For contractualist accounts of morality, actions are moral if they correspond to what rational agents would agree to do, were they to negotiate explicitly. This, in turn, often depends on each party's bargaining power and on their outside options: what each of them could get in the absence of agreement. If there is an asymmetry, with one party enjoying higher bargaining power than another, this party can usually get a better deal — as often happens in real negotiations. A strong test of contractualist accounts of morality, then, is whether moral judgments do take bargaining power into account. We explore this in three preregistered experiments (n = 1,616). We construct scenarios depicting everyday interactions between two parties in which one of them can perform a mutually beneficial but unpleasant action. We find that the same actions (asking the other to perform the unpleasant action, or explicitly refusing to do it) are perceived as less morally appropriate when performed by the party with worse outside options, as compared to the party with better outside options. Thus, participants tend to give more moral leeway to the party with higher bargaining power, and to hold the disadvantaged party to stricter moral standards. This effect appears to depend only on the relative ordering of outside options, but not the magnitude of the difference between them. We discuss implications for contractualist theories of moral cognition and the emergence and persistence of unfair norms and inequality.