Abstract. The throughput capacity of arbitrary wireless networks under the physical Signal to Interference Plus Noise Ratio (SINR) model has received a greater deal of attention in recent years. It has been shown that power control can increase the capacity of a network significantly compared to the case where all transmitters emit signals of uniform power. However, the published examples exhibit one common property: they usually position the nodes in an area of exponential size in the number of nodes and they require transmission power levels that differ by a factor exponential in the number of nodes. In this paper, we quantify the gap induced by the ability to adjust the transmission power if the available resources are bounded. We investigate the question of how much the worst-case performance of uniform and non-uniform power assignments differ under constraints such as a bound on the area where nodes are distributed or restrictions on the maximum power available. We determine th...