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The content distribution techniques have recently started embracing peer-to-peer system as an alternative to the client-server architecture, such as BitTorrent system. BitTorrent system offers a scale mechanism for distributing a large volume of data to a set of peers over the Internet, but it is not designed for minimizing the time taken for all peers to receive the file. As a result, the peers of BitTorrent system may suffer a long download time, specifically the narrow-band peers. In this paper, in order to reduce the download time of BitTorrent, we propose a weighty piece selection strategy instead of the local rarest first strategy in BitTorrent. The proposed strategy is based on the greedy concept that a peer assigns each missing piece a weight according to total number of neighbor's downloaded pieces. The peer selects the missing piece with the highest priority for next download. This strategy can speed up the cooperation between heterogeneous peers while making the BitTorrent more efficient in terms of the average download time and the total elapsed time. The simulation results show that weighty piece selection strategy can improve more than 15% average download time and reduce in average 60% total elapsed time than the BitTorrent system.