  The $\mu\tau$-reflection symmetric neutrino mass matrix can accommodate all
known neutrino mixing angles, with maximal atmospheric angle fixed, and
predicts all the unknown CP phases of the lepton sector but is unable to
predict the absolute neutrino mass scale. Here we present a highly predictive
scenario where $\mu\tau$-reflection is combined with a discrete abelian
symmetry to enforce a texture-zero in the mass matrix of the heavy right-handed
neutrinos that generate the light neutrino masses. Such a restriction reduces
the free parameters of the low energy theory to zero and the absolute neutrino
mass scale is restricted to few discrete regions, three in the few meV range
and one extending up to around 30 meV. The heavy neutrino sector is dependent
only on two free parameters which are further restricted to small regions from
the requirement of successful leptogenesis. Mass degenerate heavy neutrinos are
possible in one case but there is no resonant enhancement of the CP asymmetry.
