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We address the issue of providing quality-of-service (QoS) in an optical burst-switched network. QoS is provided by introducing prioritized contention resolution policies in the network core and a composite burst-assembly technique at the network edge. In the core, contention is resolved through prioritized burst segmentation and prioritized deflection. The burst segmentation scheme allows high-priority bursts to preempt low-priority bursts and enables full class isolation between bursts of different priorities. At the edge of the network, a composite burst-assembly technique combines packets of different classes into the same burst, placing lower class packets toward the tail of the burst. By implementing burst segmentation in the core, packets that are placed at the tail of the burst are more likely to be dropped than packets that are placed at the head of the burst. The proposed schemes are evaluated through analysis and simulation, and it is shown that significant differentiation with regard to packet loss and delay can be achieved.