  We further study the previously proposed Ansatz, Tr(M)=0, for a prediagonal
light Majorana type neutrino mass matrix. If CP violation is neglected this
enables one to use the existing data on squared mass differences to estimate
(up to a discrete ambiguity)the neutrino masses themselves. If it is assumed
that only the conventional CP phase is present, the ansatz enables us to
estimate this phase in addition to all three masses. If it is assumed that only
the two Majorana CP phases are present, the Ansatz enables us to obtain a one
parameter family of solutions for the masses and phases. This enables us to
obtain a simple "global" view of lepton number violation effects. Furthermore,
using an SO(10) motivation for the Ansatz suggests an amusing toy (clone) model
in which the heavy neutrinos have the same mixing pattern and mass ratios as
the light ones. In this case only their overall mass scale is not known
(although it is constrained by the initial motivation). Using this toy model we
make a rough estimate of the baryon to photon ratio induced by the leptogenesis
mechanism. Solutions close to the CP conserving cases seem to be favored.
