Reducing transmission redundancy is key to the efficiency of wireless network broadcast. A standard technique to achieve this is to create a network backbone consisting of a subset of nodes that are responsible for data forwarding, while other nodes act as passive receivers. On top of this, network coding (NC) is often used to further reduce unnecessary transmissions. The main problem with this backbone+NC approach is that the backbone construction process is blind of what is needed by NC, thus may produce a structure with little benefit to the NC algorithms. To address this problem, we propose a Coding Opportunity Aware Backbone (COAB) construction scheme, which seeks to maximally exploit coding opportunities when selecting backbone forwarders. We show that the better informed backbone construction process leads to significantly increased coding frequency, at minimal cost of localized information exchange. The highlight of our work is COAB's broad applicability and effectiveness. We integrate COAB with ten state-of-the-art broadcast algorithms, specified in eight publications -, and evaluate it with prototype implementations with 30 MICAz nodes. The experimental results show that our design outperforms the existing schemes substantially.