The noise characteristics of high-power fiber lasers, unlike those of other solid-state lasers such as thin-disks, have not been systematically studied up to now. However, novel applications for high-power fiber laser systems, such as attosecond pulse generation, put stringent limits to the maximum noise level of these sources. Therefore, in order to address these applications, a detailed knowledge and understanding of the characteristics of noise and its behavior in a fiber laser system is required. In this work we have carried out a systematic study of the propagation of the relative intensity noise (RIN) along the amplification chain of a state-of-the-art high-power fiber laser system. The most striking feature of these measurements is that the RIN level is progressively attenuated after each amplification stage. In order to understand this unexpected behavior, we have simulated the transfer function of the RIN in a fiber amplification stage (~80μm core) as a function of the seed power and the frequency. Our simulation model shows that this damping of the amplitude noise is related to saturation. Additionally, we show, for the first time to the best of our knowledge, that the fiber design (e.g. core size, glass composition, doping geometry) can be modified to optimize the noise characteristics of high-power fiber laser systems.