Research on the effect of school choice on student performance has generally been based on small-scale experiments or comparisons of Catholic and public schools in the United States. Recent studies indicate, however, that the market competition stemming from school vouchers does not affect all private schools equally. This study makes use of individual-level register data on the performance of more than 30,000 students in Denmark, where private schools have been voucher-financed for more than 100 years, while public schools are governed and financed by the politico-administrative system. Using an instrumental variable model to exclude selection effects, the results show no significant average effect of private schooling on final examination scores. However, a multilevel model shows that private schools of high socio-economic status perform better than similar public schools, while private schools of low socio-economic status under-perform – even for individual students with high socio-economic status. This indicates that the institutional setting of a voucher system is not enough to raise educational performance in general, arguably because some parents choose schools on the basis of non-academic criteria.