Many models for the prediction of the acoustical properties of porous media require non-acoustical parameters few of which are directly measurable. One popular prediction model by Johnson, Champoux, Allard, and Lafarge [J. Appl. Phys. 70(4), 1975-1979 (1991)] (459 citations, Scopus, April 2019) requires six non-acoustical parameters. This paper proves that the use of more than three parameters in the Johnson-Champoux-Allard-Lafarge model is not necessary at all. Here the authors present theoretical and experimental evidence that the acoustical impedance of a range of porous media with pore size distribution close to log-normal (granular, fibrous, and foams) can be predicted through the knowledge of the porosity, median pore size, and standard deviation in the pore size only. A unique feature of this paper is that it effectively halves the number of parameters required to predict the acoustical properties of porous media very accurately. The significance of this paper is that it proposes an unambiguous relationship between the pore microstructure and key acoustical properties of porous media with log-normal pore size distribution. This unique model is well suited for using acoustical data for measuring and inverting key non-acoustical properties of a wider range of porous media used in a range of applications which are not necessarily acoustic.