While extensive foundational work exist for the functional aspects of Web service orchestrations, very little exists regarding the foundations of Service Level Agreements (SLA), Service Level Specifications (SLS), and more generally Quality of service (QoS) issues. In this paper we develop a comprehensive theory of QoS for Web service Orchestrations. To support multi-dimensional or composite QoS parameters, QoS domains must be partially, not totally, ordered. We identify the needed algebra to capture how QoS get transformed when synchronising service responses and to represent how a service call contributes to the end-to-end QoS of the orchestration. SLA/SLS approaches implicitly assume that, the better a called service performs, the better the orchestration does. This property, called monotonicity, does not always hold, however. We provide conditions ensuring it. Then we show how SLA or contracts between the orchestration and the services it calls can be composed to derive an SLA or contract between the orchestration and its clients. To account for high variability in measured QoS parameters for existing Web services, we support both probabilistic and non-probabilistic approaches. Finally, we propose a mild extension of the Orc language for service orchestrations to support flexible QoS management according to our theory.