We report progress toward a general strategy for mimicking the recognition properties of specific α-helices within natural proteins through the use of oligomers that are less susceptible than conventional peptides to proteolysis. The oligomers contain both α- and β-amino acid residues, with the density of the β subunits low enough that an α-helix-like conformation can be adopted but high enough to interfere with protease activity. Previous studies with a different protein-recognition system that suggested ring-constrained β residues can be superior to flexible β residues in terms of maximizing α/β-peptide affinity for a targeted protein surface. Here, we use mimicry of the 18-residue Bim BH3 domain to expand the scope of this strategy. Two significant advances have been achieved. First, we have developed and validated a new ring-constrained β residue that bears an acidic side chain, which complements previously known analogues that are either hydrophobic or basic. Second, we have discovered that placing cyclic β residues at sites that make direct contact with partner proteins can lead to substantial discrimination between structurally homologous binding partners, the proteins Bcl-xL and Mcl-1. Overall, this study helps to establish that α/β-peptides containing ring-preorganized β residues can reliably provide proteolytically resistant ligands for proteins that naturally evolved to recognize α-helical partners.