Continuum dielectric representation of solvation requires that a cavity of a certain shape and size is defined for the solute. It is generally assumed that the cavity size is a quantity given by the structure of the solvent around the solute, and that, however complicated, there must be a relationship between the actual solute-solvent structure and the effective cavity size. We show that, when the solvent is not a true continuum (i.e., composed of discrete particles), there is no consistent cavity size even when the geometry of the system is invariant. This requires the ability to separate the structural factors from other system attributes that are mainly expressed in system polarity. Separating the system polarity and structure is virtually impossible in real solvents and ''realistic'' solvent models, while such a separation is inherent in dipole-lattice models. Thus, for representing the discreteness of the solvent we use a dipole-lattice model which has the unique advantage of eliminating electrostriction or other complicating factors associated with structural changes in more detailed solute-solvent descriptions. The optimum cavity radius that gives agreement with the solvation (the so-called ''Born radius'') in a discrete solvent is different for a charge and a dipole, suggesting that a simple cavity-in-a-continuum description of solvation cannot self-consistently capture the correct solvent response to significant changes in the salute charge distribution. Perhaps more interestingly, for a given solute, there is significant variation in the effective cavity size as a function of solvent polarity, even though the structure of the system is constant. Similar trends are obtained with Langevin dipole lattices of simple cubic and face-centered cubic structure, which are known to have rather dissimilar microscopic polarization behavior. Also, the trends obtained with Langevin dipole lattices are very similar to those observed in the more realistic Brownian dipole model of the solvent with explicit thermal fluctuations, whose dielectric constant is known to be a different function of microscopic parameters than a Langevin dipole lattice. Since this diverse set of systems gives similar results, our conclusions are likely to be qualitatively applicable to solvation in real solvents or ''realistic'' models for which the present computational experiment cannot be directly applied. (C) 1997 American Institute of Physics.