We recently reported the identification by in vitro selection of 10MD5, a deoxyribozyme that requires both Mn2+ and Zn2+ to hydrolyze a single-stranded DNA substrate with formation of 5′-phosphate and 3′-hydroxyl termini. DNA cleavage by 10MD5 proceeds with kobs=2.7 h(−1) and rate enhancement of 10(12) over the uncatalyzed P−O hydrolysis reaction. 10MD5 has a very sharp pH optimum near 7.5, with greatly reduced DNA cleavage rate and yield when the pH is changed by only 0.1 unit in either direction. Here we have optimized 10MD5 by reselection (in vitro evolution), leading to variants with broader pH tolerance, which is important for practical DNA cleavage applications. Because of the extensive Watson−Crick complementarity between deoxyribozyme and substrate, the parent 10MD5 is inherently sequence-specific; i.e., it is able to cleave one DNA substrate sequence in preference to other sequences. 10MD5 is also site-specific because only one phosphodiester bond within the DNA substrate is cleaved, although here we show that intentionally creating Watson−Crick mismatches near the cleavage site relaxes the site specificity. Newly evolved 10MD5 variants such as 9NL27 are also sequence-specific. However, the 9NL27 site specificity is relaxed for some substrate sequences even when full Watson−Crick complementarity is maintained, corresponding to a functional compromise between pH tolerance and site specificity. The site specificity of 9NL27 may be restored by expanding its “recognition site” from ATGT (as for 10MD5) to ATGTT or larger, i.e., by considering 9NL27 to have reduced substrate sequence tolerance relative to 10MD5. These findings provide fundamental insights into the interplay among key deoxyribozyme characteristics of tolerance and selectivity, with implications for ongoing development of practical DNA-catalyzed DNA hydrolysis.