We study QoS-aware management of service orchestrations, specifically for orchestrations having a data-dependent workflow. Our study supports multi-dimensional QoS. To capture uncertainty in performance and QoS, we provide support for probabilistic QoS. Under the above assumptions, orchestrations may be non-monotonic with respect to QoS, meaning that strictly improving the QoS of a service may strictly decrease the end-to-end QoS of the orchestration, an embarrassing feature for QoS-aware management. We study monotonicity and provide sucient conditions for it. We then propose a comprehensive theory and methodology for monotonic orchestrations. Generic QoS composition rules are developed via a QoS Calculus, also capturing best service binding/service discovery, however, is not within the scope of this work. Monotonicity provides the rationale for a contract-based approach to QoS-aware management. Although function and QoS cannot be separated in the design of complex orchestrations, we show that our framework supports separation of concerns by allowing the development of function and QoS separately and then "weaving" them together to derive the QoSenhanced orchestration. Our approach is implemented on top of the Orc script language for specifying service orchestrations.