D-brane actions are known to receive higher derivative corrections involving the bulk metric which can make key contributions to tadpole equations, and hence understanding these terms is important for determining the consistency of vacua. Consistency with T-duality implies that there should also be higher derivative couplings involving the B-field, and these terms, too, will be important for the consistency of certain classes of constructions. We use T-duality to predict some of these couplings, and then verify their form by computing disc amplitudes.