This paper studies the cost efficacy of universal over means-tested (targeted) programs, taking advantage of the rich diversity in state rules governing access to state-funded preschool in the U.S. Using age-eligibility rules for identification, I find that attending a state-funded universal preschool generates substantial immediate test score gains, particularly for poor children. Gains for poor children from attending targeted preschool are significantly smaller. These findings are robust to many specification checks, and cross-state differences in alternative care options, demographics, and other key features of the program environment cannot explain the difference in attendance impacts across program types. Impacts of universal public kindergarten and universal pre-K also look substantively similar within the same data, supporting an access interpretation. Benefit-cost ratios of universal programs are favorable despite their relatively high costs per poor child.