Some present day species have incurred a whole genome doubling event in their evolutionary history, and this is reflected today in patterns of duplicated segments scattered throughout their chromosomes. These duplications may be used as data to halve the genome, i.e. to reconstruct the ancestral genome at the moment of doubling, but the solution is often highly nonunique. To resolve this problem, we take account of outgroups, external reference genomes, to guide and narrow down the search.