CRISPR/Cas9 is a programmable genome editing tool widely used for biological applications and engineered Cas9s have increased discrimination against off-target cleavage compared with wild-type Streptococcus pyogenes (SpCas9) in vivo. To understand the basis for improved discrimination against off-target DNA containing important mismatches at the distal end of the guide RNA, we performed kinetic analyses on the high-fidelity (Cas9-HF1) and hyper-accurate (HypaCas9) engineered Cas9 variants. We show that DNA cleavage is impaired by more than 100- fold for the high-fidelity variants. The high-fidelity variants improve discrimination by slowing the observed rate of cleavage without increasing the rate of DNA rewinding and release. The kinetic partitioning favors release rather than cleavage of a bound off-target substrate only because the cleavage rate is so low. Further improvement in discrimination may require engineering increased rates of dissociation of off-target DNA.