One approach to meet a perceived increased demand for highly skilled workers has been to use migration policy, providing work permits and visas to highly skilled foreign workers. Our knowledge of how differences in migration policy are related to the skills of migrant populations is however fairly limited, being restricted largely to education. In contrast, we know little about how actual skills of immigrants compare to those of natives, how migrant skills differ according to migration policy, and how this is related to the labour market integration of immigrants. The purpose of this study is to explore these issues focusing on a specific set of generic skills, so-called ‘literacy skills’. Rather than only literacy in the form of reading and mathematical skills, the measure used also captures complex reasoning and problem-solving abilities and should therefore be seen as a measure of broad generic skills. Using data from the International Adult Literacy Survey, nine countries representing a wide range of migration policies are examined; Canada, Germany, Great Britain, Ireland, New Zealand, Norway, Sweden, Switzerland and the USA. The analyses seriously question the belief that stricter selection of immigrants will produce a pool of skilled immigrants, simplify their economic integration and boost national economies. Given the emphasis placed on migrant selection, it is for instance surprising that immigrants in Canada and New Zealand do not perform better. Furthermore, immigrants in Canada and New Zealand do not integrate better than other migrants. Similar results are thus obtained for other countries, with drastically different migration policies. Instead, these results imply that there are many ways to attract highly skilled immigrants and paths to successfully integration.