The microstructure and mechanical properties of materials saturate to steady states after severe plastic deformation (SPD). Despite the well-known effect of temperature on the steady-state microstructure, there is no general agreement on the significance of strain rate and the applicability of the Zener-Hollomon parameter in this regard. In this study, several pure metals (aluminum, copper, titanium, and iron) and a Cu–30Zn (wt%) brass alloy have been processed by a high-speed high-pressure torsion (HPT) equipment with controllable rotation speeds in the range of 0.06–60 rpm. It is found that crystallite/grain size, dislocation density, microhardness and shear stress at the steady state are reasonably rate-independent for the von Mises strain rates in the range of 0.004–20 s⁻¹. Because both rates of grain refinement and of dynamic recrystallization are proportional to the strain rate, it is suggested that their balance, which determines the steady state, is rate-independent.