Increasingly stringent requirements in the manufacture of integrated circuits and microscale devices are demanding new approaches to the design and operation of glow-discharge plasma process reactors. Several approaches have been proposed recently, one of which is the operation of plasma reactors in the pulsed mode where the power input to the reactor is modulated using square-wave pulses (SWPs). In this article, we propose a completely general technique for pulsed operation of plasma reactors where the power input is modulated using pulse shapes that are determined systematically using a computational method. We call this technique optimal pulse shaping (OPS) and it relies on a physical model of the plasma reactor used in conjunction with an optimal control algorithm. The OPS technique enables simultaneous control of several plasma process parameters, thus expanding the accessible plasma parameter space over that achievable by SWPs. We apply the OPS technique to a pure argon high-density plasma reactor. Optimal power input pulse shapes and pulsing frequencies are determined in order to control time-averaged values of the ion number densities, the ratio of metastable-to-ion number densities, and the electron temperatures in the bulk plasma. Results indicate that all optimal power input pulse shapes can be characterized by "on" and "off" periods, with a typical on period consisting of power input spikes accompanied by a lower plateau input. The off period consisting of either a true zero input power or a small input power. The power input spikes during the on period control the averaged ion densities, while the plateau input controls the metastable densities. The average electron temperature is controlled by the off power input.