Some porous media known as melamine foam absorb sound from their three-dimensional network of thin struts. We show here that their exceptional ability to mitigate sound energy is related to a bimodal pore size distribution, which consists of co-existing pores of distinct characteristic sizes, in which the low frequency and high frequency fluid flow will follow different paths in the pore structure. The design of this visco-inertial dissipative “multi-scale” structure can be tuned on a commercial scale and may find application in improving sound absorption by, for example, a proper modification of the proportion of the chemical agents used to produce a melamine resin foam.