Small-amplitude high-frequency noises are inevitable in practical systems and may induce adverse performance degradation, or instability, if not properly attenuated in saturation systems. This note establishes the necessary and sufficient conditions on saturation compensators for rate and amplitude constrained systems to attenuate noises in continuous time domains. For discrete systems, only necessary but not sufficient conditions can be found. Some existing compensators are analyzed using the obtained results and illustrated by a simulated example.