It is now clear that a whole-genome duplication (WGD) occurred at the base of the teleost fish lineage. Like the other anciently polyploid genomes investigated so far, teleost genomes now behave like diploids with chromosomes forming pairs at meiosis. The diploidization process is currently poorly understood. It is associated with many gene deletions, such that one of the duplicates is lost at most loci and has also been proposed to coincide with an increase in genomic instability. Here we ask whether WGD is a determinant of the genomic rearrangement rate in teleosts. We study variability of the rates of rearrangement along a vertebrate phylogenetic tree, composed of 3 tetrapods (human, chicken, and mouse) and 3 teleost fishes (zebrafish, Tetraodon, and Takifugu), whose complete genome sequences are available. We devise a simple parsimony method for counting rearrangements, which takes into account various methodological complications caused by the WGD and the subsequent gene losses. We show that there does appear to be an increase in rearrangement rate after WGD, but that there is also a great deal of additional variability in rearrangement rates across species.