A pervasive, yet little acknowledged feature of international migration to developed countries is that newly arriving immigrants are increasingly highly skilled. This paper analyses the factors affecting the change in the skill composition of immigrants in Switzerland between 1980 and 2010 using a framework suggested by Grogger & Hanson (2011). Our findings suggest that improved schooling in origin countries of immigrants and a shift in the relative demand for highly educated workers in destinations stand out as the two most important drivers. Yet, while improved schooling would predict only a modest increase in the share of highly educated immigrants and a large increase of middle educated immigrants, we show that demand shifts associated with computerisation are crucial to understand why the share of highly educated immigrants increased sharply while the share of middle educated workers merely stabilised. Additionally, our framework allows evaluating the effect of changes in immigration policy. We find that the recent abolition of quotas for workers from European countries through a bilateral agreement with the EU in 2002 had a small but negative effect on the educational quality of immigrants.