We consider a wireless network comprising a number of cochannel (hence mutually interfering) links. We study the power control problem of maximizing the rate that all links can simultaneously support under a novel setup, where receivers have interference cancelation (IC) capabilities. The problem of allocating the transmitting power is intertwined with determining the links on which receivers can perform IC and the order of cancelations. We provide and prove the theoretical results of the problem complexity and structural properties. For the problem solution, we propose a mixed-integer linear programming framework that enables jointly determining the optimal power and the IC patterns using off-the-shelf algorithms. This allows for the accurate assessment of the potential of IC for power control. Extensive numerical results are presented for performance evaluation, demonstrating the benefit of deploying IC in power control.