We present a series of new mass-gain data acquired on ancient pottery following heating at increasing temperatures from 60 degrees C to 590 degrees C to further constrain our understanding of the rehydration and rehydroxylation (RHX) processes acting within archeological fired-clay artifacts. The ancient pottery, deliberately chosen for its low-porosity, is second century ad Samian ware fragments originating from Lezoux in central France. The mass-gain data, after each temperature step, adequately define a (time)(1/N) power law. We demonstrate that values of the 1/N exponent vary systematically with heating temperature. These results suggest that the sorption of chemisorbed and rehydroxylated water into the clay matrix occurs simultaneously. The 1/N exponent values obtained are consistent with power law kinetics resulting from the combination of both one-dimensional and Brownian diffusion processes. The balance between these two end-member processes, in particular after heating at 500 degrees C, may depend on the nature of the clay and on the manufacturing conditions of the studied ceramics. The results presented herein confirm previous claims that major complexities vitiate the RHX dating method proposed by Wilson etal.