We experimentally show that, when stimulated Brillouin scattering is generated in optical fiber by use of monochromatic cw pump radiation, the transmitted pump radiation exhibits spectral broadening that is much narrower than the classical homogeneous gain-narrowed Brillouin bandwidth. The bandwidth is practically independent of the pump strength, fiber characteristics, and the waveguide-induced inhomogeneously broadened bandwidth of the Stokes emission. We show that these properties arise from strong parametric coupling of the Stokes and pump signals in the pump-depletion region.