Dried regenerated cellulose hollow fiber membranes have been studied for selective removal of moisture from a nitrogen stream. The permeance of water vapor through such a membrane was found to increase exponentially with the relative humidity of the gas stream. Using this permeance expression in a permeator model developed here, an analytical expression has been obtained to estimate the moisture removal capability of the hollow fiber permeator. The experimentally observed permeator performance data are described well by this analytical expression. The selectivity of water vapor over nitrogen as well as individual volatile organic compounds (VOCs), e.g. toluene and methanol, have also been studied in this permeator. The membrane selectivity for H2O over N-2 increased from 20 to 250 as the relative humidity was increased from a very low to a very high level. The membrane was also quite selective for H2O over toluene, much less so for H2O over methanol. For extraction of moisture from a humid atmosphere in space and other applications without drying the atmosphere totally, the regenerated cellulose membrane appears to act as a smart membrane whose moisture permeability is drastically reduced at low relative humidities.