In order to minimize interference with primary users (PU), cognitive radios should operate multidimensionally over time, frequency, and space. This paper addresses the problem with power control and predictive frequency selection. Both the methods are coupled with spectrum sensing. The proposed frequency selection method minimizes the amount of channel switches, which increases the capacity of the system and decreases the number of collisions with PUs. It is shown that the allowed transmission power of an SU scales linearly with increasing primary transmission power. The results illustrate the effect of the antenna height to the maximum power; a high-antenna PU transmitter allows more powerful SUs. Moreover, simulations indicate that the power control method reduces greatly the amount of interference imposed towards PUs.