Recently, energy-efficient (EE) communications have received increasing interest specially in cellular networks. Promising techniques, such as multiple input multiple output (MIMO) and base station (BS) cooperation schemes, have been widely studied in the past to improve the spectral efficiency and the reliability. Nowadays, the purpose is to investigate how these techniques can reduce the energy consumption of the systems. In this paper, we address for a single-user scenario, the energy efficiency of two BSs cooperation under limited backhaul capacity. In order to evaluate the EE metric, we provide first an information-theoretical analysis based on the outage probability, for a quantization model over the backhaul. Then, we extend this EE analysis to a more practical approach with data transmission over the backhaul. For both approaches, we identify by numerical/simulation results the cooperation scenarios that can save energy depending on the backhaul capacity.