Several researchers have illustrated that constraints can improve the results of a variety of clustering algorithms. However, there can be a large variation in this improvement, even for a fixed number of constraints for a given data set. We present the first attempt to provide insight into this phenomenon by characterizing two constraint set properties: inconsistency and incoherence. We show that these measures are strongly anti-correlated with clustering algorithm performance. Since they can be computed prior to clustering, these measures can aid in deciding which constraints to use in practice.