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Until a few years ago, a set of equations commonly referred to as the Summers relations gave the most accurate description of the critical current in Nb3Sn conductors as a function of applied field, temperature and axial strain. Although highly empirical, they describe reasonably well the critical current data of past Nb3Sn conductors. New data from various types of Nb3Sn conductors, as well as recent analysis of the ITER CS model coil results reveal however, that this description lacks the precision, required to correlate the conductor data to the model coil results. This discrepancy, attributed to the highly empirical background for the relations, manifests itself mainly in the strain- and temperature dependence. The development of an alternative, more accurate description of the behavior of the critical current, starting from a more fundamental description of the strain dependence, has been initiated. At the moment, the development concentrates around the improvement of the temperature dependency relations to achieve a better accuracy of the overall descriptions, especially in the high temperature region.