A compact opposed piston pump minimizes axial spacing between its pistons on the drive shaft and thereby reduces the shaking couple and noise from reciprocation. Each piston has its own eccentric element press-fit into the connecting rods so as not to occupy space between the pistons. The shaking couple can be further reduced for pistons of different masses by selecting the mass of the eccentrics to compensate for the difference in piston masses. The pump also includes an improved cylinder sealing arrangement having a circumferential groove in an angled surface at the end of the cylinder. The pump also has a special two piece cover and seal for closing the open neck of the pump crankcase and an improved multi-lobed valve stop. The pump further uses tubular transfer members for transferring intake and/or exhaust air into the crankcase and/or between valve heads.