CRISPR-Cas technologies have enabled programmable gene editing in eukaryotes and prokaryotes. However, the leading Cas9 and Cas12a enzymes are limited in their ability to make large deletions. Here, we used the processive nuclease Cas3, together with a minimal Type I-C Cascade-based system for targeted genome engineering in bacteria. DNA cleavage guided by a single CRISPR RNA generated large deletions (7-424 kilobases) in Pseudomonas aeruginosa with near-100% efficiency, while Cas9 yielded small deletions and point mutations. Cas3 generated bidirectional deletions originating from the programmed site, which was exploited to reduce the P. aeruginosa genome by 837 kb (13.5%). Large deletion boundaries were efficiently specified by a homology-directed repair template during editing with Cascade-Cas3, but not Cas9. A transferable 'all-in-one' vector was functional in Escherichia coli, Pseudomonas syringae and Klebsiella pneumoniae, and endogenous CRISPR-Cas use was enhanced with an 'anti-anti-CRISPR' strategy. P. aeruginosa Type I-C Cascade-Cas3 (PaeCas3c) facilitates rapid strain manipulation with applications in synthetic biology, genome minimization and the removal of large genomic regions.