Mapping composition is a fundamental operation in metadata driven applications. Given a mapping over schemas S1 and S2 and a mapping over schemas S2 and S3, the composition problem is to compute an equivalent mapping over S1 and S3. We describe a new composition algorithm that targets practical applications. It incorporates view unfolding. It eliminates as many S2 symbols as possible, even if not all can be eliminated. It covers constraints expressed using arbitrary monotone relational operators and, to a lesser extent, non-monotone operators. And it introduces the new technique of left composition. We describe our implementation, explain how to extend it to support user-defined operators, and present experimental results which validate its effectiveness.