This paper presents the three-fold energy, rate and delay tradeoff in mobile multimedia fading channels. In particular, we propose a rate-efficient power allocation strategy for delay-outage limited applications with constraints on energy-per-bit consumption of the system. For this purpose, at a target delay-outage probability, the link-layer energy efficiency, referred to as effective-EE, is measured by the ratio of effective capacity (EC) and the total expenditure power, including the transmission power and the circuit power. At first, the maximum effective-EE of the channel at a target delay-outage probability is found. Then, the optimal power allocation strategy is obtained to maximize EC subject to an effective-EE constraint with the limit set at a certain ratio of the maximum achievable effective-EE of the channel. We then investigate the effect of the circuit power level on the maximum EC. Further, to set a guideline on how to choose the effective-EE limit, we obtain the transmit power level at which the rate of increasing EC (as a function of transmit power) matches a scaled rate of losing effective-EE. Analytical results show that a considerable EC-gain can be achieved with a small sacrifice in effective-EE from its maximum value. This gain increases considerably as the delay constraint becomes tight.