Estimates of school voucher impacts on educational attainment have yet to explore heterogeneities in socioeconomic status among disadvantaged minority students. We theorize reasons for these heterogeneities and then estimate experimentally the differential impacts of voucher offers on college enrollment and graduation rates for minority and non-immigrant students from moderately and severely disadvantaged backgrounds. The findings are obtained from a privately sponsored, lottery-based voucher intervention in New York City that began in 1997. College enrollment and degree attainment as of the fall of 2017 were obtained from the National Student Clearinghouse. We find no significant effects of offers on minority students from severely disadvantaged backgrounds but significant effects of six to eight percentage points on those from moderately disadvantaged households. Similar results are obtained for students born of non-immigrant mothers. Some policy implications are discussed.