Peer-to-peer (P2P) communication systems have become increasingly popular in recent years due to its high scalability and low deployment cost. In those systems, resource constrained nodes are unwelcome to other peers since they contribute too few resources to route messages and store data for other nodes. As a result, it remains a great challenge to increase the service availability for resource constrained nodes in P2P communication systems with ungenerous peers. To address this issue, we propose a novel overlay construction algorithm by which most of the resource constrained nodes can use the system services through the aid of the peers of the same users. Our simulation results show that the proposed approach achieves higher service availability for resource constrained nodes compared with the traditional RELOAD, a P2P signaling protocol developed by the IETF.