This article examines the role that the choice of a dislocation mobility law has in the study of plastic relaxation at shock fronts. Five different mobility laws, two of them phenomenological fits to data, and three more based on physical models of dislocation inertia, are tested by employing dynamic discrete dislocation plasticity (D3P) simulations of a shock loaded aluminium thin foil. It is found that inertial laws invariably entail very short acceleration times for dislocations changing their kinematic state. As long as the mobility laws describe the same regime of terminal speeds, all mobility laws predict the same degree of plastic relaxation at the shock front. This is used to show that the main factor affecting plastic relaxation at the shock front is in fact the speed of dislocations.