We study a model inspired by deliberative practice, in which agents selectively disclose evidence about a set of alternatives prior to taking a final decision on them. We are interested in whether such a process, when iterated to termination, results in the objectively best alternatives being selected—thereby lending support to the idea that groups can be wise even when their members communicate with each other. We find that, under certain restrictions on the relative amounts of evidence, together with the actions available to the agents, there exist deliberation protocols in each of the two families we look at (i.e., simultaneous and sequential) that offer desirable guarantees. Simulation results further complement this picture, by showing how the distribution of evidence among the agents influences parameters of interest, such as the outcome of the protocols and the number of rounds until termination.