Quantum state propagation over binary-tree configurations is studied in the context of quantum spin networks. For a binary tree of order 2, a simple protocol is presented which allows one to achieve arbitrary high transfer fidelity. It does not require fine-tuning of local fields and two-node coupling of the intermediate spins. Instead it assumes simple local operations on the intended receiving node: their role is to brake the transverse symmetry of the network that induces an effective refocusing of the propagating signals. Some ideas on how to scale up these effects to a binary tree of arbitrary order are discussed.