Current service-oriented systems rely on asynchronous and recursive service calls. Still when analyzing the behavior of software-oriented systems the calling context of a service call is rarely considered. In earlier work, we could show that common workflow net-based analyses fail to detect deadlocks in a service-oriented system, if they are caused by recursive service calls. To investigate this issue, this work proposes different kinds of service compositions based on the context-sensitivity of recursive service calls and the concept of calling depth. Within this framework, we highlight that context-insensitive deadlock analyses fail, as they ignore the calling context. However, we could show that a context-sensitive deadlock analysis only needs to consider a calling depth of two to be successful. Our key insight is, that context-sensitivity of service composition might impact the correctness of a behavioral analysis.