CRISPR-Cas systems provide bacteria with adaptive immunity against viruses. During spacer adaptation, the Cas1-Cas2 complex selects fragments of foreign DNA, called prespacers, and integrates them into CRISPR arrays in an orientation that provides functional immunity. Cas4 is involved in both the trimming of prespacers and the cleavage of protospacer adjacent motif (PAM) in several type I CRISPR-Cas systems, but how the prespacers are processed in systems lacking Cas4, such as the type I-E and I-F systems, is not understood. In Escherichia coli, which has a type I-E system, Cas1-Cas2 preferentially selects prespacers with 3′ overhangs via specific recognition of a PAM, but how these prespacers are integrated in a functional orientation in the absence of Cas4 is not known. Using a biochemical approach with purified proteins, as well as integration, prespacer protection, sequencing, and quantitative PCR assays, we show here that the bacterial 3′–5′ exonucleases DnaQ and ExoT can trim long 3′ overhangs of prespacers and promote integration in the correct orientation. We found that trimming by these exonucleases results in an asymmetric intermediate, because Cas1-Cas2 protects the PAM sequence, which helps to define spacer orientation. Our findings implicate the E. coli host 3′–5′ exonucleases DnaQ and ExoT in spacer adaptation and reveal a mechanism by which spacer orientation is defined in E. coli.