In this paper, energy efficiency in two-user fading interference channels is studied when the transmitters are operating in the presence of quality of service (QoS) constraints. QoS constraints are imposed as limitations on the buffer violation probabilities, and effective capacity formulation is employed as the throughput metric. Three different strategies, namely time division multiplexing with power control, treating interference as noise, and simultaneous decoding, are considered. Energy efficiency of these schemes are investigated by determining the corresponding minimum energy per bit requirements and wideband slope regions. It is shown that while time division multiplexing and treating interference as noise achieve the same minimum bit energy levels, they have different wideband slope regions. For instance, it is demonstrated that treating interference as noise can achieve points outside the slope region of time division multiplexing if the interference is weak. Finally, superiority of simultaneous decoding in strong interference scenarios is shown through its reduced minimum bit energy requirements.