The use of directional antennas in wireless networks has been widely studied with two main motivations: 1) decreasing interference between devices and 2) improving power efficiency. We identify a third motivation for utilizing directional antennas: pushing the range limitations of full-duplex wireless communication. A characterization of full-duplex performance in the context of a base station transmitting to one device while receiving from another is presented. In this scenario, the base station can exploit "directional diversity" by using directional antennas to achieve additional passive suppression of the self-interference. The characterization shows that at 10 m distance and with 12 dBm transmit power the gains over half-duplex are as high as 90% and no lower than 60% as long as the directional antennas at the base station are separated by 45° or more. At 15 m distance the gains are no lower than 40% for separations of 90° and larger. Passive suppression via directional antennas also allows full-duplex to achieve significant gains over half-duplex even without resorting to the use of extra hardware for performing RF cancellation as has been required in the previous work.