When assessing the acoustic quality of a road pavement with the close-proximity (CPX) or the on-board sound intensity (OBSI) method, the rubber hardness of the reference tire substantially affects the measurement. Practical experience shows that measurement tires can get significantly harder within a single measurement season. This is why one would like to normalize measurements to a reference rubber hardness. The recently published technical specification defining the reference tires for CPX measurements (ISO/TS 11819-3), therefore, includes a new correction for tire rubber hardness. Early experiences with this new correction procedure raised questions about its accuracy. This paper takes an in-depth look on the influence of tire rubber hardness on CPX measurements for both reference tires P1 and H1. It analyses existing and new data and summarizes the research from several scientific contributions on this topic. It provides evidence that the effect of rubber hardness is tire specific and that separate correction factors for the P1 and the H1 tires lead to accuracy gains and improved repeatability and reproducibility of the method. The study concludes by proposing a revised tire-specific approach for the tire rubber hardness correction of CPX measurement results.