OPINION OF THE COURT
GARTH, Circuit Judge.
This action for a refund of federal estate taxes presents the question whether the equal protection clause is offended by a state inheritance tax statute that, as part of a more general scheme which taxes bequests to a decedent's close relatives at a lower rate than bequests to more distant relatives, imposes a higher tax rate on bequests to stepgrandchildren than it does on bequests to stepchildren, the children of [411]*411one’s adopted children, and spouses, among others. The district court held that the distinction was irrational and arbitrary, and so violated the equal protection clause. Unlike the district court, we conclude that the distinction in question is rationally related to a legitimate state purpose. Thus we will reverse the district court’s judgment in favor of the taxpayer.1
I.
John C. Kunkel died on July 27, 1970,2 leaving a will which distributed his estate in three portions. First, one-half of the adjusted gross estate was to be used to establish a marital trust (“the trust fund”) for the benefit of his surviving spouse, Katherine S. Kunkel. Mrs. Kunkel was to have the income from the trust fund for life, as well as two powers of appointment with respect to the corpus of the trust fund. Under the terms of the will, if Mrs. Kunkel failed to exercise those powers of appointment, the corpus of the trust fund would eventually pass on to her grandchildren— John Kunkel’s st'epgrandchildren.3 Second, the will provided for a bequest of $35,000 for each of Kunkel’s stepchildren (Mrs. Kunkel’s children). Third, the will made a gift of the residue of the estate to the John Crain Kunkel Foundation, a charitable organization under section 501(c)(3) of the Internal Revenue Code of 1954 (“the Code”). In connection with this last bequest, the will specifically provided that all estate, inheritance, and other taxes to which the estate might be subject were to be paid out of the residuary estate. Thus, any estate or inheritance taxes would reduce the amount of the charitable bequest while leaving the other bequests intact.
On October 29, 1981, Kunkel’s estate (“the taxpayer”) filed a federal estate tax return showing a gross estate of nearly $8,000,000 and a charitable deduction of slightly over $3,000,000. On a taxable estate of $686,742.71, the taxpayer calculated and paid a federal estate tax of $195,044.88. Subsequently, however, the Commissioner of Internal Revenue (“the Commissioner”) determined a deficiency of $315,897.67. The taxpayer paid the deficiency but then filed a claim with the Commissioner for a refund of $118,084. It is this sum which is in dispute in the present case.
A.
A full explanation of the nature of the present dispute between the taxpayer and the Commissioner — a dispute which, though turning on the constitutionality of a state inheritance tax statute, concerns federal tax liability — requires a brief description of the relevant state and federal inheritance and estate tax laws.
Section 2055(a)(2) of the Code provides that in calculating the federal estate tax, “the value of the taxable estate shall be determined by deducting from the value of the gross estate the amount of all bequests, legacies, devises, or transfers to or for the use of any corporation organized and operated exclusively for religious, charitable, scientific, literary, or educational purposes . . . . ” It was under section [412]*4122055(a)(2), then, that the taxpayer was qualified to take a charitable deduction for the gift to the Foundation. Section 2055(c), however, limits the amount of the charitable deduction that can be taken when — as in the present case — the will provides that all estate and inheritance taxes are to be payable out of the portion of the estate being given to the charitable organization:
Death taxes payable out of bequests. — If the tax imposed by section 2001, or any estate, succession, legacy, or inheritance taxes, are, either by the terms of the will, by the law of the jurisdiction under which the estate is administered, or by the law of the jurisdiction imposing the particular tax, payable in whole or in part out of the bequest, legacies, or devises otherwise deductible under this section, then the amount deductible under this section shall be the amount of such bequests, legacies, or devises reduced by the amount of such taxes.
In the circumstances of the present case, the taxpayer was allowed under section 2055 to take a charitable deduction equal to the residue of the estate after the bequests to the trust fund and to Kunkel’s stepchildren were made, less the amount of estate and other taxes determined to be due. Thus, the exact amount of the bequest to the Foundation — and so the amount of the charitable deduction allowed under section 2055 — would depend on precisely how much the federal and state taxes turned out to be.
B.
