We report (6 wt %) storage of H2 at T=77 K in processed bundles of single-walled carbon nanotubes at P=2 atmospheres. The hydrogen storage isotherms are completely reversible. D2 isotherms confirm this anomalous low-pressure adsorption and further reveal the effects of quantum mechanical zero point motion. We propose that our post-synthesis treatment of the sample not only improves access for hydrogen to the central pores within individual nanotubes, but also may create a roughened tube surface with an enhanced binding energy for hydrogen. Such an enhancement is needed to understand the strong adsorption at low pressure. We obtain an experimental isosteric heat qst=125 ± 5 meV for processed SWNT materials.