The steepest-descent optimization technique has been applied to the equations describing the steady one-dimensional flow process with heat addition. Using a simplified kinetic model for the H2-air combustion process, the effects of mixing, friction, and shock total pressure losses are simulated. The methodology is developed whereby the combustor area variation that results in the optimum system payoff, for a specified set of boundary conditions, can be determined. The specific cases considered had a specified set of initial conditions (Mach 20, 105.8 kft) and 1) minimized the combustor entropy rise for a given total temperature rise AT* or for a specified combustor length and 2) maximized the combustor exit stream thrust for a given AT< or a given combustor exit Mach nurnber. Comparisons to several relevant combustor designs are presented to indicate the improvements that can be realized due to combustor shaping; for the cases considered, improvements of up to 1.7% and 5.0% over the corresponding constant area and constant pressure combustors, respectively, were found. This paper also serves to demonstrate the applicability of optimization techniques to the design and analysis of propulsion systems. The methodology developed can be extended to include more accurate combustor models as well as to consider the tradeoffs between the diffuser, combustor, and nozzle portions of a propulsion system.