Although the offset-time-based scheme can differentiate packet/burst loss rate according to their QoS levels in optical burst switching networks, it increases end-to-end packet delays of packets in a burst with higher QoS level. This is because it increases offset time of bursts in proportional to their QoS levels. In this paper, we propose a burst assembly method that decreases end-to-end packet delays. 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 more than 21% delay reduction for bursts with the highest QoS level.