Energy harvesting is emerging as a promising approach to improve the energy efficiency (EE) and to extend the life of wireless networks. This paper focuses on energy-efficient transmission power allocation techniques for a point-to-point communication channel, equipped with a fixed-power battery, as well as a harvest-use battery. Using the fact that the harvested energy does not consume from the fixed battery, EE is formulated as the ratio of Shannon limit (as a function of the sum of the power consumed from the fixed battery and the harvest-use battery) to the sum of the circuit power and power consumed from the fixed battery. For the considered energy harvest-use technique, a time switching approach is used that in each frame, the node harvests energy for a percentage of frame time and transmits data for the rest of the frame time. Using the fact that the formulated EE is a quasi-concave function in transmission power, we use fractional programming to obtain the optimal power level, P̅u, and in-turn, the maximum achievable EE. Analytical derivations show that the maximum achievable EE monotonically increases with harvested power, whereas, P̅u monotonically decreases with it. Simulation results show the effects of harvested energy, fixed-battery power limit, and time switching rate on the maximum achievable EE.