The composition of services that are indexed in a large-scale service directory often involves many complex queries issued by the service composition algorithm to the directory. These queries may cause considerable processing effort within the directory, thus limiting scalability. In this paper we present a novel approach to increase scalability: The directory offers a compact digest that service composition clients download to solve the hard part of a composition problem locally. In this paper we compare two different digest representations, a sparse matrix and a Zero-Suppressed Reduced Ordered Binary Decision Diagram (ZDD). Our evaluation confirms that both representations are compact and shows that the ZDD enables more efficient service composition.1