To increase the resistance to liquid and substance flow through a lumen of a tubular organ, a cuff comprising a flexible, mesh base member is appended to an exterior wall of the tubular organ such that it only partially surrounds the tubular organ. Ultimately, tissue ingrowth through the mesh base member integrates the cuff into the wall of the tubular organ. When the cuff is applied to the urethra of an incontinent patient, the increased resistance to flow renders the patient continent while still allowing normal voiding. The base member may also support an optional expandable component, e.g., a balloon-like element that can be selectively inflated and/or deflated to restrict the lumen of the tubular organ by a desired degree.