Abstract. In the context of service discovery, matchmakers check the compliance of service-level objectives from providers and consumers. The problem of bounded uncertainty arises if some property is non-fixable. In this case, the provider is not able to control the value it takes at runtime, so the eventual consumer must not have the choice to select a value and fix it, but only knowing the guaranteed range of values it may take. To the best of our knowledge, there does not exist any approach which deals with this scenario. Most matchmakers work as if all properties were fixable, and a few have assumed the contrary. In either case, the accuracy of their results is likely to be in question since there may be involved both fixable and non-fixable properties at the same time, and there may also exist dependencies between them. In order to improve the accuracy, we present a holistic approach to matchmaking under bounded uncertainty and propose constraint programming as our choice to deal with it, so that matchmaking is transformed into a quantified constraint satisfaction problem.