Using the local non-linear equilibrium approach, we investigated pressure-swing-adsorption (PSA) cycles directed toward the removal of an adsorbable impurity present in large amounts in an inert substance. Three blowdown policies are compared (the blowdown is the part of the PSA cycle in which the pressure of a column is released by rejecting gas). In one such policy, the gas resulting from blowdown is rich in the impurity and is rejected as waste. In a second policy in contrast, the production is adjusted so that the blowdown gas is pure and is considered as a product or is reused to recompress or purge another column. The third policy is intermediate, in the sense that part of the blowdown gas is pure and recovered, and part is impure and rejected. The equilibrium approach presented neglects mass-transfer and dispersion effects, but accounts for non-linear equilibria and variations in gas velocity. It thus allows analytical or semi-analytical expressions to be obtained for quantities such as the inert recovery ratio, and hence an easy qualitative discussion of the effects of operating parameters on the recovery. It is shown that the intermediate policy (partial recovery of the blowdown gas) is optimal. The adsorption of methane and ethane on activated carbon from helium or hydrogen are presented as illustrations.