  We obtain bounds for the neutrino masses by combining atmospheric and solar
neutrino data with the phenomenology of neutrinoless double beta decay where
hypothetical values of |< m>| are envisaged from future
0\nu\beta\beta-experiments. Different solutions for the solar neutrino data are
considered. For the Large-Mixing-Angle solution, a bound |< m>| \leq 0.01 eV
would strongly disfavour an inverted hierarchy of the neutrino masses.
