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...