Photodesorption of HFCO, H2CO, CH2CO, and CH3Cl from Ag(111) has been studied using mass spectrometry flight-time measurements and temperature programmed desorption. All these molecules are molecularly adsorbed on Ag(111). Under nanosecond pulsed laser irradiation, desorption from Ag(111) in the experimental photon energy range of 1.17 less than or equal to h nu 4.67 eV has been detected. No threshold behavior has been established within this energy range. The translational energy distribution of the desorbing molecules is characterized by a Maxwell-Boltzmann temperature in the range 110-150 K. From the photodesorption cross section dependence on photon energy and intensity, a nonthermal, substrate mediated excitation mechanism is inferred. The common observation of low translational temperatures and low photon energy thresholds is in striking contrast to the high average translational temperatures and threshold behavior reported for photodesorption of chemisorbed molecules from metal surfaces. The unique observations can be understood through the substrate-electron mediated excitation model. However, it requires either that the substrate electrons attach to the molecules with positive electron affinities or that electron scattering excites the high frequency, upsilon=1 molecular vibrational levels, possibly through dipole interactions.