We show how global constraints such as transitivity can be treated intensionally in a Zero-One Integer Linear Programming (ILP) framework which is geared to find the optimal and coherent partition of coreference sets given a number of candidate pairs and their weights delivered by a pairwise classifier (used as reliable clustering seed pairs). In order to find out whether ILP optimization, which is NPcomplete, actually is the best we can do, we compared the first consistent solution generated by our adaptation of an efficient Zero-One algorithm with the optimal solution. The first consistent solution, which often can be found very fast, is already as good as the optimal solution; optimization is thus not needed.