The disclosure provides roll-up coverings for an architectural opening, and various embodiments of ladder tapes. Embodiments of the roll-up covering include a roller, a first outer elongate tape, a first inner elongate tape and a plurality of slats disposed between the outer and inner elongate tapes. The first inner elongate tape can further defines a plurality of collapsible hinge segments disposed along the length of the first inner elongate tape. The collapsible hinge segments can be configured to collapse in order to decrease the effective length of the first inner elongate tape when the first inner elongate tape is rolled up around the roller. The collapsible hinge segments can further be configured to expand in order to increase the effective length of the first inner elongate tape when the roll-up covering is unrolled from the roller.