This work aims at developing a distributed power control algorithm for energy efficiency maximization (measured in bit/Joule) in wireless networks. Unlike most previous works, a new formulation is proposed to jointly account for the energy efficiency and communication delay while ensuring quality-ofservice constraints. A non-cooperative game-theoretic approach is taken, and feasibility conditions are derived for the best-response of the game. Under the assumption that these conditions are met, it is shown that the game admits a unique Nash equilibrium, which is guaranteed to be reached by implementing the game best-response dynamics. Based on these results, a convergent power control algorithm is derived, which can be implemented in a fully decentralized fashion.