This paper applies local equilibrium theory to analyze pressure-swing adsorption with short dimensionless contact times for systems with two adsorbable components present in trace amounts in an inert carrier gas. We are interested in finding optimal operating conditions for both separation and purification problems with nonlinear isotherms. We consider Langmuirian systems only; however, several concepts illustrated in this paper apply irrespective of the type of isotherm. By minimizing appropriate objective functions, at the periodic state and for the purification process, the purge step is found to be of short duration, corresponding to low volumetric purge-to-feed ratios and a high degree of incomplete regeneration. In the separation process, higher or lower degrees of regeneration may be appropriate depending on whether the goal is to enrich the purge in the impurities or to recover the light component as product.