Different types of transformations have been used to model sentence simplification ranging from mainly local operations such as phrasal or lexical rewriting, deletion and re-ordering to the more global affecting the whole input sentence such as sentence rephrasing, copying and splitting. In this paper, we propose a novel approach to sentence simplification which encompasses four global operations: whether to rephrase or copy and whether to split based on syntactic or discourse structure. We create a novel dataset that can be used to train highly accurate classification systems for these four operations. We propose a controllable-simplification model that tailors simplifications to these operations and show that it outperforms both end-to-end, non-controllable approaches and previous controllable approaches.