Internal combustion engine and method with compression and expansion chambers of variable volume, a combustion chamber, a variable intake valve for controlling air intake to the compression chamber, a variable outlet valve for controlling communication between the compression chamber and the combustion chamber, means for introducing fuel into the combustion chamber to form a mixture of fuel and air which burns and expands in the combustion chamber, a variable inlet valve for controlling communication between the combustion chamber and the expansion chamber, a variable exhaust valve for controlling exhaust flow from the expansion chamber, means for monitoring temperature and pressure conditions, and a computer responsive to the temperature and pressure conditions for controlling opening and closing of the valves and introduction of fuel into to the combustion chamber to optimize engine efficiency over a wide range of engine load conditions. The relative volumes of the compression and expansion chambers and the timing of the valves are such that the pressure in the combustion chamber remains substantially constant throughout the operating cycle of the engine, and exhaust pressures are very close to atmospheric pressure regardless of the load on the engine. The engine runs so quietly and burns so cleanly that in some applications it may not require a muffler and/or a catalytic converter.