Our previous efforts have used in vitro selection to identify numerous Zn²⁺-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.