A multi-component open-air vehicle roof structured to have a retractable enclosure storage compartment along a length of a driver's and passenger's side of the roof, and retractable enclosures to be supported and protected by the retractable enclosure storage compartments, and a rear-side retractable enclosure with a choice of having either rear-side roof supports shaped to act as a storage compartment or having a rear-side compartment as part of the rear-side edge area of the roof, either to act as a roof support storage compartment for the rear-side retractable enclosure when it is retracted. On each roof side there is a wing valence support for supporting a decorative valence and an optional lighting system. The retractable enclosures may be powered or manually controlled. The roof's ribbed, single-ply construction provides for a stronger roof with a plurality of storage compartments for a plurality of accessories within the ribs.