It has been shown previously that the solvation energies of small molecules can be computed to useful accuracy with continuum models of the solvent that separate the solvation energy into electrostatic and nonpolar parts. The electrostatic part of the solvation energy can be computed with detailed solutions of the Poisson equation, but such calculations are time-consuming. This paper examines the reliability of an approximate method for computing electrostatic solvation energies within the continuum model. The central approximation is that, although the electrostatic field is weakened by the high-dielectric solvent, the shape of the field is not influenced by the solvent. This "dielectric screening" approximation appears to work well when used with a nonlinear, lattice-based model of the solvent. Here, it is developed in the context of linear, continuum electrostatics. The optimal screening function is found to depend upon the distribution of charge within the solute. The present dielectric screening method performs well in comparisons with finite-difference solutions of the Poisson equation and with experimental data, for a range of molecular systems.