Brillouin amplification of laser pulses in plasma has been shown to be a promising approach to produce picosecond pulses of petawatt power. A key challenge is preservation of the quality of the amplified pulse, which requires control of parasitic instabilities that accompany the amplification process. At high plasma densities (> cr /4), ponderomotive filamentation has been identified as the biggest threat to the integrity of the amplifying pulse. It has therefore been proposed to perform Brillouin scattering at densities below n cr /4 to reduce the influence of filamentation. However, parasitic Raman scattering can become a problem at such densities, contrary to densities above n cr /4 where it is forbidden. In this paper, we investigate the influence of parasitic Raman scattering on Brillouin amplification at densities below n cr /4. We expose the specific problems posed by both Raman backward and forward scattering, and how both types of scattering can be mitigated, leading to an increased performance of the Brillouin amplification process.