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In wireless video transmissions, encoded video frames are often large in data load and truncated into many transport packets (TPs) for reliable transmissions. These TPs are to be delivered before a deadline at certain reliability that depends on the importance of the video frame. High power and bitrate transmission schemes are often deployed to ensure low loss rate, but at the cost of substantial energy consumption. This paper addresses the energy-minimizing transmission policy for highly reliable transmissions of a group of TP with a common deadline. We jointly adapt the transmission rate, transmission power, and retransmission limit to minimize the transmission energy while ensuring that the video frame is reliably delivered before a deadline. In a slow fading channel, we formulate a deterministic transmission policy that allocates a retransmission limit to the TPs and jointly optimizes with the transmission bitrate and power. Contrary to the intuition that avoids packet loss and retransmission to preserve energy, we demonstrate that allowing some retransmissions in the joint optimization consumes less energy, without compromising the target reliability. In a Rayleigh fading channel, a conventional approach adopts a supportable transmission rate and declares off-channel at deep fading. We generalize the approach to include various transmission schemes at different fading states and propose the probabilistic combination of these schemes. Given the fading statistics and a channel state, our policy determines to pause or to deploy a proper transmission scheme such that the video frame transmission is energy minimized, timely, and highly reliable. Extensive simulations confirm that the proposed transmission policies consume less energy than existing methods. In particular, when the deadline or the target reliability are tightened, the proposed policies yield even higher energy efficiency.