In this paper we extend and apply the work of Paul Balmer and others on derived and triangular Witt Groups. We obtain a generalized form of dévissage for derived Witt Groups over Cohen-Macaulay rings. 2000 Mathematics Subject Classification: Primary: 11E81, 18E30, 19G12; Secondary: 13C10, 13D. © 2016, Ramanujan Mathematical Society. All rights reserved.