MOTIVATION: When comparing the organization of two genomes, it is important not to draw conclusions on their modes of evolution from a single most parsimonious scenario explaining their differences. Better estimations can be obtained by sampling many different genomic rearrangement scenarios. For this problem, the Double Cut and Join (DCJ) model, while less relevant, is computationally easier than the Hannenhalli-Pevzner (HP) model. Indeed, in some special cases, the total number of DCJ sorting scenarios can be analytically calculated, and uniformly distributed random DCJ scenarios can be drawn in polynomial running time, while the complexity of counting the number of HP scenarios and sampling from the uniform distribution of their space is unknown, and conjectured to be #P-complete. Statistical methods, like Markov chain Monte Carlo (MCMC) for sampling from the uniform distribution of the most parsimonious or the Bayesian distribution of all possible HP scenarios are required. RESULTS: We use the computational facilities of the DCJ model to draw a sampling of HP scenarios. It is based on a parallel MCMC method that cools down DCJ scenarios to HP scenarios. We introduce two theorems underlying the theoretical mixing properties of this parallel MCMC method. The method was tested on yeast and mammalian genomic data, and allowed us to provide estimates of the different modes of evolution in diverse lineages. AVAILABILITY: The program implemented in Java 1.5 programming language is available from http://www.renyi.hu/~miklosi/DCJ2HP/.