We consider small-cell networks with multiple antenna transceivers and base stations (BSs) cooperating to jointly design linear precoders to maximize the network energy efficiency, subject to a sum power and per-antenna power constraints at individual BSs, as well as user-specific quality of service (QoS) requirements. Assuming zero-forcing precoding, we formulate the problem of interest as a concave–convex fractional program to which we proposed a centralized optimal solution based on the prevailing Dinkelbach algorithm. To facilitate distributed implementations, we transform the design problem into an equivalent convex program using Charnes–Cooper’s transformation. Then, based on the framework of alternative direction method of multipliers (ADMM), we develop a decentralized algorithm, which is numerically shown to achieve fast convergence. Since BSs are generally power-hungry, it may be more energy-efficient if some BSs can be shut down, while still satisfying the QoS constraints. Toward this end, we investigate the problem of joint precoder design and BS selection, which is a mixed Boolean nonlinear program, and then provide an optimal solution by customizing the branch-and-bound method. For real-time applications, we propose a greedy algorithm which achieves near-optimal performance in polynomial time. Numerical results are provided to demonstrate the effectiveness of the proposed algorithms.