Although some scholars report that all students are better served by attending more prestigious postsecondary institutions, others have argued that students are better off attending colleges where they are about average in terms of academic ability and suffer worse outcomes if they attend schools that are "out of their league" at which they are "overmatched." The latter argument is most frequently deployed as a paternalistic justification for ending affirmative action. We take advantage of a natural admissions experiment at the University of California to test the effect of being overmatched for students on the margin of admission to elite universities. Consistent with the mismatch hypothesis, we find that students accumulate more credits when they attend less demanding institutions. However, students do not earn higher grades and are no more or less likely to drop out of schools where they are overmatched and are less likely to drop out than they would have been had they attended less demanding institutions.