We describe a novel and general strategy for controlling the activity of RNA-cleaving nucleic acid enzymes (ribozymes and DNAzymes) via the use of RNA and DNA effectors. Whereas in conventional heteroallosteric enzymes (including ribozymes) control of catalysis is achieved by the binding of effector molecules to the enzyme, in our strategy DNA and RNA regulators bind to both the enzyme and the substrate. The design of this system permits the control of catalysis even in the absence of a detailed knowledge of the secondary and tertiary structure of the relevant ribozyme or DNAzyme. Here, we utilize the ability of RNA and DNA to form branched three-way junctions to regulate the RNA-cleaving activity of the in vitro selected "10-23" DNAzyme by three orders of magnitude. Control is exercised by the ability of a DNA or RNA "regulator" to induce formation of stable and catalytically competent "three-way" enzyme-substrate-regulator complexes, relative to otherwise unstable and catalytically poor enzyme-substrate complexes. Such expansively regulated "three-way" ribozyme/DNAzyme systems might find utility in vivo to bring about the catalyzed destruction of one RNA transcript contingent on the presence in its immediate environment of another gene transcript.