The data on coarsening of gamma'-type precipitates (Ni3X, with the L1(2) crystal structure) in Ni-Al, Ni-Ga, Ni-Ge, Ni-Si, and Ni-Ti alloys are re-evaluated in the context of recent (TIDC) and classical (LSW) theories of coarsening, with the objective of ascertaining the best values possible of interfacial free energies, sigma, of the gamma/gamma' interfaces in these five alloy systems. The re-evaluations include fitting of the particle size distributions, reanalyzing all the available data on the kinetics of particle growth and kinetics of solute depletion, and using thermodynamic assessments of the binary alloy phase diagrams to calculate curvatures of the Gibbs free energies of mixing. The product of the work is two sets of interfacial free energies, one set for the analysis using the recent TIDC theory and the other for the analysis using the classical LSW theory. The TIDC-based analysis yields lower values of sigma by about a factor of 2/3. All the interfacial energies are considerably larger, by factors ranging from similar to 4 to 10, than those previously reported, which were for the most part calculated from data on coarsening assuming ideal-solution thermodynamics. In the TIDC theory the width of the interface, delta, is allowed to increase with particle size, r. A simple equation relating sigma to the ratio of the gradient energy and delta is used to show that sigma can remain constant even though delta increases with r. Published work supporting this contention is presented and discussed.