Molecular hydrogen yields have been measured in the gamma radiolysis of aqueous solutions with a wide variety of scavengers of the hydrated electron and its precursors. A decrease in molecular hydrogen yield with increasing scavenging capacity of the hydrated electron is found with all solutes. Scavengers with particularly high rate coefficients for reaction with the precursors to the hydrated electron compared to the hydrated electron, such as selenate and to a lesser extent molybdate, show a more rapid decrease in hydrogen yields with increasing scavenging capacity than is observed with the other solutes. The yield of molecular hydrogen is better parametrized by the scavenging capacity for the precursors to the hydrated electron than by the scavenging capacity for the hydrated electron. Good scavengers of precursors to the hydrated electrons do not exhibit a "nonscavengable" hydrogen yield in the high scavenging capacity Limit. These results suggest that the previously accepted "nonscavengable" yield of molecular hydrogen is due to precursors of the hydrated electron and it can be lowered with appropriate scavengers.