Pressure shift adsorption (PSA) process for producing a gas stream enriched with compound X from a feed gas stream, using N adsorbers with N≧5, each adsorber being subjected to a pressure cycle having a phase time corresponding to the duration of the pressure cycle divided by the number of adsorbers, and a series of active steps, characterized in that each adsorber n follows the pressure cycle with an offset of one phase time with respect to the pressure cycle of the adsorber n−1 with n≦N, and during each phase time, only one active step or a part of active step takes place.