Life uses a common set of 20 coded amino acids (CAAs) to construct proteins. This set was likely canonicalized during early evolution; before this, smaller amino acid sets were gradually expanded as new synthetic, proofreading and coding mechanisms became biologically available. Many possible subsets of the modern CAAs or other presently uncoded amino acids could have comprised the earlier sets. We explore the hypothesis that the CAAs were selectively fixed due to their unique adaptive chemical properties, which facilitate folding, catalysis, and solubility of proteins, and gave adaptive value to organisms able to encode them. Specifically, we studied in silico hypothetical CAA sets of 3-19 amino acids comprised of 1913 structurally diverse α-amino acids, exploring the adaptive value of their combined physicochemical properties relative to those of the modern CAA set. We find that even hypothetical sets containing modern CAA members are especially adaptive; it is difficult to find sets even among a large choice of alternatives that cover the chemical property space more amply. These results suggest that each time a CAA was discovered and embedded during evolution, it provided an adaptive value unusual among many alternatives, and each selective step may have helped bootstrap the developing set to include still more CAAs.