<p>Perspective invariance in Nash bargaining means that it should not matter for the final agreement whether gains with respect to the disagreement payoffs or sacrifices with respect to the maximal payoffs are considered. In a recent paper Nalebuff (Manag Sci 67:577–593, 2021) discusses a version of Nash’s (Econometrica 18: 155– 162, 1950) contraction independence condition that should allow for perspective invariance but then shows that the Nash bargaining solution is not perspective invariant. In contrast, we propose an alternative version of Nash’s Contraction Independence condition that does allow for an extension of the Nash bargaining solution which is perspective invariant. We also study a condition of restricted monotonicity, resulting in, among other solutions, a perspective invariant version of the Kalai-Smorodinsky solution.</p>