A palladium-only (i.e., platinum free) oxidation catalyst body is used to oxidize carbon monoxide and hydrocarbons in the exhaust stream of a diesel engine powered vehicle, which is operated at a fuel-lean air-to-fuel ratio (A/F) for much of the time it powers a vehicle. Periodically, a recent history of the temperatures of the exhaust gas at the inlet to the palladium oxidation catalyst body is prepared in a computer control module. And a recent history of the A/F of the operating engine is considered. These temperature and A/F values are then used in determining whether the engine should be temporarily operated in a fuel-rich or stoichiometric A/F mode to provide an exhaust gas composition suitable for rejuvenation of the palladium by reducing its oxide formed during lean operation of the engine.