It is argued that neutrinos cannot provide the missing mass in Draco and Ursa Minor, since for reasonable neutrino mass (m v ∼ 30 eV) phase-space limits would then require very large core radii (∼ 10 kpc) and masses (∼ 4 × 10 11 M ⊙ ) for these dwarfs, which would make their dynamical friction decay times in the Galactic halo significantly shorter than a Hubble time. These limits are insensitive to assumptions about the anisotropy of the neutrino distribution