Journal article: We conduct a series of experiments in which two subjects bargain over five options. Following an experimental design closely related to De Clippel et al. (Am Econ Rev 104:3434-3458, 2014), we evaluate the performance of three bargaining mechanisms: (alpha) one subject shortlists a block of three options before the other chooses one among them, (ss) both subjects veto options simultaneously and in a block, and (gamma) both subjects veto options simultaneously and gradually one after the other. We document that the non-symmetric shortlisting mechanism (alpha) is highly efficient, but our data also suggest the existence of a first-mover advantage as subjects become more experienced. The simultaneous mechanism (ss) is less efficient than (alpha) and generates a high level of ex-post inequality. The gradual veto mechanism (gamma) is no less efficient than (alpha), but has the important advantage of shutting down the possibility of any first-mover advantage.