The Nash axioms lead to different results depending on whether the negotiation is framed in terms of gains relative to no agreement or in terms of sacrifices relative to an ideal. We look for a solution that leads to the same result from both perspectives. To do so, we restrict the application of Nash’s IIA axiom to bargaining sets where all options are individually rational and none exceed either party’s ideal point. If we normalize the bargaining set so that the disagreement point is (0; 0) and maximal gains are (1; 1), then any perspective- invariant bargaining solution must lie between the Utilitarian solution and the maximal equal-gain (minimal equal-sacrifice) solution. We show that a modified version of Nash’s symmetry axiom leads to the Utilitarian solution and that a reciprocity axiom leads to the equal-gain (equal-sacrifice) solution, both of which are perspective invariant.