Abstract: Tension bridles for a cold rolling reducing mill are provided. The reducing mill reduces the thickness of a metal strip passing through the reducing mill. The tension bridles create tension on the metal strip between the bridle and the first reducing stand to receive the metal strip and between the final reducing stand and the exit bridle so that a greater reduction can be made in the thickness of the metal strip in the first reducing stand and in the final reducing stand than is ordinarily possible. When the reducing mill is a reversible mill, a tension bridle positioned at each end of the mill enhances the reducing qualities of the mill and also enhances the quality of the metal strip being coiled after it passes through the mill.