This invention provides, in certain aspects, unique devices and methods for treating fistulae. In one embodiment, an inventive device includes an elongate graft body having a proximal end and a distal end. The graft body is configurable to a first condition and a second condition, the second condition including the distal end deflected laterally relative to its position in the first condition of the body. The device also includes a tether, which is connected to the graft body, and is configured to traverse proximally along the body. The tether is manipulable to convert the graft body from the first condition to the second condition. Such a device may also include one or more additional tethers connected to the graft body. For instance, a second tether can be configured to extend distally from the distal end of the graft body, and may be effective in pulling the graft body along a fistula tract.
