The problem of answering queries using views is concerned with finding answers to a query using only answers to a set of views. In the context of data integration with LAV approach, this problem translates to finding maximally contained rewriting for a query using a set of views. When both query and views are in conjunctive form, rewritings generated by existing bottom-up algorithms in this context are generally expensive to evaluate. As a result, they often require costly post-processing to improve efficiency of computing the answer tuples.  In this dissertation, we propose a top-down approach to the rewriting problem of conjunctive queries. We first present a graph-based analysis of the problem and identify conditions that must be satisfied to ensure maximal containment of rewriting. We then present TreeWise, a novel algorithm that uses our top-down approach to efficiently generate maximally contained rewritings that are generally less expensive to evaluate. Our experiments confirm that TreeWise generally produces better quality rewritings, with a performance comparable to the most efficient of previously proposed algorithms