This paper demonstrates how to lower the average response time of search-based interactive configurators using over and under approximations of the configuration problem represented by binary decision diagrams (BDDs) on problems where fast configurators using monolithic BDDs are intractable. The paper introduces several ways to build the approximations and our experimental evaluation on industrial data shows that a search driven extension of the approximations substantially outperforms both purely search-based and purely BDDbased interactive configurators.