A joint optimization problem of link-layer energy efficiency (EE) and effective capacity (EC) in a Nakagami- m fading channel under a delay-outage probability constraint and an average transmit power constraint is considered and investigated in this paper. Firstly, a normalized multi-objective optimization problem (MOP) is formulated and transformed into a single-objective optimization problem (SOP), by applying the weighted sum method. The formulated SOP is then proved to be continuously differentiable and strictly quasiconvex in the optimum average input power, which turns out to be a cup shape curve. Further, the weighted quasiconvex tradeoff problem is solved by first using Charnes-Cooper transformation and then applying Karush-Kuhn-Tucker (KKT) conditions. The proposed optimal power allocation, which includes the optimal strategy for the link-layer EE-maximization problem and the ECmaximization problem as extreme cases, is proved to be sufficient for the Pareto optimal set of the original EE-EC MOP. Moreover, we prove that the optimum average power level monotonically decreases with the importance weight, but strictly increases with the normalization factor, the circuit power and the power amplifier efficiency. Simulation results confirm the analytical derivations and further show the effects of fading severeness and transmission power limit on the tradeoff performance.