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With a view on improving user-perceived performance on networks supporting best effort flows, e.g., multimedia/data file transfers, we propose a family of bandwidth allocation criteria that depends on the residual work of on-going transfers. Analysis and simulations show that allocating bandwidth in this fashion can significantly improve the user-perceived delay, bit transmission delay, and throughput over traditional approaches, e.g., by 58% on an 80% loaded linear network. A simple implementation based on TCP Reno, exemplifies how one might approach practically realizing such gains. We discuss several other advantages of incorporating such differentiation at the transport level. In particular we make the case that favoring small transfers combined with user impatience or peak rate constraints, both of which are natural mechanisms for users to express the utility of completing transfers, offers a lightweight approach to achieving good overall network goodput and/or utility for best effort networks.