2. Virginia's categorical exclusion of women from the educational opportunities VMI provides denies equal protection to women. Pp. 17–29.

(a) Virginia contends that single sex education yields important educational benefits and that provision of an option for such education fosters diversity in educational approaches. Benign justifications proffered in defense of categorical exclusions, however, must describe actual state purposes, not rationalizations for actions in fact differently grounded. Virginia has not shown that VMI was established, or has been maintained, with a view to diversifying, by its categorical exclusion of women, educational opportunities within the State. A purpose genuinely to advance an array of educational options is not served by VMI's historic and constant plan to afford a unique educational benefit only to males. However well this plan serves Virginia's sons, it makes no provision whatever for her daughters. Pp. 17–22.

(b) Virginia also argues that VMI's adversative method of training provides educational benefits that cannot be made available, unmodified, to women, and that alterations to accommodate women would necessarily be so drastic as to destroy VMI's program. It is uncontested that women's admission to VMI would require accommodations, primarily in arranging housing assignments and physical training programs for female cadets. It is also undisputed, however, that neither the goal of producing citizen soldiers, VMI's raison d'être, nor VMI's implementing methodology is inherently unsuitable to women. The District Court made "findings" on "gender based developmental differences" that restate the opinions of Virginia's expert witnesses about typically male or typically female "tendencies." Courts, however, must take "a hard look" at generalizations or tendencies of the kind Virginia pressed, for state actors controlling gates to opportunity have no warrant to exclude qualified individuals based on "fixed notions concerning the roles and abilities of males and females." Mississippi Univ. for Women, 458 U. S., at 725. The notion that admission of women would downgrade VMI's stature, destroy the adversative system and, with it, even the school, is a judgment hardly proved, a prediction hardly different from other "self fulfilling prophec[ies], see id., at 730, once routinely used to deny rights or opportunities. Women's successful entry into the federal military academies, and their participation in the Nation's military forces, indicate that Virginia's fears for VMI's future may not be solidly grounded. The State's justification for excluding all women from "citizen soldier" training for which some are qualified, in any event, does not rank as "exceedingly persuasive." Pp. 22–29.

3. The remedy proffered by Virginia—maintain VMI as a male only college and create VWIL as a separate program for women—does not cure the constitutional violation. Pp. 29–41.

(a) A remedial decree must closely fit the constitutional violation; it must be shaped to place persons unconstitutionally denied an opportunity or advantage in the position they would have occupied in the absence of discrimination. See Milliken v. Bradley, 433 U.S. 267, 280. The constitutional violation in this case is the categorical exclusion of women, in disregard of their individual merit, from an extraordinary educational opportunity afforded men. Virginia chose to leave untouched VMI's exclusionary policy, and proposed for women only a separate program, different in kind from VMI and unequal in tangible and intangible facilities. VWIL affords women no opportunity to experience the rigorous military training for which VMI is famed. Kept away from the pressures, hazards, and psychological bonding characteristic of VMI's adversative training, VWIL students will not know the feeling of tremendous accomplishment commonly experienced by VMI's successful cadets. Virginia maintains that methodological differences are justified by the important differences between men and women in learning and developmental needs, but generalizations about "the way women are," estimates of what is appropriate for most women, no longer justify denying opportunity to women whose talent and capacity place them outside the average description. In myriad respects other than military training, VWIL does not qualify as VMI's equal. The VWIL program is a pale shadow of VMI in terms of the range of curricular choices and faculty stature, funding, prestige, alumni support and influence. Virginia has not shown substantial equality in the separate educational opportunities the State supports at VWIL and VMI. Cf. Sweatt v. Painter, 339 U.S. 629. Pp. 30–37.