One of the attractive features of directional antennas is their higher channel reuse: by transmitting the signal only in one direction, an antenna avoids interfering with communication going on in the other directions and focuses more of the power in the primary direction. In existing directional MAC protocols a single queue is used at the MAC layer; this is inherited from omnidirectional implementations. However, while there is a single channel state in omnidrectional transmission (either the channel is busy or not), the state of the channel varies with the desired direction of transmission in directional antennas. Thus, existing implementations which use a single FIFO queue potentially leads to Head of Line blocking if the medium is busy in the direction of the packet at the top of the queue but is available in other directions. We propose a new queuing organization which could take advantage of the channel more effectively using the underlying antenna system by eliminating Head of Line Blocking. We also identify a problem with the directional virtual carrier sense implementation due to side-lobes and provide a solution to it. Our results indicate that by using a greedy approach to schedule the packet which has the least wait time increases the overall throughput and reduces end-to-end delay considerably, especially under heavy loads.