Prokaryotes use a mechanism called priming to update their CRISPR immunological memory to rapidly counter revisiting, mutated viruses, and plasmids. Here we have determined how new spacers are produced and selected for integration into the CRISPR array during priming. We show that Cas3 couples CRISPR interference to adaptation by producing DNA breakdown products that fuel the spacer integration process in a two-step, PAM-associated manner. The helicase-nuclease Cas3 pre-processes target DNA into fragments of about 30–100 nt enriched for thymine-stretches in their 3′ ends. The Cas1-2 complex further processes these fragments and integrates them sequence-specifically into CRISPR repeats by coupling of a 3′ cytosine of the fragment. Our results highlight that the selection of PAM-compliant spacers during priming is enhanced by the combined sequence specificities of Cas3 and the Cas1-2 complex, leading to an increased propensity of integrating functional CTT-containing spacers.