A surgical instrument that includes jaw members, at least one of which may be moved to closed positions relative to the other jaw member upon actuation of a closure actuator. Actuation of the closure actuator causes an axially moveable closure member to apply closure motions to at least one of the jaw members. In at least one form, the closure actuator includes a first actuator portion that is configured to move through a first range of axial travel upon actuation of the closure actuator. A second actuator portion interfaces with the axially movable closure member such that upon actuation of said closure actuator, the second actuator portion moves the axially movable closure member through a second range of axial travel that is greater than the first range of axial travel.