Convertible type vehicles conventionally include a convertible top incorporating a foldable frame and a soft top that are moved between a folded storage position and a raised use position over the occupant compartment of the vehicle. The foldable frame of such a convertible top conventionally includes a convertible top header that seats with the windshield header in the raised use position and also includes a pair of side rails that extend rearwardly from opposite lateral ends of the convertible top header. Each side rail conventionally includes a front rail member, an intermediate rail member, and a rear rail member that are connected to each other to permit folding and unfolding of the frame upon movement of the convertible top between the storage and use positions. Normally pivotal or other suitable connections connect the front rail members to the convertible top header and connect the intermediate rail members to the rear rail members. Linkage assemblies are conventionally utilized to connect the front rail members to the intermediate rail members at each side of the vehicle so as to permit the front rail members to fold 180.degree. with respect to the intermediate rail members during the movement of the convertible top between the storage and use positions. It is desirable for such linkage assemblies to have a vertical height that is as small as possible and to also have a lateral width that is as thin as possible such that the associated side rail does not occupy unnecessary space in either the storage or use position.