Resynthesis of handshake specifications obtained e.g. from Balsa or Tangram with speed-independent logic synthesis from STGs is a promising approach [CC06]. 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.