This paper considers the optimization of a class of pulse-width-modulated (PWM) control systems via an extended maximum principle. The technique developed here is applicable to single-input-single-output systems with linear plants. The amplitude of the control pulses, as well as the sign and width of each control pulse, is subject to optimization. The resulting optimization problem is shown to be a sequence of suboptimizations via a simple dual choice direct enumeration embedded in the TPBV problem.