In this paper, we propose an antenna selection method in a wireless cognitive radio (CR) system, which we term difference selection, whereby a single transmit antenna is selected at the secondary transmitter out of M possible antennas such that the weighted difference between the channel gains of the data link and the interference link is maximized. We analyze the mutual information and the outage probability of the secondary transmission in a CR system with difference antenna selection, and propose a method of optimizing these performance metrics subject to practical constraints on the peak secondary transmit power and the average interference power as seen by the primary receiver. The optimization is performed over two parameters: the peak secondary transmit power and the difference selection weight delta is an element of [0, 1]. Furthermore, we show that the diversity gain of a CR system employing difference selection is an impulsive function of delta, in that a value of delta = 1 yields the full diversity order of M and any other value of delta gives no diversity benefit. Finally, we demonstrate through extensive simulations that, in many cases of interest, difference selection using the optimal values of these two parameters is superior to the so-called ratio selection method disclosed in the literature.