Natural gas is stored in a closed vessel under a pressure of about 1400 to 4500 kPa using a carbon molecular sieve adsorbent having at least 80% of its particle pore volume as micropores having diameters greater than 0.55 nm and less than 0.65 nm, particularly about 0.6 to 0.65 nm. The capacity of such micropores for methane is at least 110 mL methane per mL of carbon (at 300 psig or 2,169 kPa abs.). The deliverable volume of natural gas from a vessel packed with carbon molecular sieve particles is at least 70 times the volume of the vessel. The deliverable volume is optimized by heating a carbonized polymer in the presence of carbon dioxide to increase the pore volume.