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Peer-to-peer networks have long being used for file sharing among the connected peers. Recently, the popular BitTorrent tool has permitted the exchange of large sized files by dividing it into fragments, and enabling the peers to exchange the fragments amongst themselves through an overlay network. Each file requires the establishment of a separate overlay among the peers. In this paper, we explore the use of proximity both in the construction of the overlay network, and the efficient exchange of the file fragments, mainly aimed at reducing the download time for the peers and reducing resource usage (esp. link bandwidth) in the underlying network. We give some analytical and simulation results to show the improvement that can be achieved using proximity.