The edge effect or variation in polishing edge profile on a substrate undergoing CMP is reduced by structuring a retaining ring, housed in a carrier head for retaining the substrate, such that the polishing edge profile shifts back and forth with respect to the center of the substrate. Embodiments include structuring the retaining ring such that the width between inner and outer surfaces varies by an amount sufficient to compensate for polishing edge profile variation. Embodiments also include structuring the retaining ring such that the distance from the outer surface to the geometric inner surface varies. Embodiments further include structuring the retaining ring such that the distance between the outer surface to the perimeter of the substrate retained by the inner surface of the retaining ring varies.