A self-consistent microscopic theory is used to calculate the mobility of rigid univalent ions in methanol, ethanol, and propanol at room temperature. The theoretical predictions are in good agreement with the long-known experimental results. In particular, the theory reproduces the nonmonotonic size dependence of the limiting ionic conductance accurately. The relation between the polar solvation dynamics of an ion and its mobility is clarified. The theory also explains how a dynamical version of the classical solvent-berg model can be recovered for small ions in the limit of slow liquids.