Service capacity and contribution of the peers have been proven to be the important factors for selecting a serving peer in the P2P overlay networks. In this paper, we study how to design a multi-parent overlay network in a contribution aware manner. Our idea is to utilize the outbound bandwidth of all overlay nodes efficiently. Different from other multisource streaming approaches, we employ push-based data delivery in order to minimize the latency. The core of our overlay is conceived in a tree structure rooted at a source. The auxiliary connections with redundancy avoidance capability are proposed to increase the resilience of the tree. Furthermore, we introduce an overlay joining algorithm where the parent whose degrees are exhausted responses the new peer with a list of potential peers having residual degrees so that the new peer can join the overlay with minimal requests. Simulations through ns2 demonstrate the efficiency of our solution.