An engine combustion cylinder is fluidly connectable to an intake system through an intake valve and to an exhaust system through an exhaust valve. A valve activation system is to activate the intake valve and the exhaust valve. The valve activation system is responsive to a controller providing command signals to the valve activation system such that, when the engine operates in a six-stroke combustion cycle, the intake valve is opened during a recompression stroke to allow a portion of the products from the first combustion stroke to exit the combustion cylinder and enter into the intake system. This may be done to match the power densities of the first and second power strokes of the piston.