We experimentally investigate the impact of pulse shape on the dynamics of laser-generated plasma in rare gases. Fast-rising triangular pulses with a slower decay lead to early ionization of the gas and depose energy more efficiently than their temporally reversed counterparts. As a result, in both argon and krypton, the induced shockwave as well as the plasma luminescence are stronger. This is due to an earlier availability of free electrons to undergo inverse Bremsstrahlung on the pulse trailing edge. Our results illustrate the ability of adequately tailored pulse shapes to optimize the energy deposition in gas plasmas.