A long-standing problem in interstellar chemistry is how molecules can be maintained in the gas phase at the extremely low temperatures in space. Photodesorption has been suggested to explain the observed cold gas in cloud cores and disk mid-planes. We are studying the UV photodesorption of ices experimentally under ultra high vacuum and at astrochemically relevant temperatures (15 – 27 K) using a hydrogen discharge lamp (7-10.5 eV). The ice desorption during irradiation is monitored using reflection absorption infrared spectroscopy and the desorbed species using mass spectrometry. We find that both the UV photodesorption rates and mechanisms are highly molecule specific. CO photodesorbs without dissocation from the surface layer of the ice. N2, which lacks dipole allowed electronic transitions in the range of the lamp, does not photodesorb. CO2 desorbs through dissociation and subsequent recombination from the top few layers of the ice. At low temperatures (15 – 18 K) the derived photodesorption rates are ~ 10−3 for CO and CO2 and < 2 × 10−4 for N2 ice per incident photon.