The widely studied network energy efficiency (EE)-optimal problems (NEPs) emphasize optimality of system EE without taking fairness into account. In this paper, we focus on the max-min EE-optimal problem (MEP) by means of power allocation in interference-limited wireless networks. The MEP offers fairness assurance for users in terms of EE by maximizing the EE of the worst-case user. We show that the MEP is NP-hard. Based on generalized fractional programming, we propose a general EE-based update algorithm (EEUA) to tackle the MEP. One key step in the EEUA involves a nonconvex optimization and NP-hard power allocation problem, and we solve it by devising an iterative power allocation algorithm using sequential convex programming. Simulation results exhibit fast convergence, low complexity, and insensitivity to initial values of the proposed algorithms and verify that the MEP guarantees EE fairness among users, as well as reveal the differences between the MEP and the NEP.