This work develops a novel power control framework for energy-efficient powercontrol in wireless networks. The proposed method is a new branch-and-boundprocedure based on problem-specific bounds for energy-efficiency maximizationthat allow for faster convergence. This enables to find the global solution forall of the most common energy-efficient power control problems with acomplexity that, although still exponential in the number of variables, is muchlower than other available global optimization frameworks.