  We present a complete analysis of scenarios with radiatively generated
neutrino masses that may occur in the Minimal Supersymmetric Standard Model
with low-scale right-handed neutrinos. For brevity, we call such a model the
$\nu_R$MSSM. We pay particular attention to the impact of the
non-renormalization theorem of supersymmetry (SUSY) on the loop-induced
neutrino masses, by performing our computations in the weak and flavour bases.
In particular, we find that the smallness of the observed light neutrino masses
may naturally arise due to a soft SUSY-screening effect from a nearly
supersymmetric singlet neutrino sector. The profound phenomenological and
cosmological implications that may originate from this screening phenomenon in
the $\nu_R$MSSM and its minimal extensions are discussed.
