The European debate on immigration is marred by stereotypes, such as the supposition that Europe is full, that asylum seekers can be separated from economic immigrants, that the sending countries suffer from brain drain and that immigrants take jobs away from the population in the receiving countries. Many of these arguments can be reversed, but recently immigrants have indeed been costly to the EU taxpayer. However, demographic decline will force Europe to devise a system by which labour immigration can be profitable again for the host countries.