One major task of the Medium Access Control (MAC) of IEEE 802.11 is to decide when and with which parameter values to transmit. In small scenarios, “collisions”, namely simultaneous transmissions by neighboring nodes, are avoided successfully to a great extent by the MAC, working according to the Carrier Sense Multiple Access with Collision Avoidance (CSMA/CA) principle. This enables simple yet effective algorithms for the transmission parameter selection. However, in wireless mesh networks (WMNs) hidden nodes and asymmetric link load lead to unpredictable interference. Therefore, existing approaches to the transmission parameter selection perform poorly, resulting in low capacity of the WMN. In this paper, we enhance the existing CSMA/CA by an Interference Avoidance (IA) component, leading to a CSMA/IA protocol. The protocol is based on traffic shaping and interference strenght prediction. Thereby, time instants and parameter values for successful frame transmission can be planned, resulting in a capacity increase in WMNs of about 90% compared to operation under the standard MAC using the best existing transmission parameter selection algorithm.