A drainage appliance includes a distal portion with a distensible retention cuff for retaining the distal portion in the rectum, intestinal or urinary tract. Cuff distension is controlled by a combination of: (a) a resiliently deformable device for urging distension of the cuff; (b) a fluid-containing chamber of variable size; and (c) a fluid-transfer damper for restricting fluid flow with respect to the chamber when the chamber changes size.