Diffusion of adparticles on stepped surfaces has been investigated via Monte Carlo simulations, with step sites assumed to exert extra binding energy, J(step). In addition repulsive nearest-neighbor interactions were added, either J(NN) = J(step), or J(NN) = - 1/2 J(step). These interactions were also assumed to be present between nearest-neighbor step sites and step and nearest-neighbor terrace sites. For both cases J(NN) largely nullifies trapping by steps and greatly reduces diffusion anisotropy at all coverages and temperatures. However fairly subtle effects balancing NN repulsion and step attraction remain and affect the temperature and coverage behavior of diffusion.