I investigate the criteria that states may legitimately use to select between immigrants, on the assumption that they are entitled to control their borders. I categorise potential immigrants along two dimensions: whether they are refugees or economic migrants, and whether they have a ‘particularity claim’ against the receiving state. In the case of refugees, states are obliged to respond to all those who lodge asylum claims, and to admit their fair share of those who qualify as refugees. But if more than this apply, they are permitted to select who in particular to take. In the case of economic migrants, selection must be based on grounds connected to the national priorities of the host community, interpreted broadly. However immigration policy must give priority to refugees, unless economic migrants can make strong particularity claims.