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The performance evaluation of mechanisms that can support precedence and pre-emption in a converged IP infrastructure is a challenging task. This paper provides approximate analysis to investigate the trade-off between VoIP call blocking and quality of experience in a DiffServ environment. Mathematical formulations are developed for EF and AF configurations incorporating token bucket, tail-drop and WRED mechanisms. Results are presented for a T1 access link over which G.711 VoIP calls are multiplexed as one class within a multi-service user demand mix. The analysis enables the quality degradation associated with precedence and pre-emption techniques to be estimated, and indicates that the impact on lower precedence traffic is not as severe as hitherto feared. This opens up the possibility of developing more flexible and scalable approaches to implementing MLPP concepts in a converged IP network infrastructure.