In a recent Letter [1], Tatischeff et al. claimed evidence for three neutral baryon resonances N* between the nucleon and the Δ(1232). Two of these have masses M = 1004 and 1044 MeV below m_N + m_π and thus their widths (Γ = ­4 to 15 MeV) are radiative. The third resonance M = 1094 MeV) also might have a radiative decay. All of the resonances have to contribute to Compton scattering on the nucleon and result in peaks at energies E_γ 68, 112, and 169 MeV, respectively, which were never observed on protons [2–5] or neutrons [6,7] loosely bound in the deuteron. Since constraints of this type are very sensitive and were not analyzed in the Letter, we give estimates...