Multi-section sleeve valves for internal combustion engines for improved aspiration. An open connecting rod section is separated from an internal, tubular passageway by a closed wall. A port section proximate the wall defines valve ports. A power stroke midsection borders the port section. An oiling section borders the midsection, and an open section adjacent the oiling section is in fluid flow communication with the tubular passageway. The lower-diameter midsection forms a relief annulus between the valve and the tunnel or sleeve in which the valve is disposed. Fluid flow occurs through the valve interior and through ports dynamically positioned above the compression cylinder, proximate aligned sleeve and head ports. Sleeve ports are separated by bridges that maintain valve rings in compression during reciprocation to prevent damage. High pressure gas is confined between axially spaced apart, stepped sealing rings that prevent gases from flowing axially about the valve exterior.