This paper proposes a multi-country model of international migration in which college-educated workers choose destination countries, preferred types of visas, and the optimal durations of stay. In this framework, I investigate the global implications of further development of the European Union (EU) program of preferential temporary visas for the highly skilled immigrants and compare them to the effects of income tax allowances for medium-term, college-educated, foreign workers. The two counterfactuals indicate a significant rise in the yearly inflows and total stocks of college-educated immigrants into the EU. The outcomes of the former policy are driven by a “visa-substitution” effect within the group of current migrants, while the latter scenario results in an increase in the pool of international migrants. Both policies induce a “destination–substitution” effect: losses of skilled migrants by non-EU states, which is reinforced by multilateral resistance to migration that is micro-founded in the model.