Optoelectronic oscillators (OEOs) are hybrid RF-photonic devices that promise to be environmentally robust high-frequency RF sources with very low phase noise. Previously, we showed that Rayleigh-scattering-induced noise in optical fibers coupled with amplitude-to-phase noise conversion in photodetectors and amplifiers leads to fiber-length-dependent noise in OEOs. In this work, we report on two methods for the suppression of this fiber-length-dependent noise: altering the amplitude-dependent phase delay of the OEO loops and suppressing the Rayleigh-scattering-induced noise in optical fibers. We report a 20 dB reduction in the flicker phase noise of a 6 km OEO via these suppression techniques.