Segmental duplications, or low-copy repeats, are common in mammalian genomes. In the human genome, most segmental duplications are mosaics consisting of pieces of multiple other segmental duplications. This complex genomic organization complicates analysis of the evolutionary history of these sequences. Earlier, we introduced a genomic distance, called duplication distance, that computes the most parsimonious way to build a target string by repeatedly copying substrings of a source string. We also showed how to use this distance to describe the formation of segmental duplications according to a two-step model that has been proposed to explain human segmental duplications. Here we describe polynomial-time exact algorithms for several extensions of duplication distance including models that allow certain types of substring deletions and inversions. These extensions will permit more biologically realistic analyses of segmental duplications in genomes.