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Resource management is the general topic of the present paper, particularly, we deal with capacity sharing for interference limited wireless networks by power control. Proportional reduction of the signal-to-interference ratio (SIR) requirements is suggested as the control mechanism to accommodate users in the case of overload. For this purpose, we carefully describe the geometrical structure and the asymptotic behavior of the set of feasible power vectors as a proportionality factor tends to its boundaries. In the case that there is no feasible power adjustment, the minimum proportional SIR reduction is determined under general power constraints. We conclude with developing a locally quadratic convergent algorithm for numerical computation of the optimum power assignment. The investigations provide both insight into the theoretical structure of optimum power allocation as well as a practical method for call admission control.