A dependence of current-induced domain-wall motion in nanowires on the temporal shape of current pulses is observed. The results show that the motion of the wall is amplified for alterations of the current on a time scale smaller than the intrinsic time scale of the domain wall which is a few nanoseconds in permalloy. This effect arises from an additional force on the wall by the spin-transfer torque due to a fast changing current and improves the efficiency of domain-wall motion. The observations provide an understanding for the efficient domain-wall motion with nanosecond current pulses.