  We observe competition between the modulation instability (MI) and stimulated
Brillouin scattering (SBS) in a 9.2-GHz broadband SBS slow light device, in
which a standard 20-km-long single-mode LEAF fibre is used as the SBS medium.
We find that MI is dominant and depletes most of the pump power when we use an
intense pump beam at ~1.55 {\mu}m, where the LEAF fibre is anomalously
dispersive. The dominance of the MI in the LEAF-fibre-based system suppresses
the SBS gain, degrading the SBS slow light delay and limiting the SBS
gain-bandwidth to 126 dB \cdot GHz. In a dispersion-shifted highly nonlinear
fibre, the SBS slow light delay is improved due to the suppression of the MI,
resulting in a gain-bandwidth product of 344 dB \cdot GHz, limited by our
available pump power of 0.82 W.
