In this paper we prove new automorphy lifting theorems for l-adic Galois representations over CM (by definition, a CM field is an imaginary quadratic extension of a totally real number field)fields satisfying a self-duality hypothesis. The main novelty is that we can prove lifting results for Galois representations which are residually reducible. This paper can therefore be viewed as a sequel to [Tho12], where we treated the residually irreducible case. However, there are a number of serious new obstacles