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On-line transducers are an important class of computational agent; we construct and compose together many software systems using them, such as stream processors, layered network protocols, DSP networks and graphics pipelines. We show an interesting use of continuations, that, when taken in a CPS setting, exposes the control flow of these systems. This enables a CPS-based compiler to optimise systems composed of these transducers, using only standard, known analyses and optimisations. Critically, the analysis permits optimisation across the composition of these transducers, allowing efficient construction of systems in a hierarchical way.