Following a cold start of a hydrocarbon-fueled engine operated in a lean-burn-combustion mode, several seconds and minutes may be required for the exhaust gas stream to heat exhaust treatment devices in the exhaust system and conduit to their effective operating temperatures. The warm-up period may be particularly long for a NOx reduction catalyst (SCR) located downstream in the exhaust flow system. Accordingly, a bed of absorbent material, such as a suitably sized bed of alumina particles, located upstream of the SCR, is used to temporarily absorb water and NOx from a relatively cold exhaust until the exhaust has suitably heated the SCR to its operating temperature. Then, the warmed exhaust will remove the water and NOx from their temporary storage material and carry them to the reduction catalyst.