The transient theory of stimulated Brillouin Scattering (SBS) in optical fibers is used to investigate the effects of weak feedback of an incident broadband laser field. When the linewidth of the laser approaches the Brillouin frequency shift, a weak reflection of the laser field overlaps with the SBS gain and can be amplified in the fiber resulting in an apparent reduction in SBS threshold. We show that a reflection of 0.01% (-40 dB) of a laser field with a linewidth equal to the Brillouin shift can reduce the SBS threshold by a factor of 2. These results have implications on the design of high power fiber laser systems that utilize spectral broadening to suppress SBS.