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Resynthesis of handshake specifications obtained e. g. from BALSA or TANGRAM with speed-independent logic synthesis from STGs is a promising approach. To deal with state-space explosion, we suggested STG decomposition; a problem is that decomposition can lead to irreducible CSC conflicts. Here, we present a new approach to solve such conflicts by introducing internal communication between the components. We give some first, very encouraging results for very large STGs concerning synthesis time and circuit area.