Two-terminal directed acyclic graphs (st-dags) are used to model problems in many areas and, hence, measures for their topology are needed. Complexity Index (CI) is one such measure and is defined as the minimum number of node reductions required to reduce a given st-dag into a single-arc graph, when used along with series and parallel reductions. In this research we present a constraint logic programming algorithm (implemented in ILOG's OPL––Optimization Programming Language) for the generation of st-dags with a given CI. To this end the complexity graph with a maximum matching of CI, the dominator tree, the reverse dominator tree and the st-dag are characterized by a set of constraints. Then a multi-phase algorithm is presented which searches the space described by the set of constraints. Finally, the computational performance of the algorithm is tested.