Solar-pumped lasers (SPLs) allow direct solar-to-laser power conversion, and hence, provide an opportunity to harness a renewable energy source. Herein, we report significant improvements in end-side-pumped solar laser collection efficiency and beam brightness using a novel 1.5-m-diameter compound solar concentrator combining a Fresnel lens and modified parabolic mirror. A key component of this scheme is the off-axis-focused parabolic mirror. An original dual-parabolic pump cavity is another feature. To determine the dependence of the SPL performance on the distance between the focus and central axis of the modified parabolic mirror, several systems with different distances were optimized using TracePro and ASLD software. It was numerically calculated that end-side pumping a 5-mm-diameter, 22-mm-long Nd:YAG crystal rod would generate 74.6 W of continuous-wave solar laser power at a collection efficiency of 42.2 W/m2, i.e., 1.1 times greater than the previous record value. Considering the laser beam quality, a brightness figure of 0.063 W was obtained, which is higher than that of other multimode SPL designs with end-side pumping. Thus, our SPL concentrator offers the possibility of achieving a beam quality as high as that obtainable via side pumping, alongside highly efficient energy conversion, which is characteristic to end-side pumping.