Abstract. Core computation in data exchange is concerned with materializing the minimal target database for a given source database. Gottlob and Nash have recently shown that the core can be computed in polynomial time under very general conditions. Nevertheless, core computation has not yet been incorporated into existing data exchange tools. The principal aim of this paper is to make a big step forward towards the practical feasibility of core computation in data exchange by developing an improved algorithm and by presenting a prototype implementation of our new algorithm.