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The problem of encoding and transmitting a video sequence over a wireless channel is considered. Our objective is to minimize the end-to-end distortion while using a limited amount of transmission energy and delay. In our approach, we jointly adapt the source-coding parameters and transmission power per packet. We introduce the concept of "variance-aware distortion estimation" (VADE), and present a framework for controlling both the expected value and the variance of the end-to-end distortion. This framework is based on knowledge of how the video is compressed, the probability of packet loss, and the concealment strategy. To the best of our knowledge, this paper is the first to address the trade-off between the mean and variance of the end-to-end distortion. Experimental results demonstrate the potential of the proposed approach.