set appropriate penalties in each case using some kind of individualized procedure, which would impose a considerable cost in judicial resources, exactly what the statute aims to avoid. Mississippi instead has chosen a partial solution that will deter many, though not all, frivolous appeals without requiring a significant commitment of governmental resources. Appellants from money judgments, and from the other types of judgments delineated in the statute, are a rational target of this scheme because the value of their claims, and thus of a proportional penalty, may be readily computed without substantial judicial intervention. Cf. Lindsey, supra, at 78 (“We discern nothing in the special purposes of the [wrongful detainer] statute or in the special characteristics of the landlord-tenant relationship to warrant this discrimination”). The Constitution does not prohibit Mississippi from singling out a group of litigants that it rationally concludes is most likely to be deterred from bringing meritless claims at the least cost to the State.
In addition, Mississippi’s statute is less likely than was the statute in Lindsey to discourage substantial appeals along with insubstantial ones. Because the penalty operates only after a judgment has been affirmed without modification, there is less risk than in Lindsey of discouraging appellants who believe they have meritorious appeals but simply lack the funds to post a substantial bond during the appellate process. And whereas the assessment in Lindsey “automatically doubled the stakes,” 405 U. S. at 79, the 15% penalty here is a relatively modest additional assessment. Cf. McCray, 291 U. S., at 571 (12% additional assessment not oppressive). Although Mississippi may not have succeeded in eliminating all danger of deterring meritorious claims, we cannot say that the residual danger is sufficient to render the statutory scheme irrational.
In short, unlike the double-bond provision condemned in Lindsey, the means chosen in § 11-3-23 are reasonably related to the achievement of the State’s objectives of discouraging frivolous appeals, compensating appellees for the intangible costs of litigation, and conserving judicial resources. See Lindsey, 405 U. S., at 70. It of course is possible that Mississippi might have enacted a statute that more precisely serves these goals and these goals only; as we frequently have explained, however, a state statute need not be so perfectly calibrated in order to pass muster under the rational-basis test. See, e. g., Vance v. Bradley, 440 U. S. 93, 108 (1979). We are satisfied that the means that the State has chosen are “reasonably tailored to achieve [the State’s legitimate] ends.” Lindsey, supra, at 78. We therefore affirm the judgment of the Mississippi Supreme Court denying appellant’s equal protection challenge to § 11-3-23.
It is so ordered.
Justice Stevens and Justice Kennedy took no part in the consideration or decision of this case.
Appellant did offer on appeal a federal due process challenge based on the alleged “chilling effect” of unrestricted punitive damages awards on the exercise of a litigant’s'right of access to the courts. See App. to Juris. Statement 135a. We read this attack on the alleged open-endedness of Mississippi’s punitive damages awards to be distinct from the attack on the size of the particular award that appellant has waged before this Court.
Similarly, appellant’s challenges in this Court to the size of the punitive damages award in no way qualify as “mere enlargements” of claims made before the Mississippi Supreme Court. Under the mere enlargement doctrine, “[p]arties are not confined here to the same arguments which were advanced in the courts below upon a Federal question there discussed.” Dewey v. Des Moines, 173 U. S. 193, 198 (1899). See also Stanley v. Illinois, 405 U. S. 645, 658, n. 10 (1972). Dewey makes clear, however, that the federal question must be brought to the attention of the court below in some manner. “A claim or right which) has never been made or asserted cannot be said to have been denied by a judgment which does not refer to it.” 173 U. S., at 200.
Several States have enacted limits on punitive damages in specified types of causes of action. See, e. g., Fla. Stat. Ann. § 713.31(2)(c) (1988) (fraudulent filing of mechanics’ lien); Wash. Rev. Code § 9A.36.080 (1987) (malicious harassment); Cal. Civ. Code Ann. § 1787.3 (West 1985) (consumer credit denial).
Section 11-3-23 of Miss. Code Ann. (Supp. 1987) provides:
“In case the judgment or decree of the court below be affirmed, or the appellant fails to prosecute his appeal to effect, the supreme court shall render judgment against the appellant for damages, at the rate of fifteen percent (15%), as follows: If the judgment or decree affirmed be for a sum of money, the damages shall be upon such sum. If the judgment or decree be for the possession of real or personal property, the damages shall be assessed on the value of the property. If the judgment or decree be for the dissolution of an injunction or other restraining process at law or in chancery, the damages shall be computed on the amount due the appellee which was enjoined or restrained. If the judgment or decree be for the dissolution of an injunction or other restraining process as to certain property, real or personal, or a certain interest in property, or be a judgment or decree for the sale of property, or some interest in it, to satisfy a sum out of the proceeds of sale, or to enforce or establish a lien or charge or claim upon or some interest in property, and the only matter complained of on the appeal is the decree as to some particular property or claim on it, the damages shall be computed on the value of the property or the interest in it, if the value of the property or interest in it be less than the judgment or decree against it; but if the value of the property or interest in it be greater than the amount of the judgment or decree against it, the damages shall be upon the amount of the judgment or decree; provided, however, the above penalty shall not be assessed against any condemnee appealing from a special court of eminent domain in any circumstances.”
The penalty would appear to apply to both defendant-appellants, such as Bankers Life, and plaintiff-appellants, who might choose to challenge a recovery they view as too meager. See Eagle Lumber & Supply Co. v. Robertson, 161 Miss. 17, 135 So. 499 (1931) (applying former Mississippi penalty statute to unsuccessful plaintiff-appellant).
The appellants in Lindsey also attacked the constitutionality of provisions of the statute that required tenants challenging eviction proceedings to proceed to trial within six months and to bring only certain claims and defenses. The Court upheld these provisions against appellants’ facial challenge. Lindsey v. Normet, 405 U. S., at 64-69.
Appellant argues that § 11-3-23 impermissibly burdens some litigants’ access to the State’s appellate system. Although the Court indicated in Lindsey that the effective foreclosure of a state right to appeal as to some litigants only — for example, indigent litigants — might well violate equal protection guarantees under even deferential scrutiny, see Lindsey, supra, at 77, 79, appellee rightly notes that appellant lacks standing to challenge § 11-3-23 on this basis, because appellant has not alleged that its own right to appeal has been foreclosed by the statute. See Broadrick v. Oklahoma, 413 U. S. 601, 610 (1973).