Abstract: After developing a general criterion for deciding which neutrino mass models belong to the category of inverse seesaw models, we apply it to obtain the Dirac analogue of the canonical Majorana inverse seesaw model. We then generalize the inverse seesaw model and obtain a class of inverse seesaw mechanisms both for Majorana and Dirac neutrinos. We further show that many of the models have double or multiple suppressions coming from tiny symmetry breaking “mu -parameters”. These models can be tested both in colliders and with the observation of lepton flavour violating processes.