Domain walls in curved Permalloy (Ni(80)Fe(20)) nanowires are depinned by nanosecond current pulses and magnetic fields. A significant dependence of the depinning probability on the pulse length is observed. We measure an oscillatory dependence with a characteristic frequency of 270 MHz. The quality of the Permalloy used for the nanowires is crucial for efficient domain-wall depinning. By sputtering Permalloy on heated substrates we are able to considerably decrease the specific resistance that is found to directly correspond to the depinning field of the domain wall. (c) 2009 American Institute of Physics. {[}DOI: 10.1063/1.3062828]