The synchronous modeling paradigm provides strong execution correctness guarantees to embedded system design while making minimal environmental assumptions. In most related frameworks, global execution correctness is achieved by ensuring endochrony: the insensitivity of (logical) time in the system from (real) time in the environment. Interestingly, endochrony can be statically checked, making it fast to ensure design correctness. Unfortunately, endochrony is not preserved by composition, making it difficult to exploit with component-based design concepts in mind. Compositionality can be achieved by weakening the objective of endochrony but at the cost of an exhaustive state-space exploration. This raise a tradeoff between performance and precision. Our aim is to balance it by proposing a formal design methodology that adheres to a weakened global design objective: the non-blocking composition of weakly endochronous processes, while preserving local endochrony objectives. This yields...