We discuss how a schooling system's structure may imply that private school enrolment leads to worse subsequent performance in further education or in the labour market, and we seek evidence of such phenomena in Italian data. If students differ not only in terms of their families' ability to pay but also in terms of their own ability to take advantage of educational opportunities (talent for short), theory predicts that private schools attract a worse pool of students when publicly funded schools are better suited to foster progress by more talented students. We analyze empirically three surveys of Italian secondary school graduates, interviewed 3 year after graduation. In these data, the impact of observable talent proxies on educational and labour market outcomes is indeed more positive for students who (endogenously) choose to attend public schools than for those who choose to pay for private education.