We propose a novel power control algorithm for the minimization of the peak load in the widely used load coupled network model, which is an abstract model able to capture the behavior of current and possibly future wireless networks. We first prove that the solution to the optimization problem we pose here requires all base stations with the same load. This necessary condition for optimality gives rise to a solver based on a bisection algorithm that requires an oracle able to answer whether a probed load is greater than the optimal value. By exploiting known properties of concave mappings, we devise an iterative oracle that, with a very mild assumption, provably gives the correct answer with a finite number of iterations. Simulations in an ultra-dense network show that the proposed algorithm can decrease the peak load by around 40% when compared to the peak load induced by the common approach of fixing the power of every base station to the maximum value.