We report femtosecond resonant soft x-ray diffraction measurements of the dynamics of the charge order and of the crystal lattice in nonsuperconducting, stripe-ordered La 1.875 Ba 0.125 CuO 4 . Excitation of the in-plane Cu-O stretching phonon with a midinfrared pulse has been previously shown to induce a transient superconducting state in the closely related compound La 1.675 Eu 0.2 Sr 0.125 CuO 4 . In La 1.875 Ba 0.125 CuO 4 , we find that the charge stripe order melts promptly on a subpicosecond time scale. Surprisingly, the low temperature tetragonal (LTT) distortion is only weakly reduced, reacting on significantly longer time scales that do not correlate with light-induced superconductivity. This experiment suggests that charge modulations alone, and not the LTT distortion, prevent superconductivity in equilibrium.