In recent work, it has been shown that conventional sound absorbing materials (e.g., lightweight fibrous media) can provide structural damping when placed adjacent to vibrating structures, including infinite panels, partially-constrained panels and periodically-supported panels typical of aircraft structures. Thus, a fibrous layer may serve two functions at once: absorption of airborne sound and the reduction of structure-borne vibration. It has also been found that the damping is primarily effective below the critical frequency of the structure, and that the damping results from viscous interaction between the fibrous layer and the evanescent near-field of the panel, in the region where incompressible flow caused by the panel vibration oscillates primarily parallel with the panel surface. By using a near-field damping (NFD) model based on the Biot model for acoustical porous media, it has been shown that a properly-optimized fibrous layer can provide levels of damping comparable with those provided by conventional, constrained-layer, visco-elastic, damping treatments. Based on the idea that vibrating structures exhibit a certain wavenumber/frequency response spectrum, the focus of the current study has been on evaluating the power dissipated by a fibrous treatment as a function of wavenumber and frequency, and on identifying the material microstructure (i.e., fiber size) required to maximize the power dissipation, and hence damping, in a specific wavenumber/frequency range. To demonstrate the wavenumber/frequency-matching procedure, an example involving a simplified model of a vehicle component will be considered here, and it will be shown how a fibrous layer can be designed to maximize its damping effectiveness when applied to a realistic base structure, such as an automotive floor pan.