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In this paper, an efficient scheme is proposed based on the introduced deadline-credit-based (DC) policy. This scheme is appropriate for any prerecorded media, but is particularly relevant for prerecorded semisoft continuous media (CM) applications. Semisoft are applications with very small initial delay tolerance and, thus, for which very small amount of content may be sent in advance. The proposed policy pushes content toward the end user during the session by taking advantage of any bandwidth underutilization periods, exploiting available storage, and building up fairly a deadline credit to be consumed during periods of overutilization. The scheduling policy is studied for the single-hop case (applicable to the server of the content), as well as for the multihop case (applicable to the server and network nodes). The derived results demonstrate the ability of the proposed scheme to decrease the amount of required bandwidth (or equivalently induced losses) with respect to alternative schemes without requiring large initial delay, which is not acceptable for semisoft CM applications.