A valve can include a closure device which selectively permits and prevents fluid communication between an interior and an exterior of the valve, an incremental displacement device which incrementally displaces the closure device in response to pressure differentials between the interior and the exterior of the valve, and an accelerator device which accelerates displacement of the closure device in response to a predetermined pattern of the pressure differentials. A method of operating a valve in a well can include applying a predetermined pattern of pressure differentials between an interior and an exterior of a tubular string in which the valve is connected, thereby incrementally displacing a closure device of the valve, and accelerating displacement of the closure device in response to the predetermined pattern of pressure differentials, thereby displacing the closure device to a selected one of an open and a closed position.