Dirac neutrinos with masses in the MeV range and having "standard model" magnetic moments are known to violate the cosmological 4He bound. We calculate the value of the magnetic dipole moment of Dirac neutrinos in the mass range 5-35 MeV which would allow for consistency with the inferred primordial abundances of 2H, 3He, 4He and 7Li. © 1992.