Commercial polymeric gas separation membranes exhibit a trade-off between productivity and selectivity. However, on this same trade-off curve molecular sieving materials like zeolites and carbon molecular sieves (CMS) lie above the upper bound for polymers. A comparison of the gas transport properties of these three different classes of materials highlights the importance of "entropic selectivity" which has hitherto not been focused on for membrane-based separation of gases. A whole new generation of polymeric membrane materials may result from enhancement of entropic selectivity of polymeric membrane materials.