A doubly Q-switched laser with both an acousto-optic (AO) modulator and a GaAs saturable absorber can obtain a more symmetric and shorter pulse with high pulse peak power, which has been experimentally proved. The key parameters of an optimally coupled doubly Q-switched laser with both an AO modulator and a GaAs saturable absorber are determined, and a group of general curves are generated for what we believe is the first time, when the single-photon absorption (SPA) and two-photon absorption (TPA) processes of GaAs are combined, and the Gaussian spatial distributions of the intracavity photon density and the initial population-inversion density as well as the influence of the AO Q-switch are considered. These key parameters include the optimal normalized coupling parameter, the optimal normalized GaAs saturable absorber parameters, and the normalized parameters of the AO Q-switch, which can maximize the output energy. Meanwhile, the corresponding normalized energy, the normalized peak power, and the normalized pulse width are given. The curves clearly show the dependence of the optimal key parameters on the parameters of the gain medium, the GaAs saturable absorber, the AO Q-switch, and the resonator. Sample calculations for a diode-pumped {\text{Nd}}^{\text{3+}}{\text{:YVO}}_{\text{4}} laser with both an AO modulator and a GaAs saturable absorber are presented to demonstrate the use of the curves and the relevant formulas.