The authors extend the standard rate equation analysis to obtain expressions for the maximum peak power, maximum pulse energy, and minimum pulsewidth of a single Q-switched output pulse; the maximum power efficiency of a repetitively Q-switched laser; and the corresponding cavity output couplings. Results are obtained analytically and numerically, and a comparison of the two sets of results is made. As a first step in this process the authors derive general expressions for the peak power, pulsewidth, pulse energy, and power efficiency. The authors next differentiate these expressions in order to find the maxima or minima that optimize the parameter of interest. Differentiation is done with respect to the cavity output coupling. >