This paper addresses issues of strategy in Web-service composition, and inter-site collaboration in general. The results are useful for both human and artificial agents of a site who are responsible for determining Web-service agreements that are most profitable for that site. We discuss three specific questions in this area. (1) How should the profit resulting from a composition of Web-services be divided among the participants? (2) How can we counter the risk of service-providers misrepresenting their services in an attempt to gain a larger share of the profit? (3) Are stable configurations guaranteed or feasible when each service-provider's decisions on how to collaborate (permit compositions) are guided solely by the goal of maximizing its profit?