Brillouin fiber ring lasers (BFRLs) are based on the amplification of the Stokes signal wave generated by a pump signal seeded inside a fiber-ring cavity. Brillouin fiber ring lasers have already been extensively studied and results have shown that the generated first order Stokes wave has less intensity and phase noise than the seeded pump. This increase in coherence is attractive for many sensing applications, whether in the field of fiber sensors or remote sensing systems such as LIDAR. For input pump powers few times the 1rst order Stokes Brillouin lasing threshold, stimulated Brillouin scattering (SBS) in the fiber acts as a low-pass filter and reduces both frequency and intensity noise of the Stokes-1 signal relative to that of the pump. Brillouin fiber lasers with several Stokes components can further increase the coherence through a cascading effect, the 1st Stokes component being the pump for the 2nd Stokes order and so on. In this communication, we experimentally demonstrate up to 40 dB FN reduction of a non-resonant pumping BFRL compare to that of the pump and show that it can reach even higher values (50 dB). To our knowledge, this is the first demonstration of such experimental FN (so its linewidth) reduction using non-resonant BFRLs. Using resonant pumping, and multi-Stokes Brillouin fiber lasers, we show that the RIN reduction is exceptionally increased (20 dB) through the cascading effect due to the saturation process of the Stokes signal used as an optical pump. We stated that the multi-Stokes operation is mandatory to obtain high RIN-Reduction, while the frequency noise reduction is maintained at a high level (30 dB). Analytical expressions obtained for the noise power density enables us to predict this reduction showing the effect of the cavity (Q-factor) and of acoustic damping rate. Chalcogenide and silica fibers are compared.