Non-Abelian plasma instabilities play an important role in the non-equilibrium dynamics of a weakly coupled quark-gluon plasma. Using the discretized hard loop framework we calculate the time evolution of soft gluonic fields in a longitudinally free streaming background. Extrapolating our results to energies probed in relativistic heavy-ion collisions we find a pressure anisotropy that persists for a few fm/c. However, the chromofields quickly develop a Boltzmann longitudi- nal energy spectrum, suggesting fast longitudinal thermalization of the quark gluon plasma even though it remains momentum-space anisotropic. In this proceedings contribution we review our recent numerical results, present new results for the scaling of the isotropization time with the initial current fluctuation amplitude, and present tests of the gauge invariance of the extracted longitudinal spectra.