A doubly Q-switched laser can obtain a shorter pulse with a stable repetition rate and high pulse peak power, which has been experimentally proved. By taking into account the Gaussian spatial distributions of the intracavity photon density and the initial population-inversion density as well as the influence of the acousto-optic (AO) Q switch, we introduce the coupled rate equations for a doubly Q-switched laser with both an AO modulator and a {\text{Cr}}^{\text{4+}} -doped saturable absorber. These coupled rate equations are solved numerically. The key parameters of an optimally coupled doubly Q-switched laser are determined based on maximizing the peak power, which include the optimal normalized coupling parameter, the optimal normalized saturable absorber parameters, and the normalized parameters of the AO Q switch. The optimal normalized peak power, the corresponding normalized energy, and the normalized pulse width are also given, and a group of general curves are generated for the first time to our knowledge. The curves can give us a good understanding of the dependence of the optimal key parameters on the parameters of the gain medium, the saturable absorber, the AO Q switch, the resonator, and the spatial distributions of the intracavity photon density. The optimal calculations for a diode-pumped {\text{Nd}}^{\text{3+}}:{\text{YVO}}_{\text{4}} laser with both an AO modulator and a {\text{Cr}}^{\text{4+}}:\text{YAG} saturable absorber are presented to demonstrate the use of the curves and the related formulas.