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: (α) one subject shortlists a block of three options before the other chooses one among them, (b) both subjects veto options simultaneously and in a block, and (c) both subjects veto options simultaneously and gradually one after the other. We document that the non-symmetric shortlisting mechanism (α) is highly efficient, but our data also suggest the existence of a first-mover advantage as subjects become more experienced. The simultaneous mechanism (b) is less efficient than (α) and generates a high level of ex-post inequality. The gradual veto mechanism (c) is no less efficient than (α), but has the important advantage of shutting down the possibility of any first-mover advantage.