Long-read sequencing of diverse humans has revealed more than 20,000 insertion, deletion, and inversion structural variants spanning more than 12 Mb in a healthy human genome. Most of these variants are too large to detect with short reads and too small for array comparative genome hybridization (aCGH). While the standard approaches to calling structural variants with long reads thrive in the 50 bp to 10 kb size range, they tend to miss exactly the large (>50 kb) copy-number variants that are called more readily with aCGH. Standard algorithms rely on reference-based mapping of reads that fully span a variant or on de novo assembly; and copy-number variants are often too large to be spanned by a single read and frequently involve segmentally duplicated sequence that is not yet included in most de novo assemblies. To comprehensively detect large variants in human genomes, we extended pbsv – a structural variant caller for long reads – to call copy-number variants (CNVs) from read-clipping and read-depth signatures. In human germline benchmark samples, we detect more than 300 CNVs spanning around 10 Mb, and we call hundreds of additional events in re-arranged cancer samples. Together with insertion, deletion, inversion, duplication, and translocation calling from spanning reads, this allows pbsv to comprehensively detect large variants from a single data type.