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In this paper, we present an efficient downlink power control scheme, for wireless networks, based on two key ideas: (i) global-local fixed-point-approximation technique (GLOFPAT) and (ii) bottleneck removal criterion (BRC). The proposed scheme copes with all scenarios including infeasible case where no power allocation can provide all multiple accessing users with target quality of service (QoS). For feasible case, the GLOFPAT efficiently computes a desired power allocation which corresponds to the allocation achieved by conventional algorithms. For infeasible case, the GLOFPAT offers valuable information to detect bottleneck users, to be removed based on the BRC, which deteriorate overall QoS. The GLOFPAT is a mathematically-sound distributed algorithm approximating desired power allocation as a unique fixed-point of an isotone mapping. The unique fixed-point of the global mapping is iteratively computed by fixed-point-approximations of multiple distributed local mappings, which can be computed in parallel by base stations respectively. For proper detection of bottleneck users, complete analysis of the GLOFPAT is presented with aid of the Tarski's fixed-point theorem. Extensive simulations demonstrate that the proposed scheme converges faster than the conventional algorithm and successfully increases the number of happy users receiving target QoS.