An internal combustion engine is provided equipped with an exhaust gas recirculating (EGR) system and means for internally cooling the exhaust gases by a spray of atomized water into the recirculated exhaust gases prior to ignition. The atomized water spray may be in the intake manifold or directly in the cylinder. The engine may employ spark or compression ignition. The internal combustion engine operates with compression ratios greater than 12:1 and lean air:fuel ratios. Also provided is a method for controlling the amount of exhaust gas recirculated in the engine, and for controlling the amount of water added. The inventive engines have elevated thermodynamic efficiencies and favorable NOx emissions.