A pervasive, yet little acknowledged feature of international migration to developed countries is that newly arriving immigrants are increasingly highly skilled since the 1980s. This paper analyses the determinants of changes in the skill composition of immigrants using a framework suggested by Grogger & Hanson (2011). We focus on Switzerland, which continuously showed very high immigration rates and dramatic changes in the skill composition of immigrants. In addition, the recent integration of Switzerland into the European labour market in 2002 serves as a policy experiment which allows analysing the influence of a reduction on immigration restrictions on immigrants from European countries in comparison to those from other countries. Our findings suggest that changes of education supply in origin countries and shifts to the relative demand for education groups stand out as the two most important drivers. Yet, while supply alone predicts only a modest increase in the case of highly educated workers and a large increase of middle educated workers, one particular demand channel, the polarisation of labour demand induced by the adoption of computer capital, is crucial to explain the sharp increase in highly educated workers and the mere stabilisation of the share of middle educated immigrant workers. The abolition of quotas for EU residents played a smaller role, yet may have slightly reduced the high skill share among immigrants relative to immigrants from other countries.