The possibility of being able to reverse the toroidal current in a tokamak, without undue loss of plasma, is studied using diffusive magnetohydrodynamics, together with a one-dimensional model in which the torus is represented by a long cylindrical slab. For a plasma with free surfaces, it predicts that the entire plasma will expand outwards and be lost before the current even changes sign. However, interaction of the outer surface with conducting limiters can impede the expansion, and other ways of preserving the plasma may exist in two dimensions, so current reversal may be feasible after all.