With respect to the state tax liability, the Pennsylvania Inheritance and Estate Tax Act of 1961 (“the Pennsylvania inheritance tax”), 72 Pa. Stat. Ann. §§ 2485-102 to -1201, imposes a tax of six percent on bequests to “Class A” beneficiaries, and fifteen percent on bequests to “Class B” beneficiaries. See id. §§ 2485-403, -404. “Class B” beneficiaries are all those not included in “Class A”; “Class A” beneficiaries include the grandparents, parents, spouse and lineal descendants, among others. Id. In turn, the term “lineal descendants” is defined to include
all children of the natural parents and their descendants, adopted descendants and their descendants, stepchildren, and children and their descendants of the natural parent who are adopted by his spouse. It does not include descendants of stepchildren or adopted children and their descendants in the natural family, except as above set forth.
Id. § 2485-102(13) (emphasis supplied). Finally, the tax imposed by the Pennsylvania inheritance tax statute is generally assessed at the time that the interest bequeathed by the will passes into the hands of the ultimate beneficiary, although the executor may elect to prepay the tax.
C.
In calculating the amount of Pennsylvania inheritance taxes due, the taxpayer assumed that the bequest establishing the trust fund would be taxed at the six percent rate applicable to gifts to “Class A” beneficiaries. The taxpayer then subtracted this amount from the value of the residue of the estate in computing the size of the charitable deduction under section 2055. The Commissioner, in determining the deficiency, contended that the taxpayer had underestimated the Pennsylvania inheritance tax liability by assuming that the six percent rate applied. As previously noted, if Mrs. Kunkel died without having exercised her powers of appointment, the corpus of the trust fund would, under the terms of the will, eventually be distributed to Mr. Kunkel’s stepgrandchildren. As stepgrandchildren are “Class B” beneficiaries, Pennsylvania would at that time assess an additional nine percent tax on the bequest establishing the trust fund, in order to bring the tax rate up to the fifteen percent level assessed on gifts to “Class B” beneficiaries. In that event, the taxpayer would turn out to have underestimated the state inheritance tax ultimately due; consequently, the taxpayer would have overstated the size of the charitable deduction allowable under section 2055. Taking the fifteen percent rate as the applicable one, the Commissioner determined the size of the charitable [413]*413deduction to be $2,106,520.62, rather than the $3,230,133.12 that the taxpayer had claimed. And that overstatement of the charitable deduction had caused the federal estate tax to be underpaid by $118,084.
In support of his position, the Commissioner relied on 26 C.F.R. § 20.2055-2(b)(l), which provides in part:
If, as of the date of a decedent’s death, a transfer for charitable purposes is dependent upon the performance of some act or the happening of a precedent event in order that it might become effective, no deduction is allowable unless the possibility that the charitable transfer will not become effective is so remote as to be negligible. If an estate or interest has passed to, or is vested in, charity at the time of a decedent’s death and the estate or interest would be defeated by the subsequent performance of some act or the happening of some event, the possibility of occurrence of which appeared at the time of the decedent’s death to be so remote as to be negligible, the deduction is allowable.
The possibility that Mrs. Kunkel would die without having exercised her powers of appointment, the Commissioner asserted, was not “so remote as to be negligible.” Thus, there was a nonnegligible possibility that the trust fund would pass to the stepgrandchildren, triggering the imposition of an additional nine percent state inheritance tax. As that nine percent differential would be paid out of the residuary portion of the estate from which the bequest to the Foundation was made, there was a nonnegligible possibility that the charitable bequest “would be defeated [to the extent of the additional inheritance tax] by ... the happening of some event” within the meaning of the regulation. Under the terms of the regulation, therefore, the Commissioner decided that the taxpayer should have assumed that the fifteen percent tax rate would apply, and that the taxpayer thereby should have claimed the smaller charitable deduction than the higher state inheritance tax rate would imply.
D.
