Using a combination of small-angle X-ray scattering (SAXS) and fluorescence resonance energy transfer (FRET) measurements we have determined the role of the H3 and H4 histone tails, independently, in stabilizing the nucleosome DNA terminal ends from unwrapping from the nucleosome core. We have performed solution scattering experiments on recombinant wild-type, H3 and H4 tail-removed mutants and fit all scattering data with predictions from PDB models and compared these experiments to complementary DNA-end FRET experiments. Based on these combined SAXS and FRET studies, we find that while all nucleosomes exhibited DNA unwrapping, the extent of this unwrapping is increased for nucleosomes with the H3 tails removed but, surprisingly, decreased in nucleosomes with the H4 tails removed. Studies of salt concentration effects show a minimum amount of DNA unwrapping for all complexes around 50-100mM of monovalent ions. These data exhibit opposite roles for the positively-charged nucleosome tails, with the ability to decrease access (in the case of the H3 histone) or increase access (in the case of the H4 histone) to the DNA surrounding the nucleosome. In the range of salt concentrations studied (0-200mM KCl), the data point to the H4 tail-removed mutant at physiological (50-100mM) monovalent salt concentration as the mononucleosome with the least amount of DNA unwrapping.