The discovery of a Semantic Web Service (SWS) is the act of locating a machine-processable description of a SWS- related resource that may have been previously unknown and that meets certain functional criteria. The increasing availability of services that offer similar functionalities re- quires the discovery process to be enhanced with a selec- tion phase that considers non-functional properties (NFPs) of services. This paper proposes a model to describe these properties and a novel approach to service selection. Our approach is based on the design of matching rules by means of mediators defined by sets of rules stating the condition for successful matches. These rules are based on the on- tological description of objects representing NFPs that are required and offered. In particular, we define a set of rule schemas to support mediation and matching for a class of user-defined NFP-constraints clustered according to speci- fied constraint operators. Rules support matching for both qualitative and quantitative non-functional properties.