A drug-infusing device is implanted into a body cavity such as a bladder. The device is implanted in an uninflated, low profile state. After insertion into the body cavity, the device is filled with a substance, such as a drug, and assumes an increased profile. After the device is filled, it is allowed to float freely within the body cavity. Alternatively, the device can be tethered to a wall of the body cavity. The device delivers the drug at a controlled rate over an extended period of time. In order to deliver the drug at a controlled rate, the device preferably has a pressure-responsive valving member. The flow resistance of the valving member is responsive to the pressure at which the drug is stored within the infusing device. The resistance of the valving member decreases as the pressure within the infusing device decreases, thereby providing a resultant controlled flow rate.