Respiratory complexes are encoded by two genomes (mitochondrial DNA [mtDNA] and nuclear DNA [nDNA]). Although the importance of intergenomic coadaptation is acknowledged, the forces and constraints shaping such coevolution are largely unknown. Previous works using cytochrome c oxidase (COX) as a model enzyme have led to the so-called “optimizing interaction” hypothesis. According to this view, mtDNA-encoded residues close to nDNA-encoded residues evolve faster than the rest of positions, favoring the optimization of protein–protein interfaces. Herein, using evolutionary data in combination with structural information of COX, we show that failing to discern the effects of interaction from other structural and functional effects can lead to deceptive conclusions such as the “optimizing hypothesis.” Once spurious factors have been accounted for, data analysis shows that mtDNA-encoded residues engaged in contacts are, in general, more constrained than their noncontact counterparts. Nevertheless, noncontact residues from the surface of COX I subunit are a remarkable exception, being subjected to an exceptionally high purifying selection that may be related to the maintenance of a suitable heme environment. We also report that mtDNA-encoded residues involved in contacts with other mtDNA-encoded subunits are more constrained than mtDNA-encoded residues interacting with nDNA-encoded polypeptides. This differential behavior cannot be explained on the basis of predicted thermodynamic stability, as interactions between mtDNA-encoded subunits contribute more weakly to the complex stability than those interactions between subunits encoded by different genomes. Therefore, the higher conservation observed among mtDNA-encoded residues involved in intragenome interactions is likely due to factors other than structural stability.