This paper presents a constraint-based method for improving protein docking results. Efficient constraint propagation cuts over 95% of the search time for finding the configurations with the largest contact surface, provided a contact is specified between two amino acid residues. This makes it possible to scan a large number of potentially correct constraints, lowering the requirements for useful contact predictions. While other approaches are very dependent on accurate contact predictions, ours requires only that at least one correct contact be retained in a set of, for example, one hundred constraints to test. It is this feature that makes it feasible to use readily available sequence data to predict specific potential contacts. Although such prediction is too inaccurate for most purposes, we demonstrate with a Naïve Bayes Classifier that it is accurate enough to more than double the average number of acceptable models retained during the crucial filtering stage of protein docking when combined with our constrained docking algorithm. All software developed in this work is freely available as part of the Open Chemera Library.