We describe a number of heuristicsfor inferring the gene orders of the hypothetical ancestral genomes in a fixed phylogeny. The optimization criterion is the minimum number of breakpoints (pairs of genes adjacent in one genome but not the other) in the gene orders of two genomes connected by an edge of the tree, summed over all edges. The key to the method is an exact solution for trees with three leaves (the median problem) based on a reduction to the Traveling Salesman Problem.