We present theoretical and practical advances on the Guided Genome Halving problem, a combinatorial optimisation problem which aims at proposing ancestral configurations of extant genomes when one of them has undergone a whole genome duplication. We provide a lower bound on the optimal solution, devise a heuristic algorithm based on subgraph identification, and apply it to yeast gene order data. On some instances, the computation of the bound yields a proof that the obtained solutions are optimal. We analyse a set of optimal solutions, compare them with a manually curated standard ancestor, showing that on yeast data, results coming from different methodologies are largely convergent: the optimal solutions are distant of at most one rearrangement from the reference.