The inversion distance, that is the distance between two unichromosomal genomes with the same content allowing only inversions of DNA segments, can be exactly computed thanks to a pioneering approach of Hannenhalli and Pevzner from 1995. In 2000, El-Mabrouk extended the inversion model to perform the comparison of unichromosomal genomes with unequal contents, combining inversions with insertions and deletions (indels) of DNA segments, giving rise to the inversion-indel distance. However, only a heuristic was provided for its computation. In 2005, Yancopoulos, Attie and Friedberg started a new branch of research by introducing the generic double cut and join (DCJ) operation, that can represent several genome rearrangements (including inversions). In 2006, Bergeron, Mixtacki and Stoye showed that the DCJ distance can be computed in linear time with a very simple procedure. As a consequence, in 2010 we gave a linear-time algorithm to compute the DCJ-indel distance. This result allowed the inversion-indel model to be revisited from another angle. In 2013, we could show that, when the diagram that represents the relation between the two compared genomes has no bad components, the inversion-indel distance is equal to the DCJ-indel distance. In the present work we complete the study of the inversion-indel distance by giving the first algorithm to compute it exactly even in the presence of bad components.