We investigate the wire-width dependence of the critical current density for the motion of a magnetic domain wall (DW) in asymmetric Co/Ni nanowires, where spin Hall torque dominates the current-induced DW motion. It is found that both the critical current density for DW motion and the pinning field of a DW increase as the wire width decreases and that the critical current density for DW motion is proportional to the pinning field of the DW; this finding suggests a tradeoff between low-power operation and thermal stability in magnetic domain-wall-motion devices driven by spin Hall torque. (C) 2014 The Japan Society of Applied Physics