It is commonly believed that variance-optimized wave functions yield "satisfactory" if not, in principle, better estimates of non-energy-related physical properties than their energy-optimized counterparts. We test this notion by calculating a number of ground-state physical properties using a variety of variance- and energy-optimized wave functions for He, H-2, and LiH. We gauge the quality of the properties using as a "metric" the sum of absolute relative errors. Our results suggest that the energy-optimized wave functions consistently provide better estimates of non-energy-related properties than variance-optimized ones. We present qualitative arguments supporting these findings. (C) 2000 American Institute of Physics. [S0021-9606(00)30711-5].