Medium access control (MAC) protocols simultaneously integrating transmission power (TP) control with directional antennas have the potential to enhance both energy savings and capacity throughput in wireless multihop Mobile Ad hoc NETworks (MANETs). In this paper, we present a model to calculate future interference in networks with directional antennas, and based on this model, we derive some relations that should exist between the required TP of RTS, CTS, DATA, and ACK frames for successful data packet delivery in MANETs based on the directional version of the IEEE 802.11 distributed coordination function. From these relations, we propose a distributed power control scheme. Furthermore, we show, via simulations, that the true potentials from the proposed control scheme cannot be shown due to the imperfection of the derived model. Based on these observations, we introduce another class of power control algorithm that instead deploys a prediction filter (Kalman or extended Kalman) to estimate future interference. Simulation experiments for different topologies are used to verify the significant throughput and energy gains that can be obtained by the proposed power control schemes.