Non-inductive current drive causes cross-field neoclassical transport in a tokamak, in much the same way that the toroidal electric field used to drive the plasma current produces the so-called Ware pinch. This transport can be either inwards or outwards, depending on the current drive mechanism, and can be either larger or smaller than the analogous Ware pinch. A Green's function formalism is used to calculate the transport produced by wave-driven currents, which is found to be inwards for electron–cyclotron and lower-hybrid current drive. Its magnitude is proportional to the collisionality of the current-carrying electrons and therefore smaller than the Ware pinch when the resonant electrons are suprathermal. In contrast, neutral-beam current drive produces outward particle transport when the beams are injected in the same toroidal direction as the plasma current, and inward particle transport otherwise. This transport is somewhat larger than the corresponding Ware pinch. Together, they may explain an observation made on several tokamaks over the years, most recently on MAST, that density profiles tend to be more peaked during counter-injection.