Abstract. The discussion of exactly which process is causing the preferred build-up of v⁻⁵-power law tails of the velocity distribution of suprathermal particles in the solar wind is still ongoing. Criteria allowing one to discriminate between the various suggestions that have been made would be useful in order to clarify the physics behind these tails. With this study, we draw the attention to the so-called "step feature" of the velocity distributions and offer a criterion that allows one to distinguish between those scenarios that employ velocity diffusion, i.e. second-order Fermi processes, which are prime candidates in the present debate. With an analytical approximation to the self-consistently obtained velocity diffusion coefficient, we solve the transport equation for suprathermal particles. The numerical simulation reveals that this form of the diffusion coefficient naturally leads to the step feature of the velocity distributions. This finding favours – at least in regions of the appearance of the step feature (i.e. for heliocentric distances up to about 11 AU and at lower energies) – the standard velocity diffusion as a consequence of the particle's interactions with the plasma wave turbulence as opposed to that caused by velocity fluctuation-induced compressions and rarefactions.