Pump-resonant excitation, in which a weakly absorbing gain medium is placed inside an optical cavity that is resonant at both the pump and laser wavelengths, is shown to reduce significantly the losses due to saturable absorption in a quasi-three-level, diode-pumped laser. Initial experiments, in which this technique is applied to the 946-nm Nd:YAG laser, have yielded incident threshold power levels below 1.3 mW and optical slope efficiencies exceeding 25%.