The motion of magnetic domain walls induced by spin-polarized current has considerable potential for use in magnetic memory and logic devices. Key to the success of these devices is the precise positioning of individual domain walls along magnetic nanowires, using current pulses. We show that domain walls move surprisingly long distances of several micrometers and relax over several tens of nanoseconds, under their own inertia, when the current stimulus is removed. We also show that the net distance traveled by the domain wall is exactly proportional to the current pulse length because of the lag derived from its acceleration at the onset of the pulse. Thus, independent of its inertia, a domain wall can be accurately positioned using properly timed current pulses.