An apparatus for providing stiffness to the upper end of an elongated section of drapery fabric which selectably allows the drapery fabric to be readily foldable when stiffness is not needed. The apparatus also connects the drapery to an overhead, traverse supporting rail, such as by an arrangement of hooks and eyelets or rotatable pendants. The apparatus includes an insert member made of a flexible, relatively stiff material which may be one continuous strip or a series of segments. The apparatus also includes member mountable to the drapery that is made of flexible, readily-foldable material. The insert member and the mounting member are configured so that the insert member may be engaged with the mounting member. When the insert member is engaged with the mounting member, the insert member and mounting member are not readily foldable and provide stiffness to support the drapery fabric between pendants. When the insert member is disengaged from the mounting member, the entire drapery fabric, including the upper end of the drapery fabric to which the mounting member is attached is uniformly foldable.