The covalence of chemical bonds of rare earth ions embedded in glasses is estimated in terms of local structural parameters obtained from an extended X-ray absorption fine structure analysis and interpreted in connection with L 3-edge white-line intensity of the rare earth ions, which, according to some suggestions, is proportional to the covalence. However, the Dy L 3-edge white-line intensity is stronger in Dy-doped sulfide glasses, even though the covalence of the Dy-S bonds is decreased. Moreover, the intensity variations of the Ho L 3-edge white lines in Ho-containing glasses and crystalline compounds reveal no clear correlation with the covalence of the Ho bonds. The amorphous nature of atomic arrangements affects the multiple scattering of photoelectrons and the local electronic density of states. These effects may need to be considered, in addition to the previously suggested screening effect on the electronic transition, when evaluating the L 3-edge white-line intensity and optical properties of rare earth elements doped in glasses.