This paper examines why some Western European countries are more successful in integrating immigrants into the labour market than others. Using data from the Programme for the International Assessment of Adult Competencies (PIAAC), we show how the country-specific immigrant composition and context of reception contribute to immigrants' disadvantages across receiving countries. Because the data provide extensive information about relevant characteristics that were often considered unobservable, we can comprehensively model the immigrant composition in receiving countries. We find considerable cross-country differences in immigrants' disadvantages, both in terms of employment and occupational status. Multivariate analyses highlight that a large part of this variation is explained by differences in immigrant compositions, whereas we find little evidence for context effects. Counterfactual simulations corroborate that the extent to which countries succeed with integrating immigrants into the labour market strongly depends on the composition of the immigrants that they receive.