  Several aspects of next-to-leading (NLO) order corrections to see-saw
formulas are discussed and phenomenologically relevant situations are
identified. We generalize the formalism to calculate the NLO terms developed
for the type I see-saw to variants like the inverse, double or linear see-saw,
i.e., to cases in which more than two mass scales are present. In the standard
type I case with very heavy fermion singlets the sub-leading terms are
negligible. However, effects in the percent regime are possible when
sub-matrices of the complete neutral fermion mass matrix obey a moderate
hierarchy, e.g. weak scale and TeV scale. Examples are cancellations of large
terms leading to small neutrino masses, or inverse see-saw scenarios. We
furthermore identify situations in which no NLO corrections to certain
observables arise, namely for mu-tau symmetry and cases with a vanishing
neutrino mass. Finally, we emphasize that the unavoidable unitarity violation
in see-saw scenarios with extra fermions can be calculated with the formalism
in a straightforward manner.
