Bacterial CRISPR-Cas systems include genomic arrays of short repeats flanking foreign DNA sequences and provide adaptive immunity against viruses. Integration of foreign DNA must occur specifically to avoid damaging the genome or the CRISPR array, but surprisingly promiscuous activity occurs in vitro. Here we reconstituted full-site DNA integration and show that the Streptococcus pyogenes type II-A Cas1-Cas2 integrase maintains specificity in part through limitations on the second integration step. At non-CRISPR sites, integration stalls at the half-site intermediate, thereby enabling reaction reversal. S. pyogenes Cas1-Cas2 is highly specific for the leader-proximal repeat and recognizes the repeat's palindromic ends, thus fitting a model of independent recognition by distal Cas1 active sites. These findings suggest that DNA-insertion sites are less common than suggested by previous work, thereby preventing toxicity during CRISPR immune adaptation and maintaining host genome integrity.