The optical attenuation induced in 6 Navy Qualified Parts List fibers by 60Co (gamma) -ray exposures to 106 rad has been measured at 3 different dose rates: 26, 1000, and 20,500 rad/min. The loss in the Corning, Lucent and Plasma Optical Fiber multimode fibers was measured at 1340 nm, while that in the Corning, Lucent, and SpecTran single mode fibers was measured at both 1315 and 1510 nm. Growth and recovery data were measured for the highest does rate exposure, while only growth data were obtained for the lower dose rates. In an effort to predict the fibers' radiation response at much lower dose rates, the data have been fit to a model based on an exponential distribution of trap depths below the glass mobility edge. Although the results of the model are in qualitative agreement with the data, additional refinement is necessary. However, the agreement is sufficient that an upper bound can be calculated for the degradation induced by low-dose-rate radiation environments.