For recent contractualist accounts of moral cognition, moral judgments should coincide with what rational agents would agree to in a negotiation, accounting for their relative bargaining positions. But past research documents widespread egalitarian moral intuitions; impartiality may also require abstracting away from power asymmetries. How can these perspectives be reconciled? We suggest a key difference lies in whether the logic of bargaining drives the interaction, turning existing asymmetries into bargaining power differences. In Study 1, two parties engage in a take-it-or-leave-it negotiation. In Study 2, they can trade with a third party. In both cases, third-party moral judgments about the morally best split of a fixed amount overwhelmingly favor the advantaged party. They can be precisely predicted using classic models from bargaining theory. By contrast, moral intuitions are completely reversed—reflecting redistributive or egalitarian concerns—in a donation setting where the logic of bargaining does not apply.