Absolute fluorescence quantum yields are reported for the rhodamine 6G cation and the fluorescein dianion dyes in nine solvents. This information is combined with previously reported fluorescence lifetimes to deduce radiative and nonradiative decay rates. Along the alcohol series from methanol to octanol, rhodamine 6G displays an increasing radiative rate, in parallel with the square of the refractive index increase, and a slightly decreasing nonradiative rate. Fluorescein is different: the apparent radiative rate actually decreases, suggesting that the emissive species is perturbed in some fashion. For both dyes, fluorescence yields are enhanced in D2O, rising to 0.98, in parallel with a corresponding increase in lifetimes. Protonated solvents invariably give shorter lifetimes and lower quantum yields, contrary to some previous speculation. From this work and an analysis of existing literature values, more precise values have been obtained for two previously proposed absolute quantum yield standards. The yield of fluorescein in 0.1 N NaOH(aq) is 0.925+/-0.015, and for rhodamine 6G in ethanol, it is 0.950+/-0.015. In both cases, the solutions are assumed to be in the limit of low concentration, excited close to their long-wave absorption band and at room temperature but may be either air-saturated or free of oxygen.