On December 28, 1978, having failed to obtain a refund from the Commissioner, the taxpayer4 sued in federal district court for a refund. On May 30, 1980, both parties moved for summary judgment. The taxpayer argued, among other things, that on the facts of this case the possibility that Mrs. Kunkel would fail to exercise her powers of appointment was so remote as to be negligible. The taxpayer further argued that imposition of the higher rate of taxation would violate the equal protection clause. Noting that under Pennsylvania law, not only a bequest to a surviving spouse, but even a bequest to a stepchild, was taxed at the lower “Class A” rate, the taxpayer contended that to tax the bequest at the higher “Class B” rate simply because it went to the decedent’s stepgrandchildren would be utterly irrational. Because the classification violates the equal protection clause, the extra nine percent differential between “Class A” and “Class B” gifts could never be collected, even if the corpus of the trust did pass to the decedent’s step-grandchildren. As a result, the taxpayer concluded, the amount of the Pennsylvania inheritance tax due was not underestimated, and the charitable deduction taken on the federal estate tax return was not overstated.
E.
In an opinion of July 23,1981, the district court rejected the taxpayer’s first argument, holding that “this court cannot characterize the possibility of Mrs. Kunkel choosing not to exercise the power of appointment as ‘so remote as to be negligible.’ ” Estate of Kunkel v. United States, 518 F.Supp. 690, 692 (M.D. Pa. 1981). The district court, however, accepted the second argument and held the Pennsylvania inheritance tax unconstitutional insofar as it dis[414]*414tinguished between stepchildren and step-grandchildren:
Plaintiffs succinctly summarize their position as follows:
It is impossible to conceive of a rational basis for a distinction between adopted grandchildren and step-grandchildren whereby the latter should be disadvantaged. Had stepchildren and step-grandchildren been disadvantaged as against adopted children and grandchildren, one might say that the policy advanced by the statute was the encouragement of adoption and thus the stability of families. However, such a policy would not be advanced by a statute which distinguishes, as this one does, between stepchildren and step-grandchildren ....
Defendant has proffered no legitimate state interest to be served by this section of the statute, nor has it established that a rational relationship exists between the statute and a legitimate state interest. The court views the statute in question as an attempt to create additional tax revenues in an arbitrary and capricious manner and finds neither a rational relationship nor a legitimate state interest being served. As such, the statute is unconstitutional on its face. Accordingly, the court will grant plaintiffs’ motion for summary judgment.
Id. at 693-94.
Noting that “[pjlaintiffs claim the amount due them, if they are successful, is $118,084,” id. at 692 n.l, and that the Commissioner had neither admitted nor denied that that particular sum was the correct amount due the taxpayer, the district court “grant[ed] 20 days to show cause why the court should not enter judgment in favor of plaintiff in the amount of $118,084. Failure to respond within the given time will result in the court entering judgment in that amount.” Id. at 694. On August 14,1981, the Commissioner conceded that, if any refund was due, the proper amount was $118,084, and the district court therefore entered judgment in favor of the plaintiff that same day. On October 9, 1981, the Commissioner filed a timely notice of appeal.
II.
On appeal, the Commissioner presents two arguments. First, the district court’s decision should be reversed on the ground that in the circumstances presented by this case, resolution of the constitutional question was unnecessary.5 Second, if the merits of the taxpayer’s constitutional claim are to be reached, the district court’s holding that Pennsylvania’s inheritance tax scheme violates the equal protection clause is unsupportable. We consider each argument in turn.
As we noted in Estate of Brooks v. Commissioner, 250 F.2d 937, 939 (3d Cir. 1958), when a taxpayer seeks to take a charitable deduction on the federal estate tax return, and there is a possibility that some of the money for which the deduction is claimed may be taken back from the charity at a future point and used for non-charitable purposes (such as the payment of additional state inheritance taxes), it is up to the taxpayer to establish that that possibility is so remote as to be negligible. See generally Connecticut Bank and Trust Co. v. United States, 439 F.2d 931, 934-36 (2d Cir. 1971). In the present case, the Commissioner argues that for the reasons outlined below, even a federal court holding that the Pennsylvania inheritance tax violates the equal protection clause could not [415]*415render negligible the possibility that the additional nine percent tax liability would in fact be collected should the trust fund ever pass to the decedent’s stepgrandchildren. Thus, even if this court were to affirm the district court’s constitutional holding on the merits, the Commissioner argues, we would be obliged to conclude that section 2055(c) nevertheless required that the taxpayer take the smaller charitable deduction that results from applying the higher “Class B” rate of fifteen percent. As the constitutional holding would thus have no practical impact on the outcome of the ease — the taxpayer would not be entitled to a refund whether or not this court affirmed the district court’s holding that the Pennsylvania inheritance tax violates the equal protection clause — this court should refrain from reaching the constitutional question in the first place.
