Pre-print, Working paper: This paper develops a simple model to explain two stylised facts about immigration. First, some countries have a low ratio of migrants in their population, while other wealthy countries have a high number of migrants. In fact such migrants are of the same order of magnitude as their domestic workforce. Secondly, migrants are often segregated in jobs. The domestic residents do not wish to be employed in these jobs due to their unattractive working conditions and payments. The model assumes that domestic residents are all identical in terms of their skills and wealth and furthermore that native and foreign workers have the same skills. However, foreign migrants cannot be excluded from the use of public services, the quality of which decreases due to congestion created or enhanced by migrants. On the basis of our model we show that the stylised facts are consistent with an optimal immigration policy, defined by domestic residents who have neither altruistic feelings nor ethnic prejudice toward foreign migrants.