This study presents a simplified model of a midsized vehicle powered by a polymer electrolyte membrane fuel cell stack together with a lead-acid battery as an energy buffer. The model is used with dynamic programming in order to find the optimal coordination of the two power sources while penalizing transient excursions in oxygen concentration in the fuel cell and the state of charge in the battery. The effects of the battery size on the overall energy losses for different drive cycles are determined, and the optimal power split policies are analyzed to quantify all the energy losses and their paths in an effort to clarify the hybridization needs for a fuel cell vehicle with constraints on dynamically varying variables. Finally, a causal nonpredictive controller is presented. The battery sizing results from the dynamic programming optimizations and the causal controller are compared.