Geometric methods are valuable tools for process synthesis and design since they provide designers with intuition and quantitative results. The calculation and graphical representation of azeotropes, residue curves and distillation boundaries provide a wealth of knowledge about the entire composition space. This paper shows how these tools can be used for optimal design of complex azeotropic distillation columns. Two examples of the design of distillation systems of industrial importance are shown. In the first example, the second feed location of a two-feed distillation column with a top decanter is optimized. In the second example, the side stream draw-stage location of a distillation column with a top decanter and a side stream draw is optimized. In both cases, a feasible and near optimal structure has been designed based on information obtained by examining the whole composition space.