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We introduce a novel source coding problem, compound conditional source coding. We describe how a number of media coding problems can be cast into this framework. We develop the achievable rate region for this problem and error exponent results. We show that the reliability function of compound conditional source coding is as least as large as the list-decoding error exponent of Slepian-Wolf coding, which we develop in addition. A message of the paper is that a number of media coding scenarios where distributed source coding techniques are being used are more exactly stated as compound conditional problems. This insight can lead to improved system performance, as we demonstrate for error exponents.