Subluminal and superluminal light pulses have attracted considerable attention in recent decades1,2,3,4, opening perspectives in telecommunications, optical storage and fundamental physics5. Usually achieved in matter, superluminal propagation has also been demonstrated in vacuum with quasi-Bessel beams6,7 or spatio-temporal couplings8,9. Although, in the first case, the propagation was diffraction free, but with hardly controllable pulse velocities and limited to moderate intensities, in the second, high tunability was achieved, but with substantially lengthened pulse durations. Here we report a new concept that extends these approaches to relativistic intensities and ultrashort pulses by mixing spatio-temporal couplings and quasi-Bessel beams to independently control the light velocity and intensity. When used to drive a laser-plasma accelerator10, this concept leads to a new regime that is dephasing free, where the electron beam energy gain increases by more than one order of magnitude.