Power control is important in interference-limited cellular, ad-hoc, and cognitive underlay networks, when the objective is to ensure a certain quality of service to each connection. Power control has been extensively studied in this context, including distributed algorithms that are particularly appealing in ad-hoc and cognitive settings. A long-standing issue is that the power control problem may be infeasible, thus requiring appropriate admission control. The power and admission control parts of the problem are tightly coupled, but the joint optimization problem is NP-hard. We begin with a convenient reformulation which enables a disciplined convex approximation approach. This leads to a centralized approximate solution that is numerically shown to outperform the prior art, and even yield close to optimal results in certain cases - at affordable complexity. The issue of imperfect channel state information is also considered. A distributed implementation is then developed, which alternates between distributed approximation and distributed deflation - reaching consensus on a user to drop, when needed. Both phases require only local communication and computation, yielding a relatively lightweight distributed algorithm with the same performance as its centralized counterpart.