One or more parameters for denitration or desulfations of a LNT is varied, whereby the saturation of NOx and/or SOx in the LNT is reduced to a lower level when an operating state makes the LNT otherwise less effective or places a greater demand for conversion efficiency on the LNT. The operating state can relate to whether the LNT is at the limit of its effective operating temperature range, a degree of poisoning, or an engine operating state. Selectively tolerating high degrees of sulfur poisoning or NOx saturation during periods of low exhaust flow allows the efficiency of denitrations and/or desulfations to be increased over a large portion of a vehicle's operating cycle, particularly when the engine uses a CVT. Another concept relates to a power generation system comprising an engine tuned to efficiently operate in a narrow speed range for all levels of power output.