The finite recovery time Ts of the bleached absorber is presented as one of the possible mechanisms accounting for the increase-maximum-decrease in pulse energy E with the pumping rate Wp in cw-pumped passively Q-switched solid-state lasers, by analytically evaluating the sign of the derivative partial differentialE/ partial differentialWP. The results show that, in the low pump regime (T>Ts, T is the interpulse period), the initial population density ni remains constant, the final population density nf decreases with Wp, and this results in a monotonic increase of E with Wp. In the high pump regime (T<Ts), ni decreases but nf remains the same with Wp; this results in a monotonic decrease of E with Wp. At the critical region (T approximately Ts), E reaches its maximum value. A cw-pumped Yb:YAG laser passively Q switched by a Cr4+:YAG absorber is demonstrated to confirm this model. The theoretical model is also applied to the analysis of three previously reported passive Q switching solid-state [Nd:GdVO4, Nd+:LaSc3(BO3)4 (Nd+:LSB), and Nd:YAG] lasers experiments.