A refined implicit aqueous solvation model is proposed for the simulation of biomolecules without the explicit inclusion of the solvent degrees of freedom. The mean force due to solvation is approximated by the derivative of a simple analytic function of the solvent accessible surface area combined with two atomic solvation parameters, as described previously, with the addition of a novel term to account for the interaction of the interior atoms of the solute with the solvent. The extended model is parametrized by comparing the structural properties and energies computed from simulations of six test proteins of varying sizes and shapes using the new solvation energy term with the corresponding values obtained from simulations in vacuum, using the original implicit solvent model and in explicit water, and from the X-ray or NMR model structures. The mean solvation model proposed here improves the structural properties relative to vacuum simulations and relative to the simpler model that neglects the volume contribution, while remaining significantly more efficient than simulations in explicit water.