A six stroke high thermal efficiency engine and a method for operating such an engine are disclosed. Oxygen or oxygen-enriched air is used as the oxidizer, heat is recovered from the two exhaust strokes, superheated steam is used in the second power stroke, and high levels of exhaust gas from stroke four are recirculated. Lean burn combustion is utilized to produce an oxygen rich exhaust which results in very low levels of particulates, unburned hydrocarbons, and carbon monoxide. Due to high thermal efficiency, carbon dioxide emissions are reduced per unit of power output. Use of oxygen or oxygen-enriched air as the oxidizer produces an exhaust containing very low levels of nitrogen oxides. The engine is insulated to conserve heat, resulting in reduced engine noise. An engine with high thermal efficiency, quiet operation, and low emissions is the result.