An improved inflatable compression dressing (10) for use in controlling swelling and promoting healing to wounds subsequent to surgery while allowing visual inspection of the wound during healing is provided. The dressing comprises a bladder (138) formed by an outer wall (114) secured to an inner wall (112) to define an elongated, cup-shaped cavity for receiving an appendage (136); an air supply delivering air to the bladder; and a sensor monitoring air pressure within the bladder and indicating said air pressure to an air pressure control (140). The air pressure control provides air to the bladder at a rate which substantially matches air leaked from the bladder. Thus, the air supply inflates the bladder so as to provide uniform air pressure to the appendage, wherein the appendage is an arm or a leg.