In the deregulated Norwegian electricity market a zonal transmission pricing system is used to cope with network capacity problems. In this paper we illustrate some of the problems with the zonal pricing system as it is implemented in Norway. Using small network examples we illustrate the difficulties involved in defining the zones, the redistribution effects of the surplus that a zonal pricing system has, as well as the conflicting interests concerning zone boundaries that are present among the various market participants. We also show that a zone allocation mechanism based on nodal prices does not necessarily lead to a zone system with maximal social surplus. Finally, we formulate an optimization model that when solved yields the zone system that maximizes social surplus given a pre-specification of the number of zones to be used.