Epitaxial Ho/Nb/Ho and Dy/Nb/Dy superconducting spin valves show a reversible change in the zero-field critical temperature (ΔT(c0)) of ∼400 mK and an infinite magnetoresistance on changing the relative magnetization of the Ho or Dy layers. Unlike transition-metal superconducting spin valves, which show much smaller ΔT(c0) values, our results can be quantitatively modeled. However, the fits require an extraordinarily low induced exchange splitting which is dramatically lower than known values for rare-earth Fermi-level electrons, implying that new models for the magnetic proximity effect may be required.