We investigate magnetic-field-dependent velocity relaxation due to boundary-roughness scattering in quantum wires, using a two-dimensional (2D) finite-difference wave-packet propagation technique. We find that for low disorder correlation lengths and far away from density-of-states singularities associated with subband minima and saddle points, the Born approximation adequately reproduces the qualitative features of the more general 2D results. However, naive application of the Born approximation in regions where disorder-induced broadening or higher-order scattering become important can lead to substantial errors. In particular, the mobility enhancement associated with the opening of a quasigap in coupled quantum wire structures can be overestimated by as much as several orders of magnitude. ©1997 American Institute of Physics.