A control is provided adjacent an overflow of a bathtub or sink. It both remotely controls operation of a basin bottom drain, and provides an option of shutting off flow through the overflow. Rotation of a handle of the control controls the bottom drain, and axial movement of the handle controls flow through the overflow. For example, a clicker-type pop-out valve can control overflow flow. Slot and projection structures restrict use of the overflow shutoff when the drain is not closed, and/or in some circumstances even when the drain is closed.