A rich theoretical literature describes the disadvantages facing plaintiffs who suffer multiple, or intersecting, axes of discrimination. This article extends extant literature by distinguishing two forms of intersectionality: demographic intersectionality, in which overlapping demographic characteristics produce disadvantages that are more than the sum of their parts, and claim intersectionality, in which plaintiffs who allege discrimination on the basis of intersecting ascriptive characteristics (e.g., race and sex) are unlikely to win their cases. To date, there has been virtually no empirical research on the effects of either type of intersectionality on litigation outcomes. This article addresses that lacuna with an empirical analysis of a representative sample of judicial opinions in equal employment opportunity (EEO) cases in the U.S. federal courts from 1965 through 1999. Using generalized ordered logistic regression and controlling for numerous variables, we find that both intersectional demographic characteristics and legal claims are associated with dramatically reduced odds of plaintiff victory. Strikingly, plaintiffs who make intersectional claims are only half as likely to win their cases as plaintiffs who allege a single basis of discrimination. Our findings support and elaborate predictions about the sociolegal effects of intersectionality.