The depinning probability of magnetic domain walls at constrictions by current pulses depends on the external magnetic field and on the temporal shape of current pulses. We investigate the depinning of domain walls in permalloy nanowires in dependence of the rise time of a current pulse. We observe a change in the depinning probability when varying the pulse rise time and the pulse amplitude at a constant magnetic field. The experiments reveal that the current density for domain-wall depinning can be strongly reduced by current pulses with short rise times. (C) 2010 American Institute of Physics. {[}doi:10.1063/1.3518486]