Anthropogenic noise pollution of the ocean is an acute and growing problem. This letter explores one possible mechanism of noise abatement. The far-field acoustic pressure due to a compact underwater source can be suppressed by placing a small compliant body in the vicinity of the source. Here, the feasibility and efficiency of the suppression are evaluated by quantifying the reduction in radiated acoustic energy for several simple geometries, which include sound sources in an unbounded fluid, near a reflecting boundary, or in a shallow-water waveguide. The analysis is streamlined using analytic solutions for sound diffraction by simple shapes.