A transmission profile refers to a transmission power and a modulation and coding scheme to be used for packet transmissions over a wireless link. The goal of this paper is to develop transmission profile selection policies so as to minimize the average power consumption on a wireless link while satisfying a certain delay constraint given in terms of a delay violation probability. Toward the assessment of profile selection policies, a multi-regime Markov fluid queue model is proposed to obtain the average power consumption and the queue waiting time distribution which allows one to analyze the energy-delay tradeoff in queuing systems for which the packet transmission duration is allowed to depend on the delay experienced by the packet until the beginning of service. Numerical examples are presented with transmission profiles obtained from realistic LTE simulations. Several transmission profile selection policies are proposed and subsequently compared using the analytical model.