We predict interatomic Calpha distances by two independent data driven methods. The first method uses statistically derived probability distributions of the pairwise distance between two amino acids, whilst the latter method consists of a neural network prediction approach equipped with windows taking the context of the two residues into account. These two methods are used to predict whether distances in independent test sets were above or below given thresholds. We investigate which distance thresholds produce the most information-rich constraints and, in turn, the optimal performance of the two methods. The predictions are based on a data set derived using a new threshold which defines when sequence similarity implies structural similarity. We show that distances in proteins are predicted more accurately by neural networks than by probability density functions. We show that the accuracy of the predictions can be further increased by using sequence profiles. A threading method based on the predicted distances is presented. A homepage with software, predictions and data related to this paper is available at http://www.cbs.dtu.dk/services/CPHmodels/.