A joint energy and spectral efficient power allocation strategy for a point-to-point multi-carrier link, subject to a delay-outage probability constraint, is proposed in this paper. Since the two objectives, namely, link-layer energy efficiency (EE) and effective capacity (EC), conflict with each other, the tradeoff problem falls into the scope of multi-objective optimization problems (MOP). With the ε-constraint approach, the MOP is converted into a single-objective optimization problem (SOP) by maximizing the multi-carrier EC, subject to an EE constraint. Then, by introducing an adjustable performance indicator, EE-loss-rate (αEE), into the EE constraint limit, the tradeoff level is flexibly controlled. Finally, we prove that the proposed tradeoff formulation is a concave maximization problem and the optimum power allocation strategy can be derived using Lagrangian method. Analytical results indicate that the proposed power allocation has a similar structure to the one for EE-maximization problem over a frequency-selective fading channel, but with a different cut-off threshold.