The composition of immigrants depends not only on immigrant choice but also on immigration policy, because slots are rationed. Policy determines immigrant attainment, as evidenced by immigrants from Algeria having higher educational attainment than those from Israel or Japan. Theory predicts and evidence confirms that immigrant attainment is inversely related to the number admitted from a source country and positively related to population and education levels at home. A parsimonious specification has only two variables yet explains a majority of the variation in educational attainment of U.S. immigrant groups. The theory and predictions are bolstered by Swedish data.