  In the context of the Type I seesaw mechanism, we carry out a systematic
study of the constraints that result from zeros in both the Dirac and
right-handed Majorana neutrino mass matrices. We find that most constraints can
be expressed in the standard form with one or two element/cofactor zeros alone,
while there are 9 classes of nonstandard constraints. We show that all the
constraints are stable under one-loop renormalization group running from the
lightest right-handed neutrino mass scale to the electroweak scale. We study
the predictions of the nonstandard constraints for the lightest neutrino mass,
Dirac CP phase and neutrinoless double beta decay.
