We discuss the question of which residues are sufficiently important for protein-protein interaction to be under notable evolutionary pressure. Its interest stems from the applicability of this knowledge in the reverse direction, to detect a protein-protein interface on a single protomer, starting from the rate of mutation of participating residues. Using the analysis of trajectories produced by the molecular dynamics simulations, we suggest that, in the case of water soluble proteins, a large fraction of evolutionarily privileged residues can be found by considering the dynamic behavior of the protein interface and by looking for residues which exchange water molecules with the bulk of the solvent outstandingly slowly (tentatively termed "dry residues"). We show that the dry interface residues are better conserved across homologues than the generic "geometric footprint" and can be quite reliably detected through comparative analysis of protein homologues, without strong dependence on the choice of method. Furthermore, we show that dry residues distinguish themselves through a set of biophysical properties consistent with the known mechanisms of protein oligomerization: their compositional shift toward nonpolar, overlap, and co-location with residues exhibiting low mobility, their two- to threefold increased propensity over the rest of the geometric footprint to form hydrogen bonds, and four- to almost tenfold increased likelihood to participate in formation of salt bridges. These properties, consistently, help understand the observed increase in the evolutionary pressure that dry residues experience.