Continuum solvation models have proven to yield very valuable information about solvation effects, if cavities close to the van der Waals surface of the solutes are used for the calculation of the screening charges. Unfortunately, such cavity size implies that a small but significant portion of the solute electron density reaches out of the cavity. This outlying charge causes serious problems in the context of the dielectric continuum treatment of the solvent. The present paper presents a critical consideration of the origin, the magnitude, and the different strategies for treatment of this problem. Finally, a novel ansatz using an additional, outer cavity is presented which provides rather accurate correction of the corresponding error.