  We consider a version of the low-scale type I seesaw mechanism for generating
small neutrino masses, as an alternative to the standard seesaw scenario. It
involves two right-handed (RH) neutrinos $\nu_{1R}$ and $\nu_{2R}$ having a
Majorana mass term with mass $M$, which conserves the lepton charge $L$. The RH
neutrino $\nu_{2R}$ has lepton-charge conserving Yukawa couplings $g_{\ell 2}$
to the lepton and Higgs doublet fields, while small lepton-charge breaking
effects are assumed to induce tiny lepton-charge violating Yukawa couplings
$g_{\ell 1}$ for $\nu_{1R}$, $l=e,\mu,\tau$. In this approach the smallness of
neutrino masses is related to the smallness of the Yukawa coupling of
$\nu_{1R}$ and not to the large value of $M$: the RH neutrinos can have masses
in the few GeV to a few TeV range. The Yukawa couplings $|g_{\ell 2}|$ can be
much larger than $|g_{\ell 1}|$, of the order $|g_{\ell 2}| \sim 10^{-4} -
10^{-2}$, leading to interesting low-energy phenomenology. We consider a
specific realisation of this scenario within the Froggatt-Nielsen approach to
fermion masses. In this model the Dirac CP violation phase $\delta$ is
predicted to have approximately one of the values $\delta \simeq \pi/4,\,
3\pi/4$, or $5\pi/4,\, 7\pi/4$, or to lie in a narrow interval around one of
these values. The low-energy phenomenology of the considered low-scale seesaw
scenario of neutrino mass generation is also briefly discussed.
