Structural properties of a protein residue's microenvironment have long been implicated as agents of selective constraint. Although these properties are inherently quantitative, structure-based studies of protein evolution tend to rely upon coarse distinctions between "surface" and "buried" residues and between "interfacial" and "noninterfacial" residues. Using homology-mapped yeast protein structures, we explore the relationships between residue evolution and continuous structural properties of the residue microenvironment, including solvent accessibility, density and distribution of residue-residue contacts, and burial depth. We confirm the role of solvent exposure as a major structural determinant of residue evolution and also identify a weak secondary effect arising from packing density. The relationship between solvent exposure and evolutionary rate (d(N)/d(S)) is found to be strong, positive, and linear. This reinforces the notion that residue burial is a continuous property with quantitative fitness implications. Next, we demonstrate systematic variation in residue-level structure-evolution relationships resulting from changes in global physical and biological contexts. We find that increasing protein-core size yields a more rapid relaxation of selective constraint as solvent exposure increases, although solvent-excluded residues remain similarly constrained. Finally, we analyze the selective constraint in protein-protein interfaces, revealing two fundamentally different yet separable components: continuous structural constraint that scales with total residue burial and a more surprising fixed functional constraint that accompanies any degree of interface involvement. These discoveries serve to elucidate and unite structure-evolution relationships at the residue and whole-protein levels.