Current distributed publish/subscribe systems consider all participants to have similar QoS requirements and contribute equally to the system's resources. However, in many real-world applications, the message delay tolerance of individual participants may differ widely. Disseminating messages according to individual delay requirements not only allows for the satisfaction of user-specific needs, but also significantly improves the utilization of the resources that participants contribute to a publish/subscribe system. In this article, we propose a peer-to-peer-based approach to satisfy the individual delay requirements of subscribers in the presence of bandwidth constraints. Our approach allows subscribers to dynamically adjust the granularity of their subscriptions according to their bandwidth constraints and delay requirements. Subscribers maintain the overlay in a decentralized manner, exclusively establishing connections that satisfy their individual delay requirements, and that provide messages exactly meeting their subscription granularity. The evaluations show that for many practical workloads, the proposed publish/subscribe system can scale up to a large number of subscribers and performs robustly in a very dynamic setting. Copyright © 2011 John Wiley & Sons, Ltd.