This paper analyses admission decisions when students from different high school tracks apply for admission to university programmes. I derive a criterion that is optimal in the sense that it maximizes the graduation rates of the university programmes. The paper contains an empirical analysis that documents the relevance of theory and illustrates how to apply optimal admission procedures. Indirect gains from optimal admission procedures include the potential for increasing entire cohorts of students' probability of graduating with a higher education degree, thereby increasing the skill level of the work force.