compartment 5 the four cover parts 14 15 16 form a flat covering 4 of the convertible top 2 fig3 or the opening 37 of the convertible top compartment as a result of the arrangement of the cover 4 which is symmetrical to the lengthwise center line m of the motor vehicle the description is made essentially using the right half of the cover 4 and its assigned bearing and adjustment means the front cover part 14 is pivotally supported on its lateral outside edge section 17 via a support part 18 which projects down from the front cover part 14 see also fig8 to 14 only in fig1 the front cover part 14 the rear cover part 15 and the lateral cover part 16 being shown on the head bearing part 19 of a roughly vertical bearing rail 20 of the bearing and adjustment means for the covering 4 such that the top of the front cover part 14 can be pivoted forward out of the roughly horizontal cover position fig3 fig2 amp 4 to 6 the bearing rail 20 is mounted in the respective side area of the body spaced away from the seats 3 of the motor vehicle a carrier part 21 spaced away from its lateral outside end.