In order to help infer an evolutionary tree (phylogeny) from experimental data, we propose a new method for pre-processing the corresponding dissimilarity matrix, which is related to the property that the distance matrix of a phylogeny (called an additive matrix) describes a sandwich family of chordal graphs. As experimental data often yield distance values which are known to be under-estimated, we address the issue of correcting the data by increasing the distances which are incorrect. This is done by computing, for each graph of the sandwich family, a maximal chordal subgraph.