Single-photon avalanche detectors (SPADs) are well-suited for satellite-based quantum communication because of their advantageous operating characteristics as well as their relatively straightforward and robust integration into satellite payloads. However, space-borne SPADs will encounter damage from space radiation, which usually manifests itself in the form of elevated dark counts. Methods for mitigating this radiation damage have been previously explored, such as thermal and optical (laser) annealing. Here we investigate in a lab, using a CubeSat payload, laser annealing protocols in terms of annealing laser power and annealing duration, for their possible later use in orbit. Four Si SPADs (Excelitas SLiK) irradiated to an equivalent of 10 years in low Earth orbit exhibit very high dark count rates (>300 kcps at -22 C operating temperature) and significant saturation effects. We show that annealing them with optical power between 1 and 2 W yields reduction in dark count rate by a factor of up to 48, as well as regaining SPAD sensitivity to a very faint optical signal (on the order of single photon) and alleviation of saturation effects. Our results suggest that an annealing duration as short as 10 seconds can reduce dark counts, which can be beneficial for power-limited small-satellite quantum communication missions. Overall, annealing power appears to be more critical than annealing duration and number of annealing exposures.