Scoped broadcast disseminates a message to all the nodes within a designated physical/logical region in an overlay network. It can be a basic building block for applications such as information search, data broadcasting, and overlay structure diagnostic. In this paper, we study scoped broadcast in peer-to-peer (P2P) overlay networks based on distributed hash tables (DHT). Since P2P networks have very dynamic behavior due to peer joining and departure, it is interesting to know how many peers can be reached with one scoped broadcast. This depends mainly on the cost we would like to pay for maintaining the geometric structure of the DHT-based overlay. The maintenance cost is affected primarily by the failure detection and failure recovery mechanisms. We evaluated the effects of maintenance overhead on scoped broadcast via extensive simulations. The evaluation shows that it is important to exploit fresh nodes as the neighbors of a node. In addition, cooperative failure discovery and recovery can efficiently and effectively disseminate scoped broadcast messages.