How does morality allocate responsibility for what it requires? I am concerned here with one fundamental part of this question, namely, how morality determines responsibility when multiple agents are capable of contributing to or completing a moral task, and special relationships capable of generating duties with respect to the task are non-existent, insufficient as a moral response, or partly indeterminate. On one view, responsibility falls to the agents who can bear it with the least burden. I show why this is (...) initially attractive and mistaken. Instead, I defend an equity-based approach that accommodates the intuitions that both support and trouble the least-cost principle. One upshot is that sometimes we ought prefer a distribution of responsibility that is more expensive and less local than needed to complete the task. I illustrate the practical significance of the argument in terms of the human rights of refugees. (shrink)