We develop a model for the reversible denaturation of proteins and for the effects of single-site mutations on the denatured states. The model is based on short chains of sequences of H (hydrophobic) and P (other) monomers configured as self-avoiding walks on the two-dimensional square lattice. The N (native) state is defined as the unique conformation of lowest contact energy, whereas the D (denatured) state is defined as the collection of all other conformations. With this model we are able to determine the exact partition function, and thus the exact native-denatured equilibrium for various solvent conditions, using the computer to exhaustively enumerate every possible configuration. Previous studies confirm that this model shows many aspects of protein-like behavior. The present study attempts to model how the denatured state (1) depends on the amino acid sequence, and (2) is changed by single-site mutations. The model accounts for two puzzling experimental results: (1) the replacement of a polar residue by a hydrophobic amino acid on the surface of a protein can destabilize a native protein, and (2) the "denaturant slope," m = partial delta G/partial c (where c is the concentration of denaturant--urea, guanidine hydrochloride), can sometimes change by as much as 30% due to a single mutation. The principal conclusion of the present study is that, under strong folding conditions, the denatured conformations that are in equilibrium with the native state are not open random configurations. Instead, they are an ensemble of highly compact conformations with a distribution that depends on the residue sequence and that can be substantially altered by single mutations. Most importantly, we conclude that mutations can exert their dominant effects on protein stability by changing the entropy of folding.