The critical current density of multifilamentary Nb3Sn conductors depends on the diameter of the filaments. At low fields (less than about 12 T) increases with decreasing filament diameter because of the finer grain size. At high fields increases with increasing filament diameter. Measurements of the critical current under externally applied tensile stress revealed that changes of the internal compression of the Nb3Sn within the composite account for this effect. The larger the filament diameter, the smaller the compressive strain, the higher the upper critical field and therefore at high fields. The decrease of compressive strain with increasing filament size results from a decrease in the yield stress of the bronze which is caused by an increase in grain size of the bronze between the filaments.