A spatially local region of mechanical property heterogeneity is a source of scattering, by which a structure-borne mechanical wavefield is released as sound, to a surrounding fluid. We consider the case of a scatterer which is of the order of the size of the wavelength of a plate-wave field for a frequency which is below coincidence. A design strategy for reducing the strength of the scattered sound field in the fluid, at far-field distances from the scatterer, by adding a small-scale structure to the heterogenity, is presented. The design is accomplished in a wavelet-based phase-space. Emphasized is a significant distinction required of the added structure, depending on the heterogeneity applying to a measure of the local mass density or the local bending stiffness.