Work of low-skilled migrant workers from developing countries in developed economies is a growing phenomenon and a key political and economic issue. An extensive literature has found (for the most part) that these workers come from the lower part of the skill distribution. This paper revisits the issue, using a self-selection model, a unique data-set on migrant workers as well as on workers that chose not to migrate (?stayers?), and direct estimation of the moments of the latent unobserved skill distributions. The main findings are that there are two dimensions to self-selection: in terms of observed skills, a substantial migration premium lures migrant workers, while very low returns to skills in the foreign economy deter skilled workers, leading to negative self-selection. In terms of unobservable skills, self-selection is found to be positive rather than negative. The latter finding entails substantial increases in mean wages and reduction in wage inequality, relative to random assignment and to the alternative of not migrating. The analysis also demonstrates that estimates of skill premia for migrants – an important issue in the immigration literature – are upward biased if selection is not accounted for. Relevant skills are multi-dimensional, hence assignments in this context are non-hierarchical.