The structure of an existing optimizer for the very high-level, set theoretically oriented programming language SETL is described, and its capabilities are illustrated. The use of novel techniques (supported by state-of-the-art interprocedural program analysis methods) enables the optimizer to accomplish various sophisticated optimizations, the most significant of which are the automatic selection of data representations and the systematic elimination of superfluous copying operations. These techniques allow quite sophisticated data-structure choices to be made automatically.