[en] The role of highly vibrationally-excited hydrogen molecules has been postulated to be of great importance in H^- ion sources. However the difficulty of making in-situ measurements has led to a paucity of direct determinations of these species within the plasma of these sources. Recently, vacuum-ultraviolet (VUV) laser absorption spectroscopy has been used to measure the H₂ rovibrational populations up to v'' = 5 and J'' = 8 in a medium-power hydrogen plasma. This work extends those measurements to v'' = 8 and to J'' = 13. The populations of the vibrational levels still appear to be almost Boltzmann. The theoretically predicted plateau is not observed up to the detection limit. The dependence of several vibrational levels on discharge current and filling pressure is shown. 15 refs., 4 figs