Geometrical validation around the Cα is described, with a new Cβ measure and updated Ramachandran plot. Deviation of the observed Cβ atom from ideal position provides a single measure encapsulating the major structure-validation information contained in bond angle distortions. Cβ deviation is sensitive to incompatibilities between sidechain and backbone caused by misfit conformations or inappropriate refinement restraints. A new ϕ,ψ plot using density-dependent smoothing for 81,234 non-Gly, non-Pro, and non-prePro residues with B < 30 from 500 high-resolution proteins shows sharp boundaries at critical edges and clear delineation between large empty areas and regions that are allowed but disfavored. One such region is the γ-turn conformation near +75°,−60°, counted as forbidden by common structure-validation programs; however, it occurs in well-ordered parts of good structures, it is overrepresented near functional sites, and strain is partly compensated by the γ-turn H-bond. Favored and allowed ϕ,ψ regions are also defined for Pro, pre-Pro, and Gly (important because Gly ϕ,ψ angles are more permissive but less accurately determined). Details of these accurate empirical distributions are poorly predicted by previous theoretical calculations, including a region left of α-helix, which rates as favorable in energy yet rarely occurs. A proposed factor explaining this discrepancy is that crowding of the two-peptide NHs permits donating only a single H-bond. New calculations by Hu et al. [Proteins 2002 (this issue)] for Ala and Gly dipeptides, using mixed quantum mechanics and molecular mechanics, fit our nonrepetitive data in excellent detail. To run our geometrical evaluations on a user-uploaded file, see MOLPROBITY (http://kinemage.biochem.duke.edu) or RAMPAGE (http://www-cryst.bioc.cam.ac.uk/rampage). Proteins 2003;50:437–450. © 2003 Wiley-Liss, Inc.