We report here significant progresses in both multimode and TEM00-mode solar-pumped laser collection efficiencies by end-side-pumping a 4.0 mm diameter 35 mm length Nd: YAG single-crystal rod with a heliostat parabolic mirror solar energy concentration system. An aspheric fused silica lens was used to couple the concentrated solar radiations from the focal zone of a 1.4 m effective diameter parabolic mirror into the laser rod within a conical pumping cavity. 37.2 W continuous-wave multimode solar laser power was measured, corresponding to 31.5 W/m(2) multimode laser collection efficiency and 8.9% slope efficiency. 9.3 W continuous wave TEM00-mode (M-2 <= 1.2) solar laser power and consequently 7.9 W/m(2) fundamental-mode laser collection efficiency was registered, doubling the previous record.