A method is provided for compressing a gas in a single cycle and in a single cylinder to a pressure of at least 17.2 Mpa with a compression ratio of at least about five to one. The method further comprises dissipating heat from the cylinder during the compression stroke whereby the gas is discharged with a temperature significantly less than isentropic. The apparatus comprises a hollow cylinder and a reciprocable free-floating piston disposed therein. The piston divides the cylinder into: (a) a compression chamber within which a gas can be introduced, compressed, and discharged; and, (b) a drive chamber, into which a hydraulic fluid can be introduced and removed for actuating the piston. The apparatus further comprises a piston stroke length to piston diameter ratio of at least seven to one. For operating the apparatus with a compression ratio of at least five to one, an outlet pressure of at least 17.2 Mpa, and a gas discharge temperature significantly less than isentropic, the apparatus can further comprise a variable displacement hydraulic pump for controlling piston velocity, an electronic controller for maintaining an average piston velocity that is less than 0.5 feet per second, and a heat dissipator for dissipating heat from the cylinder.