Stimulated Brillouin scattering (SBS) amplification of probe signals is highly polarization dependent. Maximum and minimum gain values are associated with a pair of orthogonal states of polarization (SOP) at the fiber output. Since the maximum gain is much higher than the minimum, the output probe SOP is pulled towards that of the maximum amplification. Polarization pulling is restricted, however, by pump depletion. In this work, we propose, analyze and demonstrate a method for enhanced SBS polarization pulling, using two orthogonal pumps: the one amplifies the probe wave whereas the other attenuates it. The method provides the same polarization pulling as that of a single amplifying pump, however it is considerably more tolerant to depletion.