The Bologna Process in Europe aims to increase student mobility, with the purpose of increasing average university quality through fiercer competition for students in a larger, more unified market. However, this beneficial effect of increased student mobility will only occur if student mobility is guided by quality considerations. We examine whether the quality of a country's higher education system helps explain macro-flows of foreign tertiary students in Europe. Using various measures for the quality of a country's higher education system in an extended gravity model, we find that quality has a positive and significant effect on the size and direction of flows of students exchanged between 31 European countries. At the graduate level, however, the driving force for student mobility appears to be the lack of educational opportunities in the home country.