SIMPLICITY is the keynote of the only two types of sleeve-valve engines that have stood the test of time, namely, the double-sleeve, or Knight, engine and the single-sleeve, or Burt-McCollum, engine, the latter type being the subject of this paper. After noting the vicissitudes through which the single-sleeve-valve engine has passed since its first introduction in 1911 and outlining the patent situation, the author describes the mechanical construction of the valve and the sleeve-driving mechanism, discusses the inherent advantages of the characteristic twisting-movement of sleeve-valves, points out the advantages of a detachable head for each cylinder, explains the principles underlying the determination of the size, shape and number of the ports and tabulates the average timing-practice of single-sleeve-valve engines. He states that the chief advantages of the single-sleeve-valve engine are sustained operating efficiency, good power-output, and silent operation. Sleeve valves obviate the grinding-in of the valves, the ingress of unwanted air through worn valve-guides, the distortion or sticking of the valve, the adjustment of clearance, the breakage of valve springs, and frequent decarbonization. Rapid opening of the ports, the type of port opening obtained, positive timing, unobstructed intake passages, and increased compression-ratio all contribute to good power-output. Other features of the single-sleeve-valve engine are said to be silence, favorable comparison in weight with that of the poppet-valve engine; added strength and rigidity due to the depth of engine body and shortness of the sleeve-valve cylinder, when a separate cylinder-block is used, allowing the use of aluminum; lubrication by a pressure-feed system of orthodox design; and freedom from detonation on account of the absence of hot exhaust-valves. In the appendix is given a simple method for determining quickly the size and the arrangement of the ports in this type of engine.