Subluminal and superluminal light pulses have attracted a considerable attention in the past decades [1][2][3][4] opening perspectives in telecommunications, optical storage, and fundamental physics 5 . Usually achieved in matter, superluminal propagation has also been demonstrated in vacuum with quasi-Bessel beams 6, 7 or Spatio-Temporal Couplings 8, 9 (STCs). While in the first case the propagation was diffraction-free, but with hardly controllable pulse velocities and limited to moderate intensities, in the second a high tunability was achieved, yet with significantly lengthened pulse durations. Here, we report on a new concept that extends these approaches to relativistic intensities and ultra-short pulses by mixing STCs and quasi-Bessel beams to control independently the light velocity and intensity. When used to drive a Laser-Plasma Accelerator 10 (LPA), this concept leads to a new regime, dephasing-free, where the electron beam energy gain increases by more than one order of magnitude.Electrical breakdown limits electric fields in radio frequency accelerators to about 100 MeV/m. LPAs commonly overcome this restriction by focusing ultra-short laser pulses in a gas to generate