A novel method of desulfating lean NOx traps has been developed. Rapid, large amplitude modulation of the air to fuel ratio creates an exotherm of approximately 300°C in the LNT. AFR modulation results in oxidant and reductant breakthough in a three-way catalyst mounted upstream of the LNT. During lean modulation, oxygen is stored in the LNT. During rich modulation, the reductant reacts catalytically with the stored oxygen in the LNT, generating a substantial exotherm. Rich and lean AFR events are selected commensurate with the number of cylinders in the engine, resulting in each cylinder having exactly the same AFR history. This permits a deterministic programming of spark advance and precise coordination of spark advance with the transient fueling effect. The spark advance is retarded for the rich events and increases stepwise for groups of lean events. This strategy results in minimal disturbances in the engine imep.