A bargaining procedure, or mechanism, is a set of rules for two bargainers to follow as they make offers in order to reach a mutually satisfactory agreement on, say, a price. The efficiency of a mechanism is the expected surplus it delivers to the bargainers, relative to the surplus that a social planner would deliver, or that the bargainers themselves might achieve if they truthfully revealed their reservation prices. A theoretical limit on this efficiency is known, as is a specific procedure that achieves this maximum. But this procedure induces players to make offers that do not truly reflect their reservation prices. This paper discusses three procedures that induce honest offers, although they necessarily fail to achieve maximum efficiency. Each procedure has its own characteristics and costs, and each may have some uses in particular circumstances.