This paper presents the design, implementation, and experimental evaluation of CMAP (Conflict Maps), a system that increases the number of successful concurrent transmissions in a wireless network, achieving higher aggregate throughput compared to networks that use carrier sense multiple access (CSMA). CMAP correctly identifies and exploits exposed terminals in which two senders are within range of one another, but each intended receiver is far enough from the other sender that the two transmissions can succeed even if done concurrently. CMAP includes a reactive channel access scheme in which nodes transmit concurrently (even if there's the possibility of a collision), then observe the loss probability to determine whether they are better off transmitting concurrently or not. Experimental results from a 50-node 802.11a testbed show that CMAP improves throughput by 2× over CSMA with exposed terminals, while converging to the performance of CSMA when the senders and receivers are all close to each other. CMAP also improves throughput by up to 47% over CSMA in realistic access point-based networks by exploiting concurrent transmission opportunities.