Theoretical arguments and MHD simulations have suggested that the potential drop across the polar-cap ionosphere approaches a constant value when the IMF is very large and southward. This idea has been difficult to test because the conditions producing this effect are extremely rare. During the 31 March 2001 storm the IMF was directed southward for over 6 hours with a magnitude of ~36 nT to ~20 nT while the DMSP-F13 satellite crossed the polar region, obtaining a good measure of the true polar cap potential drop. The observed potentials are compared with predictions from a theoretical model of the saturation process <Hill et al., 1976; Siscoe et al., 2002>. Clear evidence of a non-linear response consistent with the model predictions for height-integrated Pedersen conductivities in the range of 5--10 S are shown.