  In the type I + II seesaw formula the mass matrix of light neutrinos m_nu
receives contributions from the exchanges of both heavy Majorana neutrinos and
SU(2)_L-triplet Higgs bosons. We propose a new parameterization for the
Dirac-type Yukawa coupling matrix of neutrinos in this case, which generalizes
the well known Casas-Ibarra parameterization to type I + II seesaw and is
useful when the triplet term in m_nu is known. Neutrino masses and mixing,
lepton flavor violation in decays like mu -> e \gamma within mSUGRA models and
leptogenesis can then be studied within this framework. We illustrate the
usefulness of our new parameterization using a number of simple examples.
