H2 molecules were ionized by Ti:sapphire (45 fs, 800 nm) and Nd-doped yttrium aluminum garnet lasers (6 ns, 1064 nm). The relative populations of the vibrational levels of the H+2 ions were determined and found to be concentrated in the lowest vibrational levels. Tunneling ionization calculations with exact field-modified potential curves reproduce the experimental results. The reason for the departure from conventional Franck-Condon-like distributions is the rapid variation of the ionization rate with internuclear distance.