By way of a discussion of the deliberately hard case of humanitarian intervention, this article considers the merits of an alternative cosmopolitan ethics to that of liberal cosmopolitanism, one which founds its universalism on an ethics of hospitality rather than the rights of man. Jacques Derrida describes the ethics of hospitality as defined by an unconditional welcome which nonetheless must become conditional in order to function. This leads to a profound paradox - an 'undecidability' - in the practice of the ethics of hospitality, the implications of which need to be better understood if the ambition of 'another cosmopolitanism' is to be realised. Interrogating the ethics of hospitality and the undecidability to which it gives rise in relation to humanitarian intervention, it is argued that responsibilities to others, which sometimes imply intervention, must always be kept in tension with openness to the coming of the Other, which limits intervention. Far from being blind or paralysing action, such 'bounded undecidability', it is suggested, actually defines the site of responsible, just decisions in humanitarian intervention.