The effect of solvation by a continuum dielectric on the size of an ion is examined using electronic structure calculations. Various measures correlated with size are considered, including the root-mean-square radius of the electronic charge density, the amount of solute charge penetrating outside the cavity, the electronic radial distribution function, the nucleus-electron potential energy, and the electron-electron potential energy. Calculations are made on several representative ionic solutes, and it is found that every measure indicates that the application of a dielectric makes the cations larger and the anions smaller. These counterintuitive trends are examined, and a plausible explanation is offered for the observed behavior.