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A novel dynamic programming formulation is proposed for computing optimal power control, source coding, and channel coding policies when the source traffic has tight delay constraints. Our solution minimizes power consumption subject to constraints on delay for all channel gains. This provides a much tighter delay bound than an average delay constraint, averaged over time varying channel gains. We present numerical results that show the tighter delay constraints come at a significant cost in terms of power consumption. However, we also show this power penalty can be greatly mitigated through optimal source-channel coding.