A covering for an architectural opening with improved insulating properties in one embodiment includes face-to-face cellular insulative components defining a fabric with dual layers of cells with the fabric being retractably mounted in a headrail so as to either be rolled about a roller or gathered adjacent to the bottom of the headrail. A first component of the fabric includes a pair of spaced parallel sheets of material interconnected with horizontally-extending flexible vanes so as to define a plurality of horizontally-extending, vertically adjacent cells of generally rectangular cross-sectional configuration. A second component of the fabric is mounted on one sheet of the first component of the fabric so as to form a plurality of vertically adjacent drooping segments of fabric forming a roman-shade appearance. Single or multiple layers of the components can be used with or without the other type of component.