An experiment investigating laser self-focusing in underdense plasmas is presented. It was shown experimentally that the critical power for relativistic self-focusing Pc is not the only relevant parameter, in particular when the laser pulse duration is comparable to plasma particle motion times: ωp-1 for electrons and ωpi-1 for ions. Using time resolved shadowgraphy, it was demonstrated that: (i) a pulse does not relativistically self-focus if its duration is too short compared to ωp-1, even in the case where the power is greater than Pc. This is due to defocusing by the longitudinal wake which is generated by the laser pulse itself. (ii) For pulses longer than ωpi-1, self-focusing can occur even for powers lower than Pc. This is due to the radial expansion of ions, creating a channel whose effect combines with relativistic focusing and helps the pulse to self-focus.