CRISPR immunity depends on acquisition of fragments of foreign DNA into CRISPR arrays. For type I-E CRISPR-Cas systems two modes of spacer acquisition, näive and primed adaptation, were described. Näive adaptation requires just two most conserved Cas1 and Cas2 proteins; it leads to spacer acquisition from both foreign and bacterial DNA and results in multiple spacers incapable of immune response. Primed adaptation requires all Cas proteins and a CRISPR RNA recognizing a partially matching target. It leads to selective acquisition of spacers from DNA molecules recognized by priming CRISPR RNA, with most spacers capable of protecting the host. Here, we studied spacer acquisition by a type I-F CRISPR-Cas system. We observe both näive and primed adaptation. Both processes require not just Cas1 and Cas2, but also intact Csy complex and CRISPR RNA. Primed adaptation shows a gradient of acquisition efficiency as a function of distance from the priming site and a strand bias that is consistent with existence of single-stranded adaption intermediates. The results provide new insights into the mechanism of spacer acquisition and illustrate surprising mechanistic diversity of related CRISPR-Cas systems.