In this paper, a set of two-segment dielectric resonator antennas is investigated for 5~6 GHz WLAN applications, which covers the requirements of most of the new standards in this area. It is shown that by choosing a high dielectric constant for the upper segment of the antenna, a good miniaturization can be achieved in spite of a proper wide impedance bandwidth. A practical antenna is then studied in detail which attains more than 50% size reduction and 20% impedance bandwidth