Large-scale mutational events that occur when stretches of DNA sequence move throughout genomes are called genome rearrange-ment events. In bacteria, inversions are one of the most frequently ob-served rearrangements. In some bacterial families, inversions are biased in favor of symmetry as shown by recent research [6, 8, 10]. In addition, several results suggest that short segment inversions are more frequent in the evolution of microbial genomes [4,6,15]. Despite the fact that symme-try and length of the reversed segments seem very important, they have not been considered together in any problem in the genome rearrange-ment field. Here, we define the problem of sorting genomes (or permu-tations) using inversions whose costs are assigned based on their lengths and asymmetries. We present five procedures and we assess these proce-dure performances on small sized permutations. The ideas presented in this paper provide insights to solve the problem and set the stage for a proper theoretical analysis.