Using an information theoretic formalism, we optimize classes of amino acid substitution to be maximally indicative of local protein structure. Our statistically-derived classes are loosely identifiable with the heuristic constructions found in previously published work. However, while these other methods provide a more rigid idealization of physicochemically constrained residue substitution, our classes provide substantially more structural information with many fewer parameters. Moreover, these substitution classes are consistent with the paradigmatic view of the sequence-to-structure relationship in globular proteins which holds that the three-dimensional architecture is predominantly determined by the arrangement of hydrophobic and polar side chains with weak constraints on the actual amino acid identities. More specific constraints are imposed on the placement of prolines, glycines, and the charged residues. These substitution classes have been used in highly accurate predictions of residue solvent accessibility. They could also be used in the identification of homologous proteins, the construction and refinement of multiple sequence alignments, and as a means of condensing and codifying the information in multiple sequence alignments for secondary structure prediction and tertiary fold recognition.