We discuss the generation of small neutrino masses from effective operators higher than dimension five, which open new possibilities for low scale see-saw mechanisms. In order to forbid the radiative generation of neutrino mass by lower dimensional operators, extra fields are required, which are charged under a new symmetry. We discuss this mechanism in the framework of a two Higgs doublet model. We demonstrate that the tree level generation of neutrino mass from higher dimensional operators often leads to inverse see-saw scenarios in which small lepton number violating terms are naturally suppressed by the new physics scale. Furthermore, we systematically discuss tree level generalizations of the standard see-saw scenarios from higher dimensional operators. Finally, we point out that higher dimensional operators can also be generated at the loop level. In this case, we obtain the TeV scale as new physics scale even with order one couplings.

22 pages, 3 figures, 2 tables. Some references added