There is growing evidence that health factors affect tertiary education success in a causal way. This study assesses the effect of sleep quality on academic achievement at university. To this end, we surveyed 804 students about their sleep quality by means of the Pittsburgh Sleep Quality Index (PSQI) before the start of their first exam period in December 2013 at Ghent University. PSQI scores were merged with course marks in this exam period. Instrumenting PSQI scores by sleep quality during secondary education, we find that increasing total sleep quality with one standard deviation leads to 4.85 percentage point higher course marks. Based on this finding, we suggest that higher education providers might be incentivised to invest part of their resources for social facilities in professional support for students with sleep and other health problems.