Wave–particle interactions are described in the quasi-linear formulation by bounce-averaged diffusion coefficients for equatorial pitch angle α 0 and for momentum p , along with a mixed or cross diffusion coefficient D α 0 p . Because the cross terms complicate the associated time-dependent diffusion equation, and because D α 0 p has a somewhat unfamiliar character (e.g., it may be negative), it has frequently been omitted in numerical simulations of multidimensional diffusion. Generally, D α 0 p becomes increasingly important for small values of f pe / f ce , as does D pp , and for small widths of the wave frequency and wavenormal angle distributions. Here we use very simple models of diffusion to investigate the effect of the cross terms, and to demonstrate numerical problems associated with them.