In this work, we revisit the prediction of gene adjacencies within ancestral genomes, a problem solved in polynomial-time by the DeCo algorithm contributed by Berard et al, which relies on a complex dynamic-programming scheme. More precisely, we assess the robustness of predictions obtained in a parsimonious model by: 1) positing a Boltzmann-Gibbs distribution on the set of (sub)- optimal solution, and analyzing the probabilities associated with the gain/loss of adjacencies; and 2) by using a parametric framework that offers an exact partitioning of the parameter space. Boltzmann probabilities provide a way to filter predictions, and limit the presence of synthenic conflicts within predicted ancestral genomes. The parametric framework reveals an overwhelming robustness of parsimonious predictions to changes in the parameters. This suggests that the predicted ancestral adjacencies primarily depend on the topologies of gene and species trees, rather than on finer properties of the evolutionary model, ie the probabilities/scores associated to the genome rearrangemetn operations. The algorithmic ideas underlying our two main algorithms are generic, and can be easily adapted to any predictive DP algorithm.