The storage of large quantities of hydrogen at safe pressures is a key factor in establishing a hydrogen-based economy. Previous strategies--where hydrogen has been bound chemically, adsorbed in materials with permanent void space or stored in hybrid materials that combine these elements--have problems arising from either technical considerations or materials cost. A recently reported clathrate hydrate of hydrogen exhibiting two different-sized cages does seem to meet the necessary storage requirements; however, the extreme pressures (approximately 2 kbar) required to produce the material make it impractical. The synthesis pressure can be decreased by filling the larger cavity with tetrahydrofuran (THF) to stabilize the material, but the potential storage capacity of the material is compromised with this approach. Here we report that hydrogen storage capacities in THF-containing binary-clathrate hydrates can be increased to approximately 4 wt% at modest pressures by tuning their composition to allow the hydrogen guests to enter both the larger and the smaller cages, while retaining low-pressure stability. The tuning mechanism is quite general and convenient, using water-soluble hydrate promoters and various small gaseous guests.