A roll-up covering for an architectural opening, comprising: a) a roller having a first end and a second end and defining a width between the first end and the second end, the roller defining a central rotational axis; b) a first outer elongate tape having a first end, a second end, and defining a length between the first end and the second end, the first outer elongate tape further defining a lateral width, a thickness and a first central longitudinal axis between the first end and second end of the first outer elongate tape, the first end of the first outer elongate tape being attached to the roller such that the first central longitudinal axis of the first outer elongate tape is oriented generally orthogonally with respect to the central rotational axis of the roller; c) a first inner elongate tape disposed proximate to the outer elongate tape, the first inner elongate tape having a first end, a second end, and defining a length between the first end and the second end, the first inner elongate tape further defining a lateral width, a thickness and a second central longitudinal axis between the first end and second end of the first inner elongate tape; d) a plurality of slats disposed between and coupled to the first outer elongate tape and the first inner elongate tape, the slats being oriented transversely with respect to the first and second central longitudinal axes (X1, X2), the plurality of slats, first outer elongate tape and first inner elongate tape defining a sub assembly that is configured to be rolled up around the roller, wherein the first inner elongate tape is located radially inwardly with respect to the first outer elongate tape when the sub assembly is rolled up around the roller; characterized in that: the first inner elongate tape further defines a plurality of collapsible hinge segments disposed along the length of the first inner elongate tape, the collapsible hinge segments being 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 being further 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, the first end of the first inner elongate tape being attached to the roller such that the second central longitudinal axis is oriented generally orthogonally with respect to the central rotational axis. a) a roller having a first end and a second end and defining a width between the first end and the second end, the roller defining a central rotational axis; b) a first outer elongate tape having a first end, a second end, and defining a length between the first end and the second end, the first outer elongate tape further defining a lateral width, a thickness and a first central longitudinal axis between the first end and second end of the first outer elongate tape, the first end of the first outer elongate tape being attached to the roller such that the first central longitudinal axis of the first outer elongate tape is oriented generally orthogonally with respect to the central rotational axis of the roller; c) a first inner elongate tape disposed proximate to the outer elongate tape, the first inner elongate tape having a first end, a second end, and defining a length between the first end and the second end, the first inner elongate tape further defining a lateral width, a thickness and a second central longitudinal axis between the first end and second end of the first inner elongate tape; d) a plurality of slats disposed between and coupled to the first outer elongate tape and the first inner elongate tape, the slats being oriented transversely with respect to the first and second central longitudinal axes (X1, X2), the plurality of slats, first outer elongate tape and first inner elongate tape defining a sub assembly that is configured to be rolled up around the roller, wherein the first inner elongate tape is located radially inwardly with respect to the first outer elongate tape when the sub assembly is rolled up around the roller; characterized in that: the first inner elongate tape further defines a plurality of collapsible hinge segments disposed along the length of the first inner elongate tape, the collapsible hinge segments being 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 being further 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, the first end of the first inner elongate tape being attached to the roller such that the second central longitudinal axis is oriented generally orthogonally with respect to the central rotational axis. the first inner elongate tape further defines a plurality of collapsible hinge segments disposed along the length of the first inner elongate tape, the collapsible hinge segments being 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 being further 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, the first end of the first inner elongate tape being attached to the roller such that the second central longitudinal axis is oriented generally orthogonally with respect to the central rotational axis.