In a previous study [Beaudry, A. A., & Joyce, G. F. (1992) Science 257, 635-641], an in vitro evolution procedure was used to obtain variants of the Tetrahymena ribozyme with 100-fold improved ability to cleave a target single-stranded DNA under physiologic conditions. Here we report continuation of the in vitro evolution process to achieve 10(5)-fold overall improvement in DNA-cleavage activity. In addition, we demonstrate that, by appropriate manipulation of the selection constraints, one can optimize specific catalytic properties of the evolved ribozymes. We first reduced the concentration of the DNA substrate 50-fold to favor ribozymes with improved substrate binding affinity. We then reduced the reaction time 12-fold to favor ribozymes with improved catalytic rate. In both cases, the evolving population responded as expected, first improving substrate binding 25-fold, and then improving catalytic rate about 50-fold. The population of ribozymes has undergone 27 successive generations of in vitro evolution, resulting in, on average, 17 mutations relative to the wild type that are responsible for the improved DNA-cleavage activity.