Our previous efforts have used in vitro selection to identify numerous Zn(2+)-dependent deoxyribozymes that ligate two RNA substrates with reaction at a 2',3'-cyclic phosphate. Each deoxyribozyme creates one of several different RNA linkages, including native 3'-5' and non-native 2'-5' phosphodiester bonds as well as many unnatural linkages. In this report, we describe experiments to reveal design aspects of the selection strategy that favor site-selective and regioselective synthesis of native 3'-5' RNA linkages. The results also reveal that an explicit selection pressure for RNA substrate sequence generality must be developed if the deoxyribozymes are to have practical generality.