The present invention discloses a method for shaping glass sheets to deeply sagged configurations using a lower outline mold and an upper shaping mold while minimizing marking of the sheets by shaping molds. The outline mold includes a support rail which generally corresponding to the desired curvature of a peripheral portion of the sheets to be shaped and supports the glass sheets as they are heated and sagged by gravity to a preliminary shape. The outline mold and the upper mold are then moved relative to each other to position the molds either in close proximity to each other or to press the upper mold against the glass sheets. Pressurized gas is then directed from the mold to at least the unsupported central portions of the preliminarily shaped sheets, to urge these unsupported portions downward and shape the sheets to a desired configuration.