Does access to 4-year colleges affect degree completion for students who would otherwise attend 2-year colleges? Admission to Georgia’s 4-year public sector requires minimum SAT scores. Regression discontinuity estimates show that access to this sector increases 4-year college enrollment and college quality, largely by diverting students from 2-year colleges. Access substantially increases bachelor’s degree completion rates for these relatively low-skilled students. SAT-retaking behavior suggests students value access to 4-year public colleges, though perhaps less than they should. Our results imply that absolute college quality matters more than match quality, and they suggest potential unintended consequences of free community college proposals.