A convertible vehicle includes a roof having roof parts including a rear roof part. The roof is movable between a closed position in which the parts cover the vehicle and a stored position in which the parts are stacked within a storage compartment of the vehicle. A trunk lid opens and closes the compartment. The rear roof part includes C-pillars on respective sides of the vehicle and a window. The window is independently movable from the rear roof part between a normal position in which the window lies between the C-pillars and a raised position in which the window lies outside of the rear roof part. An adjusting device connected between the rear roof part and the window moves the window between the normal and raised positions. A storage shelf connected to the trunk lid extends below the rear roof part into the vehicle when the roof is closed.