  Assuming that neutrinos are Majorana particles, we explore what information
can be inferred from future strong limits (i.e. non-observation) for
neutrinoless double beta decay. Specifically we consider the case where the
mass hierarchy is normal and the different contributions to the effective mass
$\langle m \rangle_{ee}$ partly cancel. We discuss how this fixes the two
Majorana CP phases simultaneously from the Majorana Triangle and how it limits
the lightest neutrino mass $m_1$ within a narrow window. The two Majorana CP
phases are in this case even better determined than in the usual case for
larger $\langle m \rangle_{ee}$. We show that the uncertainty in these
predictions can be significantly reduced by the complementary measurement of
reactor neutrino experiments, especially the medium baseline version
JUNO/RENO-50. We also estimate the necessary precision on $\langle m
\rangle_{ee}$ to infer non-trivial Majorana CP phases and the upper limit
$\langle m \rangle_{ee} \lesssim 1\,\mbox{meV}$ sets a target for the design of
future neutrinoless double beta decay experiments.
