The total order of the genes or markers on a chromosome inherent in its representation as a signed per-mutation must often be weakened to a partial order in the case of real data. This is due to lack of resolution (where several genes are mapped to the same chromosomal position) to missing data from some of the datasets used to compile a gene order, and to conflicts between these datasets. The available genome rearrangement algorithms, however, require total orders as input. A more general approach is needed to handle rearrangements of gene partial orders.