Today?s Internet technology enables the customers to reach services through the web. However, some of the user demands may have a complex nature and can not be answered by a single web service. Composite services have to be constructed to fulfill complex service demands. Generally, these composite structures appear to be user specific. In addition to this, due to the highly dynamic nature of the web, it is not possible to determine the atomic services that will constitute the composition in advance. Therefore composite service model should include user?s constraints and the composition should be performed dynamically and efficiently. The composition calls for the discovery of the services that fulfill the requirements of the user. In majority of the works on web service composition, the service discovery is based on service matching according to the requirements and constraints only on the atomic services. However, the requirements on the overall composition affect the selection of the services, as well. Another important point is to provide flexibility for the definition of the constraints. In this paper, we propose a system that can compose web services under the constraints on the overall composite service as well as requirements on the atomic services. We use a logic-based formalism, namely CCTR, for the definition of the composite web service and constraints, and the selection of the services. This framework provides a flexible constraint definition for the user by defining an acceptance level for constraints. The presented framework uses existing technologies for the discovery of services and for the service selection refinement and composition, CCTR scheduling mechanism is used.