The physics of the interaction of high-intensity laser pulses with underdense plasma depends not only on the interaction intensity but also on the laser pulse length. We show experimentally that as intensities are increased beyond 1020 W cm−2 the peak electron acceleration increases beyond that which can be produced from single stage plasma wave acceleration and it is likely that direct laser acceleration mechanisms begin to play an important role. If, alternatively, the pulse length is reduced such that it approaches the plasma period of a relativistic electron plasma wave, high-power interactions at much lower intensity enable the generation of quasi-mono-energetic beams of relativistic electrons