A new engineered version of SpCas9, called HypaCas9, displays enhanced accuracy of editing without significant loss of efficiency at the desired target. One of the main concerns about the use of CRISPR in genomic editing is the possibility of 'off-target' events. Scientists have been modifying the central enzyme involved in CRISPR editing, Cas9 or its homologues, to reduce this unwanted property. Jennifer Doudna and colleagues describe a new version of this nuclease, HypaCas9, which enables more accurate editing, without substantial loss of efficiency on the desired target. The RNA-guided CRISPR–Cas9 nuclease from Streptococcus pyogenes (SpCas9) has been widely repurposed for genome editing1,2,3,4. High-fidelity (SpCas9-HF1) and enhanced specificity (eSpCas9(1.1)) variants exhibit substantially reduced off-target cleavage in human cells, but the mechanism of target discrimination and the potential to further improve fidelity are unknown5,6,7,8,9. Here, using single-molecule Förster resonance energy transfer experiments, we show that both SpCas9-HF1 and eSpCas9(1.1) are trapped in an inactive state10 when bound to mismatched targets. We find that a non-catalytic domain within Cas9, REC3, recognizes target complementarity and governs the HNH nuclease to regulate overall catalytic competence. Exploiting this observation, we design a new hyper-accurate Cas9 variant (HypaCas9) that demonstrates high genome-wide specificity without compromising on-target activity in human cells. These results offer a more comprehensive model to rationalize and modify the balance between target recognition and nuclease activation for precision genome editing.