In this paper we consider the problem of extracting a design for an existing software system. This problem is clearly relevant to understanding and maintaining software systems. The basis of our approach is a formalization of top-down design with information hiding. This formalization allows an accurate and concise formulation of constructing an a posteriori design for a software system using only the source text. The theory predicts that in general there are many possible designs and that these designs can be partially ordered and form a lattice. The lattice has a smallest element and this element is the best top-down design in the sense that it has the most information hiding. We show how this element can be constructed.