  Recently the electron dephasing and energy relaxation due to different
magnetic impurities have been extensively investigated experimentally in thin
wires and in this Letter these quantities are theoretically studied. It was
shown earlier that a magnetic impurity in a metallic host with strong
spin-orbit interaction experiences a surface anisotropy of the form $H=K_d
({\bf n}{\bf S})^2$ which causes size effects for impurities with integer spin.
Here we show that the dephasing and the energy relaxation are influenced by the
surface anisotropy in very different ways for integer spin having a singlet
ground state. That must result also in strong size effects and may resolve the
puzzle between the concentrations estimated from the two kind of experiments.
