The invention is an improved method of making an improved carbon molecular sieve (CMS) membrane in which a precursor polymer (e.g., polyimide) is pyrolyzed at a pyrolysis temperature to form a CMS membrane that is cooled to ambient temperature (about 40° C. or 30° C. to about 20° C.). The CMS membrane is then reheated to a reheating temperature of at least 250° C. to 400° C. to form the improved CMS membrane. The CMS have a novel microstructure as determined by Raman spectroscopy. The improved CMS membranes have shown an improved combination of selectivity and permeance as well as stability for separating light hydrocarbon gas molecules such as C1 to C6 hydrocarbon gases (e.g., methane, ethane, propane, ethylene, propylene, butane, butylene).