We present a binary routing tree protocol for distributed hash table overlays. Using this protocol each peer can independently route messages to its parent and two descendants on the fly without any maintenance, global context, and synchronization. The protocol is then extended to support tree change notification with similar efficiency. The resulting tree is almost perfectly dense and balanced, and has O(1) stretch if the distributed hash table is symmetric Chord. We use the tree routing protocol to overcome the main impediment for implementation of local thresholding algorithms in peer-to-peer systems -- their requirement for cycle free routing. Direct comparison of a gossip-based algorithm and a corresponding local thresholding algorithm on a majority voting problem reveals that the latter obtains superior accuracy using a fraction of the communication overhead.