The kinetics of gamma'-type (Ni3X) precipitate growth and solute depletion in Ni-Al, Ni-Ga, Ni-Ge, Ni-Si, Ni-Ti and Ni-Al-Cr alloys is successfully predicted by the trans-interface diffusion-controlled theory of coarsening using non-integer temporal exponents, n, satisfying 2 a parts per thousand currency sign n a parts per thousand currency sign 3, which are obtained from analyses of particle size distributions (PSDs). The origin of non-integer n is concentration-dependent diffusion through the gamma/gamma' interface. The literature on diffusion of Al and Ni in Ni3Al is specifically examined. It is shown unequivocally that the concentration-dependent diffusion of Al can account semi-quantitatively for the value of n that successfully describes the PSDs and kinetics of coarsening of the gamma' precipitates. There is no need to invoke a particle size-dependent gamma/gamma' interface width, as was done in prior work. It is argued that existing theory and computational modeling of coarsening in systems with highly disparate diffusion mobilities in both phases do not correctly represent the mobilities in the matrix, precipitate, and interface in Ni-Al alloys. These theories predict temporal exponents satisfying 3 a parts per thousand currency sign n a parts per thousand currency sign 4, for which there is no experimental support.