The structure of bovine pancreatic trypsin inhibitor could be re-determined both with data at 1.55 and 1.75 Å resolution using direct methods strengthened by the application of about 90 and 130 triplet phases, respectively, assumed known with a mean error of ±20°. From the known triplets a similar number of single phases were derived and used as starting values, thereby reducing or eliminating the need for permuting reflections in the starting set. The known triplets provide better estimates for the mean direction parameters in the corresponding Cochran distributions. This improvement is crucial for obtaining a structure solution. Single phases derived from these triplets could be combined to yield a larger set of triplets which forms the basis for a new figure of merit (FOM). The new FOM appears superior to the conventional ones for initial selection of the best phase model, and can also be used for assessing the correctness of structure expansion if the number of triplet phase relationships is sufficient.