Many scholars have argued that clear and strong property rights are appropriate when transaction costs are low, because property rights encourage people to bargain. This Article shows, however, that uncertain or weakly protected entitlements may produce more efficient trade than absolute property rights-because ''dividing'' claims to an entitlement between two bargainers can induce more forthright negotiation. Liability rules, for example, have an information-forcing quality that can induce more efficient contracting than can property rules. Many other types of entitlement ''divisions'' (including physical, temporal, probabilistic, and activity-level divisions) can also facilitate Coasean trade by inducing more truthful bargaining. More absolute (undivided) property rights are still efficient in many contexts, but the efficiency of such rules cannot be justified by the common, unqualified assertion that property rules encourage trade.