An engine (10, 100) utilizes “regular EGR cooling” when operating in HCCI mode within a low load range and “enhanced EGR cooling” that allows the engine to continue to operate in HCCI mode when engine load increases beyond the low load range. When engine load increases to a high load range, the combustion mode changes over to conventional diesel combustion, and exhaust gas recirculation reverts to “regular EGR cooling”. In a first embodiment, cooling is provided by two heat exchangers, one being a regular EGR cooler always used when cooling is needed and the other, an enhancing EGR cooler that is selectively used. In a second embodiment, cooling is also provided by two heat exchangers, one being an EGR cooler through which liquid coolant always flows when cooling is needed, and the other being a radiator used selectively to cool the liquid coolant before it enters the EGR cooler.