A combinatorial library composition and method for using the library to construct oligomers effective to bind to a selected ligand is disclosed. The library composition includes at least two sets of ar oligomer libraries, each library set having selected oligomer subunit positions filled by known subunits, and other subunit positions containing permutations of subunits. In the selection method, oligomers from each library set are identified, and a new permutation library formed of subunits corresponding to the highest binding affinity oligomers in each library is screened for binding affinity to the selected ligand.