Many strains of the human pathogen Neisseria meningitidis carry a compact Cas9 (NmeCas9) that can serve to limit genetic exchange via natural transformation. Cas9 orthologues (including NmeCas9) have recently been adopted for RNA-guided genome engineering and DNA binding, adding to the need to define better their activities and properties. The present invention examines DNA cleavage activities and substrate requirements of NmeCas9, including a set of unusually complex PAM recognition patterns. Unexpectedly, NmeCas9 is found able to cleave single-stranded DNA (ssDNA) targets in a manner that is RNA-guided but both PAM- and tracrRNA-independent. Beyond the requirement for guide-target pairing, this activity has no apparent sequence requirements, and the cleavage sites are measured from the 5′ end of the DNA substrate's RNA-paired region. These results indicate that tracrRNA domains are not strictly required for enzymatic activation of NmeCas9, and expand the list of targeting activities exhibited by these revolutionary RNA-guided nucleases.