Superconductive Cu2Ba2RCu2O8 samples with R ranging from Gd to Tm have been synthesized through a sol-gel route. Both iodometric titration and CuL-edge x-rayabsorption near-edge structure (XANES)spectroscopy data indicate that the average Cu valence remains constant, whereas Tc increases with decreasing size of the R constituent. An explanation for this trend is revealed from O K-edge XANESspectra, which show that the smaller-for-larger R-cation substitution results in a shift of holes from the Cu2O2 charge reservoir to the superconductive CuO2 planes. Since Cu2Ba2RCu2O8 samples are underdoped, such a shift of holes raises the value of Tc.