A growing and important class of traffic in the Internet is so-called `streaming media,' in which a server transmits a packetized multimedia signal to a receiver that buffers the packets for playback. This playback buffer, if adequately sized, counteracts the adverse impact of delay jitter and reordering suffered by packets as they traverse the network, and if large enough also allows lost packets to be retransmitted before their playback deadline expires. We call this framework for retransmitting lost streaming-media packets `soft ARQ' since it represents a relaxed form of Automatic Repeat reQuest (ARQ). While state-of-the-art media servers employ such strategies, no work to date has proposed an optimal strategy for delay-constrained retransmissions of streaming media-specifically, one which determines what is the optimal packet to transmit at any given point in time. In this paper, we address this issue and present a framework for streaming media retransmission based on layered media representations, in which a signal is decomposed into a discrete number of layers and each successive layer provides enhanced quality. In our approach, the source chooses between transmitting (1) newer but critical coarse information (e.g., a first approximation of the media signal) and (2) older but less important refinement reformation (e.g., added details) using a decision process that minimizes the expected signal distortion at the receiver. To arrive at the proper mix of these two extreme strategies, we derive an optimal strategy for transmitting layered data over a binary erasure channel with instantaneous feedback. To provide a quantitative performance comparison of different transmission policies, we conduct a Markov-chain analysis, which shows that the best transmission policy is time-invariant and thus does not change as the frames' layers approach their expiration times.