Mapping composition is a fundamental operation in metadata driven applications. Given a mapping over schemas σ₁ and σ₂ and a mapping over schemas σ₂ and σ₃, the composition problem is to compute an equivalent mapping over σ₁ and σ₃. We describe a new composition algorithm that targets practical applications. It incorporates view unfolding. It eliminates as many σ₂ 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.