This paper proposes new algorithms for computing pairwise rearrangement scenarios that conserve the combinatorial structure of genomes. More precisely, we investigate the problem of sorting signed permutations by reversals without breaking common intervals. We describe a combinatorial framework for this problem that allows to characterize classes of signed permutations for which one can compute in polynomial time a shortest reversal scenario that conserves all common intervals. In particular we define a class of permutations for which this computation can be done in linear time with a very simple algorithm that does not rely on the classical Hannenhalli-Pevzner theory for sorting by reversals. We apply these methods to the computation of rearrangement scenarios between permutations obtained from 16 synteny blocks of the X chromosomes of the human, mouse and rat.