We use a human-subjects experiment to investigate how bargaining outcomes are affected by changes in bargainers? disagreement payoffs. Subjects bargain against changing opponents, with randomly drawn asymmetric disagreement outcomes that vary over plays of the game, and with complete information about disagreement payoffs and the cake size. We find that subjects only respond about half as much as theoretically predicted to changes in their own disagreement payoff and to changes in their opponent?s disagreement payoff. This effect is observed in a standard Nash demand game and a related unstructured bargaining game, in both early and late rounds, and is robust to moderate changes in stake sizes. We show theoretically that standard models of expected utility maximisation are unable to account for this under-responsiveness, even when generalised to allow for risk aversion. We also show that quantal-response equilibrium has, at best, mixed success in characterising our results. However, a simple model of other-regarding preferences can explain our main results.