The Commissioner’s assertion that the district court’s resolution of the taxpayer’s constitutional claim was superfluous starts from the premise that the Commonwealth of Pennsylvania is not bound by the decision in this case, because it was not a party to the litigation. Consequently, if the trust fund does eventually pass to the decedent’s stepgrandchildren, Pennsylvania will seek to collect the additional nine percent tax due under the state inheritance tax statute. If the taxpayer resists payment of the additional tax, and the matter ends up in the Pennsylvania courts, those courts would not be bound by the district court’s ruling that the state inheritance tax statute is unconstitutional. Thus, the Pennsylvania courts might uphold the statute as constitutional, and the additional nine percent would, in the end, be collected. In those circumstances, not only would a district court’s ruling on a constitutional question turn out to be without any practical effect, but also it would allow the taxpayer to take a charitable deduction for an amount equal to the additional nine percent even though “there is still a significant chance that the additional taxes ‘would waste a part ... of the charitable interest.’ ” Appellant’s Brief at 18 (quoting Henslee v. Union Planters Bank, 335 U.S. 595, 599, 69 S.Ct. 290, 292, 93 L.Ed. 259 (1949)). Such a result would be contrary to the purpose of section 2055(c), which is to ensure that charitable deductions are taken only for sums of money which are certain, or nearly so, to benefit the charity.
The taxpayer replies that the Commonwealth is bound by the district court’s decision, because pursuant to 28 U.S.C. § 2403(b),6 the district court notified the Commonwealth that the constitutionality of its inheritance tax statute was being challenged, and the Commonwealth did not intervene. Even if the Commonwealth is not bound by its failure to intervene, the taxpayer continues, the Commissioner’s argument should be rejected. It would be unjust to force the taxpayer to pay a higher federal estate tax now simply because “there would remain a non-negligible possibility that a Pennsylvania court might wrongly conclude, at some point in the future, that the [Pennsylvania inheritance tax] statute is constitutional.” Appellees’ Brief at 13 (emphasis in original).
We are not persuaded by the Commissioner’s argument. Assuming without deciding that the Commonwealth could not be bound by the district court’s decision, the Commissioner’s position amounts to an assertion that it would never be proper in a section 2055 case to rule on the constitutionality of a state tax statute. In our view, [416]*416however, it would be questionable at best to refrain from passing on a contention that a state tax statute is unconstitutional when— as here — the dispute over the taxpayer’s federal tax liability turns on that very contention. Where the taxpayer seeks a refund, the federal courts provide the only forum in which the taxpayer may present that claim; certainly the taxpayer cannot go to the state courts to seek a refund of federal taxes from the Commissioner.7 Thus we turn to the merits of the taxpayer’s argument that the Pennsylvania inheritance tax violates the equal protection clause.
The statutory classifications under attack here are not based on race, sex, illegitimacy, or other similar factors, nor do they impinge on a fundamental right. Consequently, in order to sustain a challenge to the classifications made by the Pennsylvania inheritance tax statute, the taxpayer has the burden of demonstrating that those classifications are not rationally related to any legitimate state purpose. See generally Hopkins v. Kelsey-Hayes, Inc., 628 F.2d 801, 808-11 (3d Cir. 1980), vacated and remanded on other grounds sub nom. G.D. Searle & Co. v. Cohn, 455 U.S. 404, 102 S.Ct. 1137, 71 L.Ed.2d 250 (1982); Eatough v. Albano, 673 F.2d 671, 675-76 (3d Cir.), cert. denied, -U.S.-, 102 S.Ct. 2931, 73 L.Ed.2d 1331 (1982). In our view, that burden has not been met in the present case, and the district court’s holding that the statute is unconstitutional was in error.
