The transient theory of stimulated Brillouin scattering (SBS) in optical fibers is used to investigate the effects of weak feedback of incident broadband laser fields exhibiting different spectral shapes. The proper boundary conditions are given for the forward- and backward-propagating electric fields inside the fiber with a finite amount of reflectivity at the fiber ends. 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. It is shown that the spectral shape of the incident field and its overlap with the SBS gain spectrum affects the SBS signal. Numerical examples are presented for incident laser fields that (1) simulate a pulsed, multilongitudinal-mode laser and (2) are a constant amplitude with a sinusoidal phase modulation. For the pulsed field with mode spacing much less than the Brillouin linewidth, calculations show that an end reflection of 0.01% (−40  dB) of the laser field with a linewidth equal to 0.75 of the Brillouin frequency shift can reduce the effective SBS threshold by a factor of 1.5. When the incident laser field is constant amplitude and phase modulated with a sinusoid, calculations predict sharp and distinct enhancement of the reflected power when the ratio of the Brillouin frequency shift to the modulation frequency is an integer for end reflections as low as 0.001% (−50  dB). Experiments performed with a sinusoidal phase modulated signal confirm the theoretical predictions. These results have implications on the design of high-power fiber laser systems that utilize spectral broadening to suppress SBS.