Modular programming enjoys many well-known advantages but the composition of modular units may also lead to inefficient programs. In this paper, we propose an invasive composition method which strives to reconcile modularity and efficiency. Our technique, network fusion, automatically merges networks of interacting components into equivalent sequential programs. We provide the user with an expressive language to specify scheduling constraints which can be taken into account during network fusion. Fusion allows to replace internal communications by assignments and alleviates most time overhead. We present our approach in a generic and unified framework based on labeled transition systems, static analysis and transformation techniques.