Cryoadsorption is a promising method of enhancing gravimetric and volumetric onboard H2 storage capacity for future transportation needs. Inexpensive carbide-derived carbons (CDCs), produced by chlorination of metal carbides, have up to 80 % open-pore volume with tunable pore size and specific surface area (SSA). Tuning the carbon structure and pore size with high sensitivity by using different starting carbides and chlorination temperatures allows rational design of carbon materials with enhanced C-H2 interaction and thus increased H2 storage capacity. A systematic experimental investigation of a large number of CDCs with controlled pore size distributions and SSAs shows how smaller pores increase both the heat of adsorption and the total volume of adsorbed H2. It has been demonstrated that increasing the average heat of H2 adsorption above 6.6 kJ mol-1 substantially enhances H2 uptake at 1 atm (1 atm = 101 325 Pa) and -196 °C. The heats of adsorption up to 11 kJ mol-1 exceed values reported for metal-organic framework compounds and carbon nanotubes.