Four-wave mixing between two initial closely-spaced pumps can generate mixing tones which deplete the initial pumps, and reduce total stimulated Brillouin scattering compared to a single pump. We present theoretical and experimental results confirming this reduction. This mechanism explains why it is actually possible to obtain large gains in some fiber optical parametric amplifiers, without requiring pump dithering to suppress stimulated Brillouin scattering, which is of significant practical importance.