Cas9 (from Streptococcus pyogenes) in complex with a guide RNA targets complementary DNA for cleavage. Here, we developed a single-molecule FRET analysis to study the mechanisms of specificity enhancement of two engineered Cas9s (eCas9 and Cas9-HF1). A DNA-unwinding assay showed that mismatches affect cleavage reactions through rebalancing the unwinding-rewinding equilibrium. Increasing PAM-distal mismatches facilitates rewinding, and the associated cleavage impairment shows that cleavage proceeds from the unwound state. Engineered Cas9s depopulate the unwound state more readily with mismatches. The intrinsic cleavage rate is much lower for engineered Cas9s, preventing cleavage from transiently unwound off-targets. Engineered Cas9s require approximately one additional base pair match for stable binding, freeing them from sites that would otherwise sequester them. Therefore, engineered Cas9s achieve their improved specificity by inhibiting stable DNA binding to partially matching sequences, making DNA unwinding more sensitive to mismatches and slowing down the intrinsic cleavage reaction.