The absence of property rights leads to dissipation of resource rents in fisheries. Economists have long recommended the assignment of property rights to the fishery as a means to internalize the stock externalities that lead to rent dissipation. However, there is less agreement and little research on the optimal nature of property rights for fisheries. Sole ownership of the fishery, while potentially efficient, is generally not politically acceptable. Individual transferable quota (ITQ) systems may fail to achieve an efficient outcome for a variety of reasons, many of which are related to spatial phenomena. Territorial user rights in fisheries (TURFs), also will generally fail to achieve efficient outcomes. This paper illustrates a number of cases where inefficiency may persist in a rights-based fishery management system. Some of the potential benefits and costs of territorial stock use rights in fisheries (T-SURFs) are discussed along with the role of marine zoning.