Device-to-device (D2D) communication integrated into cellular networks is a means to take advantage of the proximity of devices and allow for reusing cellular resources and thereby to increase the user bitrates and the system capacity. However, when D2D (in the 3rd Generation Partnership Project also called Long Term Evolution (LTE) Direct) communication in cellular spectrum is supported, there is a need to revisit and modify the existing radio resource management (RRM) and power control (PC) techniques to realize the potential of the proximity and reuse gains and to limit the interference at the cellular layer. In this paper, we examine the performance of the flexible LTE PC tool box and benchmark it against a utility optimal iterative scheme. We find that the open loop PC scheme of LTE performs well for cellular users both in terms of the used transmit power levels and the achieved signal-to-interference-and-noise-ratio (SINR) distribution. However, the performance of the D2D users as well as the overall system throughput can be boosted by the utility optimal scheme, because the utility maximizing scheme takes better advantage of both the proximity and the reuse gains. Therefore, in this paper we propose a hybrid PC scheme, in which cellular users employ the open loop path compensation method of LTE, while D2D users use the utility optimizing distributed PC scheme. In order to protect the cellular layer, the hybrid scheme allows for limiting the interference caused by the D2D layer at the cost of having a small impact on the performance of the D2D layer. To ensure feasibility, we limit the number of iterations to a practically feasible level. We make the point that the hybrid scheme is not only near optimal, but it also allows for a distributed implementation for the D2D users, while preserving the LTE PC scheme for the cellular users.