Although the offset-time-based scheme can differentiate loss rates of packets according to their QoS levels in optical burst switching networks, it also increases end-to-end delay of packets with higher QoS level. This is because it increases offset time of bursts in proportional to QoS levels of packets which are included in the bursts. In this paper, we propose a burst assembly method that reduces end-to-end delay. Our proposed method includes packets that arrive during the offset time into the currently assembled bursts while the conventional method includes them into the burst assembled next time. Simulation results show that our method offers 12-23% delay reduction for packets with the highest QoS level.