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Data-driven (or swarming based) streaming is one of the popular ways to distribute multimedia streaming traffic over live Peer-to-Peer (P2P) networks. In data-driven streaming networks, each peer independently selects its neighbors based on gossip-style overlay construction and then exchanges streaming data with the neighbors using data scheduling. In a P2P network the major advantage is that each peer contributes its own resources to the network. As a result, there is an increase in the amount of overall resources of the network, such as bandwidth, storage space, and computing power. However such type of networks exhibit end user bandwidth heterogeneity. Consequently, the overall bandwidth increase requires proper distribution of the number of neighbors for every peer, so that the upload capacity of high bandwidth peers is efficiently utilized. In this paper we improve a fixed random neighbor-selection algorithm FRNS (implemented in p2pstrmsim simulator), in order to achieve proper distribution of neighbors to the peers. We propose VRNS, a variable random neighbor-selection algorithm by modifying FRNS and find that there is efficient use of upload capacities at high bandwidth peers. Our work is evaluated by performing simulations with the improved p2pstrmsim simulator. Our results show that there is significant improvement in overall network performance and also around 60% decrease in peer elimination by using VRNS.