When the size of CeAl2 and CePt(2+x) particles is reduced to the nanometer scale, antiferromagnetism is suppressed and Kondo behavior predominates, with the Kondo temperature T(K) either decreasing (CeAl2) or increasing (CePt(2+x)) relative to the bulk. Local structure measurements show that these nanoparticles are significantly distorted. While such distortions should strongly affect magnetic and electronic properties, we find they cannot explain the observed changes in T(K). Other size-induced changes to the electronic structure must, therefore, play a significant role.