An internally cooled internal combustion piston engine and method of operating a piston engine is provided, with the combination of liquid water injection, higher compression ratios than conventional engines, and leaner air fuel mixtures than conventional engines. The effective compression ratio of the engines herein is greater than 13:1. The engines may employ gasoline or natural gas and use spark ignition, or the engines may employ a diesel-type fuel and use compression ignition. The liquid water injection provides internal cooling, reducing or eliminating the heat rejection to the radiator, reduces engine knock, and reduces NOx emissions. The method of engine operation using internal cooling with liquid water injection, high compression ratio and lean air fuel mixture allow for more complete and efficient combustion and therefore better thermal efficiency as compared to conventional engines.