Genome doubling simultaneously doubles all genetic markers. Genome rearrangement phylogenetics requires that all genomes analyzed have the same set of orthologs, so that it is not possible to include doubled and unduplicated genomes in the same phylogeny. A framework for solving this difficulty requires separating out various possible local configurations of doubled and unduplicated genomes in a given phylogeny, each of which requires a different strategy for integrating genomic distance, halving and rearrangement median algorithms. In this paper we focus on the two cases where doubling precedes a speciation event and where it occurs independently in both lineages initiated by a speciation event. We apply these to a new data set containing markers that are ancient duplicates in two yeast genomes.