By allowing service calls to be guarded by contexts, Asymmetric Event Structures (AES for short) and contextual nets are a convenient framework to model composite Web services or service orchestrations. We equip AES with QoS domains as a framework to capture a number of QoS metrics and their combination. We use the resulting model to formalize QoS-based late service binding in composite services. When subject to QoS-based late service binding, composite services may be non-monotonic with respect to QoS, meaning that strictly improving the QoS of aservice may strictly decrease the end-to-end QoS of the composite service, an embarrassing feature for QoS-aware management; we study this issue. Branching cells of AES play a central role in this study.