We address the issue of power-controlled shared channel access in future wireless networks supporting packetized data tra#c, beyond the voice-oriented continuous tra#c primarily supported by current generation networks. First, some novel formulations of the power control problem are introduced, which become progressively more general by incorporating various relevant costs. The analysis of the models under simple, yet natural, assumptions yields certain ubiquitous structural properties of `optimal' power control algorithms. Based on such structural properties, we design a new family of distributed and asynchronous PCMA algorithms and evaluate them experimentally by simulation. They are found to perform substantially better than a standard benchmark algorithm for power control. This is a first step towards the design of full PCMA protocols for autonomous channel access in high-performance wireless networks. I. Introduction Controlling the transmitter powers in wireless communication ne..