Data-driven (or swarming based) streaming is one of the popular ways to distribute live multimedia streaming traffic over peer-to-peer (P2P) networks. The efficiency and user satisfaction highly depend on the constructed overlays. The common neighbor selection algorithms in existing overlay construction schemes usually randomly select a fixed number of neighbors which satisfy the selection requirements, such as end-to-end delay or a peerpsilas sojourn time. However, this fixed random neighbor-selection algorithm (FRNS) neglects the peerspsila upload bandwidth heterogeneity and therefore, the upload bandwidth cannot be efficiently used. In this paper, we propose a variable random neighbor-selection (VRNS) scheme to alleviate the problems due to bandwidth heterogeneity, and in which the number of neighbors with different upload bandwidths is dynamically determined by the statistical bandwidth information of the system. Our proposed scheme is shown to outperform FRNS based upon a large volume of carefully designed simulations.