Stable and unstable configurations for a curved-mirror optical resonator containing an inhomogeneous focusing medium have been computed on the basis of ray theory. These computations indicate the existence of six distinct regions on the stability chart of Boyd and Kogelnik. Most significantly, resonators initially within three of the regions become more stable, and those within the three remaining regions less stable, when perturbed by focusing effects due to a (convergent) inhomogeneous medium.