The functional effects of most amino acid replacements accumulated during molecular evolution are unknown, because most are not observed naturally and the possible combinations are too numerous. We created 168 single mutations in wildtype Escherichia coli isopropymalate dehydrogenase (IMDH) that match the differences found in wild-type Pseudomonas aeruginosa IMDH. 104 mutant enzymes performed similarly to E. coli wild-type IMDH, one was functionally enhanced, and 63 were functionally compromised. The transition from E. coli IMDH, or an ancestral form, to the functional wild-type P. aeruginosa IMDH requires extensive epistasis to ameliorate the combined effects of the deleterious mutations. This result stands in marked contrast with a basic assumption of molecular phylogenetics, that sites in sequences evolve independently of each other. Residues that affect function are scattered haphazardly throughout the IMDH structure. We screened for compensatory mutations at three sites, all of which lie near the active site and all of which are among the least active mutants. No compensatory mutations were found at two sites indicating that a single site may engage in compound epistatic interactions. One complete and three partial compensatory mutations of the third site are remote and lie in a different domain. This demonstrates that epistatic interactions can occur between distant (>20Å) sites. Phylogenetic analysis shows that incompatible mutations were fixed in different lineages.