We show that the more energetic superluminal neutrinos with quadratically dispersed superluminalities δ=β^2-1, for β=v/c where v is the neutrino velocity, also lose significant energy to radiation to the ν+e^-+e^+ final state in travelling from CERN to Gran Sasso as has been shown to occur for those with constant superluminality by Cohen and Glashow if indeed δ≃ 5× 10^-5. In addition, we clarify the dependence of such radiative processes on the size of the superluminality.