Consider a model of bargaining, in which two players, 1 and 2, share a pie of size y. The bargaining environment is described by a set of parameters λ that may affect agents’ preferences over the agreement sharing, the status quo outcome, or both. The outcomes (i.e., whether an agreement is reached, and if so the individual shares) and the environment (including the size of the pie) are known, but neither the agents’ utilities nor their threat points. Assuming that the agents adopt a Nash bargaining solution, we investigate the empirical content of this assumption. We first show that in the most general framework, any outcome can be rationalized as a Nash solution. However, if (i) the size of the pie y does not influence the players’ threat points and (ii) there exist (at least) two parameters λ1 and λ2 that are player-specific, in the sense that λi does not influence the utility or the threat point of player j ≠ i, then Nash bargaining generates strong testable restrictions. Moreover, the underlying structure of the bargaining, i.e., the players’ utility and threat point functions, can be recovered under slightly more demanding conditions.