Improved decompression-type, four-cycle internal-combustion engine which has the conventional compression chamber, reciprocable piston, and intake valve therein; comprising, in accordance with the invention, means for delaying the closing time of the valve, in the course of the compression stroke, with the piston moving upwards, for obtaining reduced compression pressure; and means for closing the valve to its at least nearly closed condition within the closing delay period. The inventive delaying and closing means is preferably embodied in a specifically shaped cam for controlling the operation of the intake valve, with respective depressed, slightly protruding as well as flat portions at preferred, predetermined crank angle positions.