Dual capacity compressor including a power generating part including a reversible motor and a crank shaft inserted in the motor, a compression part including a cylinder, a piston in the cylinder, and a connecting rod connected to the piston, a crank pin in an upper part of the crank shaft eccentric to an axis of the crank shaft, an eccentric sleeve having an inside circumferential surface rotatably fitted to an outside circumferential surface of the crank pin, and an outside circumferential surface rotatably fitted to an end of the connecting rod, a key member for coupling the eccentric sleeve with the crank pin positively in all rotation directions of the motor, and damping means for damping impact occurred between the eccentric sleeve and members adjoin thereto, thereby preventing relative motion and wear/noise between parts that maintain an eccentricity.