  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 "$\mu$-terms". These models can be tested both in colliders and with
the observation of lepton flavour violating processes.
