Abstract This paper looks at how migrants with different skill profiles make use of their education in order to avoid unemployment compared with natives in three European countries with significantly different labour markets and policies for attracting highly skilled migration: France, Spain and the UK. The paper also explores the role played by the quality of the education migrants and natives received in accounting for these differentials, an explanation rarely tested in the literature due to a lack of appropriate data. We here use PIAAC data (OECD), which for the first time offers an interesting proxy of the quality of education, namely the cognitive skills of a representative sample of adult workers in our selected countries. The paper reaches three clear conclusions. Firstly, that it is among the most educated that inequality in obtaining returns to education by migrant status reaches a maximum. Secondly, that there are important differences in how this happens across countries, with the UK minimizing migrant-native differentials when compared with France and Spain. And that thirdly, and most surprisingly, differences in cognitive abilities, our proxy of the quality of education, are somewhat irrelevant in explaining this inequality.