This article considers a previously overlooked feature in carbon molecular sieve (CMS) membranes that we term a "hyperskin" present at the outermost region of dense CMS selective layers. Such a feature with much lower permeability, but similar selectivity compared to the bulk of the skin, reduces CMS hollow fiber permeance below that predicted from corresponding dense films. Effects of the hyperskin are considered for CMS hollow fibers with low skin thicknesses based on two polyimide precursors - Matrimid (R) and 6FDA:BPDA-DAM. Although the fundamental formation mechanism for the hyperskin feature suggests its existence on virtually all CMS membranes, its impact on transport properties is shown to differ dramatically, depending on the detailed characteristic properties of the specific CMS membrane. Indeed, for hollow fibers with very low nominal resistance (i.e. Selective layer thickness determined by SEM/Intrinsic permeability of thick dense CMS films), the observed permeance only reaches a small fraction of the predicted permeance. The selectivity between different gas penetrants, however, is not altered by the presence of this hyperskin. While identifying this issue is the major focus of this article, strategies to address this limitation, without compromising the molecular sieving properties of CMS membranes are briefly discussed.