The district court characterized the differential tax rates for bequests to “Class A” and “Class B” beneficiaries as an arbitrary “attempt to create additional tax revenues” by taxing the latter at a higher rate. The purpose of the statute, however, could just as easily be characterized as the promotion of close family relationships: bequests to close relatives are encouraged by taxing those bequests at a lower rate than are bequests to more distant relatives and non-relatives. Having made this observation, the inquiry into the validity of the challenged classifications is at an end; a legitimate purpose has been identified, and a rational relationship between that purpose and the means chosen to foster it has been established. See, e.g., Vance v. Bradley, 440 U.S. 93, 97, 99 S.Ct. 939, 942, 59 L.Ed.2d 171 (1979). It is not for the courts to conduct a more exacting inquiry into the “true” purpose of the statute, or to ask whether some alternative means would have been more closely tailored to achievement of the end sought.
The taxpayer asserts, however, that even under this extremely deferential standard, the statute must be held unconstitutional. While apparently conceding that the promotion of close family relationships is a legitimate aim, the taxpayer asserts that the statute cannot, on any possible rational basis, be considered to advance that aim. If “close relatives” are deemed to be those related by blood to the decedent, then it makes no sense to distinguish between stepchildren (“Class A” beneficiaries) and step-grandchildren (“Class B” beneficiaries). On the other hand, if “close relatives” are those who have close family ties to the decedent, apart from blood relationship, then it is illogical to distinguish between the children of the decedent’s adopted children (“adopt[417]*417ed grandchildren,” who are “Class A” beneficiaries) and the decedent’s stepgrandchildren (“Class B” beneficiaries). Under Pennsylvania law, the taxpayer argues, a stepchild generally cannot be adopted unless the natural parent is dead; thus the decedent might have been as close to his stepchild as he would be to an adopted child, and yet find that, for a reason entirely beyond his control, bequests to his step-grandchildren are taxed at a higher rate than bequests to his adopted grandchildren. See Appellees’ Brief at 16-17.
The fatal difficulty in the taxpayer’s argument, however, is that the equal protection clause does not require that a state, in deciding which bequests to tax at a lower rate, consider only one factor to the exclusion of others. Rather, it is for the legislature, and not the courts, to decide how much weight, if any, to place on factors such as blood relationship and family ties in determining which relatives should be included in “Class A” and which in “Class B.” The exact point at which the lines are drawn inevitably will have a degree of arbitrariness; yet as one court has noted, “[legislative line drawing . . . may produce different tax consequences in nearly identical situations, but such lines must be drawn to make a tax system workable and alterable.” Beals v. Commissioner of Corporations and Taxation, 370 Mass. 781, 352 N.E.2d 692, 695 (1976). That unfortunate, but inevitable degree of arbitrariness, cannot provide a basis for invalidating a statutory classification under the equal protection clause. See Vance v. Bradley, 440 U.S. at 108, 99 S.Ct. at 948 (“[e]ven if the classification ... is to some extent both underinclusive and overinclusive, and hence the line drawn by the [legislature] is imperfect, it is nevertheless the rule that in a case like this ‘perfection is by no means required’ ”).
In so holding, we of course pass no judgment on the admittedly rather obscure wisdom of distinguishing bequests to step-grandchildren from bequests to adopted grandchildren. Our holding instead is based on the fact that if imperfection were grounds for striking down a statute as violative of the equal protection clause, no statute could survive even minimal scrutiny. Thus, as several state courts have recognized when confronted with similar claims that inheritance tax classifications violate the equal protection clause, the legislature must be accorded considerable discretion in the drawing of lines and the establishment of statutory classifications. See In re Estate of Kittenbrink, 200 Neb. 678, 264 N.W.2d 868 (1978) (upholding inheritance tax distinction between nephew related to decedent by blood and nephew not related to decedent by blood); Beals, supra (upholding distinction between adopted children of lineal decedents and natural children of lineal decedents); First National Bank of Denver v. People, 183 Colo. 320, 516 P.2d 639 (1973) (en banc) (upholding distinction between grandchildren and stepgrandchildren).8
Thus, we hold that the Pennsylvania inheritance tax statute, as applied to the facts [418]*418of the present case, does not violate the equal protection clause.
