Valve assembly and method in which a valve member is connected to an elongated lever arm for controlling communication between two chambers in an engine. The valve assembly is disposed at least partially within one of the chambers, and the valve member is moved between open and closed by an actuator connected to the lever arm. In some disclosed embodiments, a pilot valve is opened to equalize pressure on both sides of the valve member prior to moving the valve member toward the open position. In others, where a piston in an expansion cylinder is driven by hot, expanding gases from a separate combustion chamber or heat exchanger, the exhaust valve is closed before the piston has completed its exhaust stroke, and pressure is allowed to build up in the expansion cylinder to a level corresponding to the pressure in the combustion chamber before the valve member is moved toward the open position.