In this paper, we obtain an energy-efficient power allocation technique for a Rayleigh block-fading channel with delay-limited applications. In particular, we consider a probabilistic delay constraint as the user quality-of-service (QoS) requirement, and incorporate the concept of effective capacity to obtain the maximum arrival rate, at which, the delay constraint is satisfied. We obtain the energy efficiency (EE), which is formulated as the ratio between the effective capacity and the total expenditure power, of this system and derive the power allocation strategy that maximizes the EE. Numerical results are conducted to corroborate our theoretical results. In addition, for comparison reasons, we plot the maximum achievable EE under two well-known power allocations schemes, namely, water-filling (wf) and constant power allocation (cons) when considering delay constraints. The results show that in stringent delay limited systems, adaptive power allocation improves the maximum achievable EE significantly.