A system, method, and software for controlling regeneration and desulfurization of a NOx adsorber is disclosed. An electronic control unit is connected with an engine for selectively controlling operation of the engine between a rich operating mode and a lean operating mode. A NOx adsorber is in fluid communication with a flow of exhaust from the engine. A NOx adsorber manager module is executable by the electronic control unit to determine the need to operate in a de-NOx mode or a de-SOx mode. If the NOx adsorber manager module determines a need exists to operate in the de-NOx mode and the de-SOx mode at the same time, the NOx adsorber manager module executes the de-SOx mode.