We demonstrated that a pair of positions in phosphoglycerate kinase that score highly by three nonparametric covariation measures are important for function even though the positions can be occupied by aliphatic, aromatic, or charged residues. Examination of these pairs suggested that the majority of the covariation scores could be explained by within-clade conservation. However, an analysis of diversity showed that the conservation within clades of covarying pairs was indistinguishable from pairs of positions that do not covary, thus ruling out both clade conservation and extensive homoplasy as means to identify covarying positions. Mutagenesis showed that the residues in the covarying pair were epistatic, with the type of epistasis being dependent on the initial pair. The results show that nonconserved covarying positions that affect protein function can be identified with high precision.