This paper asks two questions about spatial competition. First, does spatial price discrimination lead to lower prices and higher welfare than mill pricing? If firms hold the Bertrand conjecture, the answer is yes for most values of fixed cost. But for the Cournot conjecture, the opposite is true. Second, does the introduction of space into the oligopoly models of Bertrand and Cournot change their results? The answer is generally no; however, spatial Bertrand prices exceed marginal cost, unlike their spaceless counterparts. These answers are obtained using models of spatial competition, of which the Cournot mill pricing models are new. IN SPATIAL competition, significant transport costs and economies of scale bestow market power upon firms. This paper addresses two questions about spatial competition. First, does spatial price discrimination yield lower prices and higher social welfare (producer plus consumer surplus) than fo.b. mill pricing? Under spatial price discrimination, differences in the delivered prices charged by a firm bear no necessary relationship to differences in transport costs. In contrast, a mill pricing firm sets a single price at its plant, and customers bear the cost of transport. This paper answers this question for the cases in which firms adopt the Bertrand or Cournot conjectures concerning how rivals will react to price and output changes. This question is important because of the superficial appeal of mill pricing, which stems from its imitation of the spatial structure of marginal costs. The presence of spatial price discrimination, by contrast, is often considered to be evidence of the presence of market power. At least in part for these reasons, the US Robinson-Patman antitrust act and Great Britain's Price Commission favor mill pricing. Nevertheless, spatial price discrimination remains ubiquitous in the US, Europe, and Japan (Greenhut [1981]). The second question is: how does the introduction of space into the original oligopoly models of Cournot and Bertrand change their results? Cournot