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.