The corresponding states principle (CSP) thermodynamic generalization methods described in [1] and references cited therein rest entirely on the empirical fact that key saturated liquid and vapor properties are universal functions (UFs) of reduced pressure P+= P/PσThis was highlighted in Figs. 2-4 of a recent paper in Heat Transfer Engineering [2]. However, these figures included only four to eight different substances, mostly common refrigerants, and were partially based on published physical properties dating back to the 1960s. The prime objective of the present communication is to document more thoroughly the extremely broad validity and accuracy of the UF (P+) that are most relevant in two-phase flow and heat transfer engineering analyses. For this purpose 21 different substances (including thermodynamically “similar” as well as “dissimilar” chemical species, pure substances, and azeotropic mixtures) are assessed on the basis of recent (1980s) thermophysical properties [3, 4] with the help of more precise modern computer-aided graphical/analytical techniques.