Magnetic domain wall (DW) motion induced by nanosecond current pulses is investigated in Co/Ni nanowires where the DW motion is driven by either adiabatic spin transfer torque (STT) or spin Hall torque (SHT). The DW displacement, including transient displacement and steady-state displacement, is found to be linearly related to the current pulse duration for both current-induced torques. The transient displacement is found to be less than 10% of the DW displacement. This result implies that the DW position can be controlled by tuning the duration of the current pulse, which enables a robust operation of racetrack memory. (C) 2015 The Japan Society of Applied Physics