A lean NOX trap is a diesel exhaust aftertreatment system is selectively denitrated based on a measure relating to the state and/or the performance of the exhaust aftertreatment system, or a portion thereof comprising the lean NOX trap, reaching a critical value. The critical value is varied according to the demands currently being place on the exhaust aftertreatment system. In one embodiment, the critical value is set based on engine speed-load information. The method regenerates more frequently when exhaust aftertreatment demands are high and less frequently when demands are low. The method improves aftertreatment performance while reducing aftertreatment fuel penalty.