Wireless Mesh Networks have emerged recently as a technology for next-generation wireless networking. To increase the performance of wireless nodes in such networks many approaches have been proposed, including directional and adaptive antennas. However, while adaptive antennas can improve the utilization of the wireless medium by reducing radio interference and the impact of the exposed nodes problem, they can also exacerbate the hidden nodes problem. Thus, MAC protocols for adaptive antennas need to be carefully designed to cope with this issue. In this regard we propose a novel MAC protocol that exploits the potentials offered by adaptive antennas in Wireless Mesh Networks to improve system performance. As key innovative feature of the proposed MAC protocol with respect to existing solutions, the information about wireless medium reservation is spread to the maximum possible extent without interfering with the connections already established in the network. This is achieved by transmitting RTS/CTS frames in all antenna sectors at the maximum allowed power that does not cause interference with ongoing transmissions. The DATA/ACK exchange then takes place directionally and at the minimum necessary power. We measure the performance of the proposed MAC protocol by simulation in several realistic network scenarios, and we compare it with the most notable solutions proposed in the literature. The results show that our proposed scheme allows to increase considerably both the total traffic accepted by the network and fairness between competing connections.