An internal combustion engine has cylinder wall cavities located near the top dead center stroke end to allow optimizing the compression ratio in first stage compression, as function of fuel octane number used. The volume of the cylinder wall cavities is designed to be adjustable, even when the engine is operating. Using a conventional piston motion, the second stage compression becomes accelerated as soon the upper piston ring seals-off the cylinder wall cavities. This is due to the sudden significant reduction in volume. During the power stroke, after the upper piston ring opens the cylinder wall cavities; their fuel content is ignited by second stage combustion products. Because the torque required during accelerated compression is no greater than during first stage compression, stresses in the crankshaft are no more than in conventional spark ignition engines. This allows small displacement engines to be of light weight and to be hand cranked.