Power control is important in interference-limited cellular, ad-hoc, and cognitive wireless 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 problem is NP-hard. In recent work, we developed a convex relaxation-based deflation approach to the joint problem, which was shown to outperform the prior art, and yield close to optimal solutions at moderate computational cost. In this paper, we derive a distributed version of our joint power and admission control algorithm. The algorithm 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 which also attains close to optimal performance.