Service composition is currently done by (hierarchical) orchestration and choreography. However, these approaches do not support explicit control flow and total compositionality, which are crucial for the scalability of service-oriented systems. In this paper, we propose exogenous connectors for service composition. These connectors support both explicit control flow and total compositionality in hierarchical service composition. To validate and evaluate our proposal, we present a case study based on the popular MusicCorp.