A convertible has a top which can be opened and can be put away and which has a rear window frame and, when the top is closed, at least one surface bow situated in front of said rear window frame in the direction of travel. A coupling linkage for carrying out a relative movement of the surface bow with respect to the rear window frame is arranged between the rear window frame and the surface bow. It is essential for the invention that at least two surface bows which are situated in front of the rear window frame in the direction of travel are provided, which surface bows, when the top is closed, form a continuous roof contour together with the rear window frame. Furthermore, the coupling linkage is designed in such a manner that, at the beginning of the opening of the top, the second surface bow can be moved downward relative to the adjacent first surface bow and relative to the rear window frame out of the roof contour.