Directional antennas have been recently suggested to be used in wireless ad hoc networks to reduce interference outside the antenna direction and to increase spatial reuse of wireless channels. Several MAC schemes that exploit directional antennas have been proposed, among which the two D-MAC schemes proposed in [5] may have received the most attention. In this paper, we carefully analyze how the second D-MAC scheme proposed in [5] operates in the hidden/exposed terminal scenarios and show that it not only introduces new collisions, but also reduces spatial reuse to some extent. To remedy these problems, we propose an enhanced version of the second D-MAC scheme, called fragmentation based D-MAC (FD-MAC), to reduce collision, to achieve better spatial reuse (than the second D-MAC scheme), and to improve fairness. Through ns-2 simulation, we demonstrate the effectiveness of FD-MAC, and in particular, we show that in complex scenarios such as multihop forwarding and mesh topologies, FD-MAC significantly outperforms DCF with RTS/CTS and the two D-MAC schemes, both in terms of throughput and fairness.