Existing data-integration systems based on the mediation architecture employ a variety of mechanisms to describe the query-processing capabilities ofsources. However, these systems do not compute the capabilities of the mediators based on the capabilities of the sources they integrate. In this paper, we propose a framework to capture a rich variety of query-processing capabilities of data sources and mediators. We present algorithms to compute the set of supported queries of a mediator, based on the capability limitations of its sources. Our algorithms take into consideration a variety of query-processing techniques employed by mediators to enhance the set of supported queries.