The development of a smooth solvation potential from which analytic derivatives can be derived is important for molecular applications that require geometry optimization and conformational sampling. Derivatives in conventional boundary element solvation methods are typically treated approximately, and contain singularities that arise from discontinuities in the potential. We present a simple smooth solvation potential that is based on the conductor-like screening model proposed by Klamt and Schuurmann (Klamt, A.; Schuurmann, G. J. Chem. Sec., Perkin. Trans. 2, 1993, 799). The model uses a simple solvent accessible surface with an atomic sphere discretization based on high-order angular quadrature schemes for spherical harmonics. Surface elements are modeled by spherical Gaussian functions with exponents calibrated to obtain the exact Born ion energy and uniform surface charge density and to avoid Coulomb singularities present in conventional point-charge surface element models. The set of linear equations are modified to produce a rigorously smooth solvation potential by allowing the effect of new surface elements to be turned on or off over a finite switching region around each atom. Numerical tests of the method are provided, in addition to discussions of rotational variance, generalization to arbitrary internal dielectric, use of constraints, and extension to a smooth surface area model.