This paper examines the structure of moral responsibility for outcomes. A central feature of the analysis is a condition that we term the ‘avoidance potential’, which gives precision to the idea that moral responsibility implies a reasonable demand that an agent should have acted otherwise. We show how our theory can allocate moral responsibility to individuals in complex collective action problems, an issue that sometimes goes by the name of ‘the problem of many hands’. We also show how it allocates moral responsibility in the classic Frankfurt example.