Why do liberal states face a moral dilemma when confronted, as many are at present, with pressures for mass inward migration? On the one hand, liberal principles of freedom, equality and human rights push them towards leaving the door as wide open as possible. On the other hand, as democratic welfare states that wish to remain stable over time, they are unavoidably concerned about the size and composition of their own citizen bodies. This impels them to impose limits on immigration and to give priority to those who are already connected in one way or another to the political community. The resulting balance is, however, upset when many of those seeking to enter are refugees. What are liberal states required to do in these circumstances? I argue that because of the arbitrary way in which asylum claims are likely to be lodged, states are morally obliged to co-operate in creating burden-sharing schemes for refugee admissions, and to fulfil their obligations under these schemes. They cannot, however, be forced into such schemes unwillingly, nor can they be obliged to ‘take up the slack’ if other states default once the scheme has been established. As a result, we cannot rule out the possibility of a tragic clash between the human rights of the refugees and the right of a liberal state to control its own destiny.