In computable general equilibrium (CGE) models, it is typically assumed that agricultural resources are smoothly substitutable in neoclassical production or cost functions, with flexible wages, rents and prices generating market equilibrium in a setting with full resource employment. 1 Although this specification is often adequate, it is also often inadequate, especially when the analysis focuses on resource allocation and production technology issues. With more disaggregation, which is becoming common in CGE models with an agricultural focus, the use of smooth, twice-differentiable, production or cost functions to specify agricultural technology is increasingly unrealistic. The purpose of this paper is to show how CGE models formulated as non-linear mixedcomplementarity (MC) problems can incorporate alternative, more realistic, specifications of agricultural technology and supply, drawing on the extensive literature on mathematical programming models applied to agriculture.2 First, we present a stylized standard neoclassical CGE model, which is then extended to a CGE-MC format to include Leontief (activity analysis) technology, endogenous determination of the market regime for agricultural factors (unemployment or full employment) and inequality constraints on agricultural factor use. In an analysis of reduced agricultural water supplies in Egypt, it is then shown how such a model can generate realistic results concerning water use and productivity that cannot be captured in a standard CGE model. The main conclusion is that, in analyses focused on agricultural supply issues, CGE-MC models that selectively incorporate features from the mathematical programming literature offer a powerful alternative to standard models. The underlying producer optimization problems for the different situations are presented in an Appendix.