In a multi-part cover for a vehicle top storage compartment of a convertible vehicle with removable top, which cover includes a center part and adjacent side parts which, for opening the storage compartment are movable out of the positions adjacent the center part into an overlapping position with the center part while undergoing a height displacement, the side parts are elastic resiliently connected to the center parts. Stops are provided on the vehicle body, by which the side parts are engaged when the cover is closed so that the side parts are biased against the elastic support into a reference plane defined by the center part for flush alignment with the center part.