We have determined the general constraints that govern sequence divergence in proteins that retain entirely, or very largely, the same structure and function. To do this we collected data from three different groups of orthologous sequences: those found in humans and mice, in humans and chickens, and in Escherichia coli and Salmonella enterica. In total, these organisms have 21,738 suitable pairs of orthologs, and these contain nearly 2 million mutations. The three groups differ greatly in the taxa from which they come and/or in the time that separates them from their last common ancestor. Nevertheless, the results we obtain from the three different groups are strikingly similar. For each group, the orthologous sequence pairs were assigned to six different divergence categories on the basis of their sequence identities. For categories with the same divergence, common accepted mutations have similar frequencies and rank orders in the three groups. With divergence, the width of the range of common mutations grows in the same manner in each group. We examined the distribution of mutations in protein structures. With increasing divergence, mutations increase at different rates in the buried, intermediate, and exposed regions of protein structures in a manner that explains the exponential relationship between the divergence of structure and sequence. This work implies that commonly allowed mutations are selected by a set of general constraints that are well defined and whose nature varies with divergence.