Private school students do not always perform better in standardized tests. We suggest that this may be explained by choice of private schooling by less capable students in countries where government schools are better suited to talented students. To assess the empirical relevance of this mechanism, we exploit cross-country variation in the PISA 2009 survey of differences between private and state school regarding organizational features that are differently suitable for students with different learning ability. We seek and find evidence of this mechanism's empirical relevance in controlled regressions that treat within-country variation of PISA scores as an indicator of unobserved ability to learn.