  In the framework of the seesaw mechanism, and adopting a typical form for the
Dirac neutrino mass matrix, we discuss the impact of minimal forms of the
Majorana neutrino mass matrix. These matrices contain four or three texture
zeros and only two parameters, a scale factor and a hierarchy parameter. Some
forms are not compatible with large lepton mixing and are ruled out. Moreover,
a normal mass hierarchy for neutrinos is predicted.
