The ancestral karyotype of the house mouse (Mus musculus) consists of 40 acrocentric chromosomes, but numerous races exist within the domesticus subspecies characterized by different metacentric chromosomes formed by the joining at the centromere of two acrocentrics. An exemplary case is present on the island of Madeira where six highly divergent chromosomal races have accumulated different combinations of 20 metacentrics in 500–1000 years. Chromosomal cladistic phylogenies were performed to test the relative performance of Robertsonian (Rb) fusions, Rb fissions and whole-arm reciprocal translocations (WARTs) in resolving relationships between the chromosomal races. The different trees yielded roughly similar topologies, but varied in the number of steps and branch support. The analyses using Rb fusions/fissions as characters resulted in poorly supported trees requiring six to eight homoplasious events. Allowance for WARTs considerably increased nodal support and yielded the most parsimonious trees since homoplasy was reduced to a single event. The WART-based trees required five to nine WARTs and 12 to 16 Rb fusions. These analyses provide support for the role of WARTs in generating the extensive chromosomal diversification observed in house mice. The repeated occurrence of Rb fusions and WARTs highlights the contribution of centromere-related rearrangements to accelerated rates of chromosomal change in the house mouse.