It is known that wireless ad hoc networks employing omnidirectional communications suffer from poor network throughput due to inefficient spatial reuse. Although the use of directional communications is expected to provide significant improvements in this regard, the lack of efficient mechanisms to deal with deafness and hidden terminal problems makes it difficult to fully explore its benefits. The main contribution of this work is to propose a Medium Access Control (MAC) scheme which aims to lessen the effects of deafness and hidden terminal problems in directional communications without precluding spatial reuse. The simulation results have shown that the proposed directional MAC provides significant throughput improvement over both the IEEE802.11DCF MAC protocol and other prominent directional MAC protocols in both linear and grid topologies.