The COMPARABILITY EDITING problem appears in the context of hierarchical disease classification based on noisy data. We are given a directed graph G representing hierarchical relationships between patient subgroups. The task is to identify the minimum number of edge insertions or deletions to transform G into a transitive graph, that is, if edges (u, v) and (v, w) are present then edge (u, w) must be present, too. We present two new approaches for the problem based on fixed-parameter algorithmics and integer linear programming. In contrast to previously used heuristics, our approaches compute provably optimal solutions. Our computational results demonstrate that our exact algorithms are by far more efficient in practice than a previously used heuristic approach. In addition to the superior running time performance, our algorithms are capable of enumerating all optimal solutions, and naturally solve the weighted version of the problem.