III.
The taxpayer raises one other issue concerning its claim for a refund. As noted earlier, see note 3 supra, the decedent’s will gave an interest in the trust fund not only to Mrs. Kunkel, but also to the stepchildren and stepgrandchildren. Speaking generally, Mrs. Kunkel in effect was given a “life interest” in the trust fund (that is, the right to the trust income for life); the stepchildren were given a “contingent life interest” in the trust fund (that is, the right to the trust income during their lives, contingent upon Mrs. Kunkel’s dying without having exercised her powers of appointment); and the stepgrandchildren were given a “contingent remainder interest” (that is, the right to the corpus of the trust fund, contingent also upon Mrs. Kunkel’s dying without having exercised her powers of appointment).
Before this court, the taxpayer argues that the Commissioner erroneously failed to take account of the fact that the value of the “contingent life interest” the stepchildren received would be taxed at the rate of six percent, not fifteen percent:
[t]he Commissioner assessed additional Federal estate tax based upon the entire remainder of the marital Trust becoming subject to Pennsylvania inheritance tax at 15 percent. However, Decedent’s stepchildren, under Pennsylvania law, are Class A Beneficiaries and the interest passing to them will be taxed at the six percent rate. Thus, even if the statute were constitutionally valid, only the value of the interest passing to the issue of Decedent’s stepchildren would be taxed at the rate of 15-percent.
Appellees’ Brief at 23-24. Characterizing this contention as an attack “on the actuarial computation upon which the adjustment to the estate’s tax liability was made,” Reply Brief at 5, the Commissioner replies that that computation is not in the record, and that the taxpayer never raised the issue before the district court. Thus, the Commissioner concludes, it would be inappropriate for this court to pass on the merits of the taxpayer’s claim, and the taxpayer is not entitled to a remand to the district court for determination of this claim.
We believe that resolution of the taxpayer’s claim for at least a partial refund is properly a matter for the district court in the first instance. Certainly, we are in no position to make the findings of fact necessary to resolve this issue; the only serious question is whether the taxpayer’s failure to raise the issue before the district court should preclude a remand. Under the particular circumstances of this case, we think it should not. Even had the taxpayer raised the issue of the accuracy of the Commissioner’s calculations before the district court, it is highly unlikely that the district court would have passed upon it. Having held that the taxpayer was entitled to a full refund because the Pennsylvania inheritance tax statute violated the equal protection clause, there would have been no reason for the district court to engage in speculation about how much of a partial refund the taxpayer would be due if the statute were constitutional. Even if the issue had been raised before the district court, then, the need for the remand would be just as strong as it is in the present case.9 In that respect, we are faced with a significantly different situation from that presented in the cases on which the Commissioner relies for his assertion that absent extraordinary circumstances, appeals courts will not direct a remand in order “to permit a litigant to repair the gaps in its original trial strategy.” Reply Brief at 7. In Caisson Corp. v. Ingersoll-Rand Co., 622 F.2d 672, 679-81 (3d Cir. 1980), for example, this court expressed concern over the potential for inefficiency and unfairness to the pre[419]*419vailing party that would result if a district court’s evidentiary rulings could be reversed on the basis of arguments presented for the first time on appeal. Had the district court been presented with the alternative argument, the Caisson court noted, it might have ruled differently than it did and so obviated any claim of error. In the present case, on the other hand, given that the district court ruled the statute unconstitutional, we fail to see what difference it would have made had the taxpayer presented its contention that it was due a partial refund if the statute were upheld.10 Thus, we believe that a remand is appropriate to allow the district court to pass on the taxpayer’s claim for a partial refund based on the contention that the Commissioner committed computational or other such errors in determining the taxpayer’s estate tax deficiency.11
IV.
Accordingly, we will reverse the district court’s holding that the Pennsylvania inheritance tax statute violates the equal protection clause, and remand the case for such further proceedings as the district court deems appropriate in light of this opinion.