In on-demand ad-hoc routing protocols, control packets are flooded into a network during path discovery. Especially in dense ad-hoc networks, these protocols generate a large number of broadcast packets that cause contention, packet collisions and battery power wastage in mobile nodes. We propose an efficient route establishment method that adaptively lowers re-broadcasting overhead based on the number of adjacent nodes and the number of routes that these nodes accommodate. Through simulation, we demonstrate that our proposed method is especially efficient in densely populated areas. It achieves efficiency by lowering the number of control packets for path discovery without causing a drop in the path discovery success ratio. Also, by taking path concentration into account, our method further improves packet delivery. We provide useful guidelines based on simulation results.