Optical burst switching (OBS) has been proposed as a competitive switching technology to support the next generation optical Internet. However, due to their one-way resource reservation mechanism, OBS networks experience high bursts (thus packets) loss rate. In OBS networks, the contention is resolved either by dropping one of the contending bursts or more efficiently by dropping from one of the contending bursts only the parts that overlap with the other bursts. In both situations, only one data source will suffer the data loss in favor to the other. In this paper, a novel burst dropping policy based on even selection of burst (BDPES) has been proposed in conjunction with an appropriate mechanism to provide differentiated service in order to support the quality of service (QoS) requirements of different applications. In the proposed burst dropping policy, the dropped segments are selected evenly from both contending bursts and the truncated bursts are guaranteed to be larger than the minimum burst-length allowed by the network. Furthermore, the proposed policy is enhanced via a flow control mechanism. Simulation results show that the performance of proposed policy is better than existing burst dropping mechanisms in terms of reducing burst (packets) loss rate.