A spinal stabilization system including an insert positionable in the channel of the housing of a vertebral anchor, and an associated support construct including a spacer and at least one cord extending through the insert. In some instances the construct includes first and second cords extending through first and second bores of the insert. A clamping member clamps the cord(s) in the insert. In some instances the clamping member includes first and second tabs movable in channels in first and second flanges of the insert.