The high-activity waste from Savannah River Site fuel reprocessing is stored as a two-layered mixture in mild steel tanks. The solid layer contains the hydrolyzable cations, including most of the actinides; the supernatant liquid is a strong base-salt solution that includes I37Cs. To gain storage capacity, the supernate is evaporated to solids, then redissolved for waste processing. The solubility of uranium and plutonium in the supernate is low, but evaporation raises the possibility of an accumulation in the evaporator. This study of uranium and plutonium solubility by statistical design experiments and under simulated evaporator conditions found that uranium solubility decreases to 5 to 10 ppm as the supernate is evaporated; plutonium solubility increases from 1 to ∼10 ppm. The possibility of uranium accumulation in an evaporator exists, but the possibility of plutonium accumulation appears to be small.