We prove that for general models of random gene-order evolution of k xe2x89xa5 3 genomes, as the number of genes n goes to xe2x88x9e, the median value approximates k times the divergence time if the number of rearrangements is less than cn/4 for any c <1. For some c* xe2x89xa5 1, if the number of rearrangements is greater than c*n/4, this approximation does not hold. 