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The use of two separate ultraintense laser pulses in laser-proton acceleration was compared to the single pulse case employing the same total laser energy. A double pulse profile, with the temporal separation of the pulses varied between 0.75-2.5 ps, was shown to result in an increased maximum proton energy and an increase in conversion efficiency to fast protons by up to a factor of 3.3. Particle-in-cell simulations indicate the existence of a two stage acceleration process. The second phase, induced by the main pulse preferentially accelerates slower protons located deeper in the plasma, in contrast to conventional target normal sheath acceleration.