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We propose an admission control for the IP telephony service over DiffServ-based IP networks. The proposal has three important features. First, the proposed control is fully distributed; each edge router autonomously admits or rejects connection-set-up requests based on the stored information of resource availability. Secondly, the resource availability is expressed in terms of the maximum number of multiplexable IP telephony sources in advance. This feature allows making connection acceptance judgment in real time without measuring IP-telephony traffic. Finally, our proposal can specify QoS performance targets as an arbitrary x-percentile queueing delay. This feature allows the full receiving of the benefit of statistical multiplexing gain.