  The observation of neutrinoless double beta decay would allow to establish
lepton number violation and the Majorana nature of neutrinos. The rate of this
process in the case of 3-neutrino mixing is controlled by the neutrinoless
double beta decay effective Majorana mass $|\langle m \rangle|$. For a neutrino
mass spectrum with normal ordering, which is favoured over the spectrum with
inverted ordering by recent global fits, $|\langle m \rangle|$ can be
significantly suppressed. Taking into account updated data on the neutrino
oscillation parameters, we investigate the conditions under which $|\langle m
\rangle|$ in the case of spectrum with normal ordering exceeds
$10^{-3}~(5\times 10^{-3})$ eV: $|\langle m \rangle|_\text{NO} >
10^{-3}~(5\times 10^{-3})$ eV. We analyse first the generic case with
unconstrained leptonic CP violation Majorana phases. We show, in particular,
that if the sum of neutrino masses is found to satisfy $\Sigma > 0.10$ eV, then
$|\langle m \rangle|_\text{NO} > 5\times 10^{-3}$ eV for any values of the
Majorana phases. We consider also cases where the values for these phases are
either CP conserving or are in line with predictive schemes combining flavour
and generalised CP symmetries.
