The immunization of bacteria and archaea against invading viruses via CRISPR adaptation is critically reliant on the efficient capture, accurate processing, and integration of CRISPR spacers into the host genome. The adaptation proteins Cas1 and Cas2 are sufficient for successful spacer acquisition in some CRISPR-Cas systems. However, many CRISPR-Cas systems additionally require the Cas4 protein for efficient adaptation. Cas4 has been implied in the selection and processing of spacer precursors, but the detailed mechanistic understanding of how Cas4 contributes to CRISPR adaptation is lacking. Here, we biochemically reconstitute the CRISPR-Cas type I-D adaptation system and show two functionally distinct adaptation complexes: Cas4-Cas1 and Cas1-Cas2. The Cas4-Cas1 complex recognizes and cleaves protospacer adjacent motif (PAM) sequences in 3′ overhangs in a sequence-specific manner, while the Cas1-Cas2 complex defines the cleavage of non-PAM sites via host-factor nucleases. Both sub-complexes are capable of mediating half-site integration, facilitating the integration of processed spacers in the correct interference-proficient orientation. We provide a model in which an asymmetric adaptation complex differentially acts on PAM-and non-PAM-containing overhangs, providing cues for the correct orientation of spacer integration.