For a CRISPR guide RNA (gRNA) with a specific target but activity at known "off-target" sequences, we present a method to screen hundreds of thousands of gRNA variants with short, randomized 5' nucleotide extensions near its DNA-targeting segment-a modification that can increase Cas9 gene editing specificity by orders of magnitude with certain 5'- extension sequences, via some as-yet-unknown mechanism that makes de novo design of the extension sequence difficult to perform manually-to robustly identify extended gRNAs (x-gRNAs) that have been counter-selected against activity at those off-target sites and that exhibit significantly enhanced Cas9 specificity for their intended targets.