We study one stage-simultaneous offer bargaining between a buyer and a seller of an indivisible object who have incomplete information about each other’s valuations. The set of possible valuations for each trader is assumed to be finite, and their respective valuations are either independent or positively associated. Pure strategy Bayesian equilibria are shown to be classified by three features: the degree of pooling, the partition of types of each trader induced by offer strategies, and the exact prices quoted by alternative types; these represent three sources of indeterminacy of the “outcome”. Equilibria with maximal separation of alternative trader types may not exist if each trader has at least three alternative valuations. Such equlibria may be interim Pareto-dominated by ex post efficient pooling equilibria when it is common knowledge there are large gains from trade.