A cover assembly for the stowage compartment of a vehicle roof movable between a covered position in which the roof covers the vehicle interior and a stowage position in which the roof is lowered into the stowage compartment. A swivel arm connects middle and cover sections such that the cover section is movable upon movement of the swivel arm relative to the middle section between the covered position in which the cover section is disposed to a side of the middle section and the stowage position in which the cover section is disposed beneath the middle section. In the covered position the cover section is supportable on the body of the vehicle. A floating bearing supports the cover section on the end of the swivel arm connected to the cover section such that the cover section is adjustable along X, Y, and Z axes relative to the swivel arm.