  We analyze a class of supersymmetric models first introduced by Arkani-Hamed
et al and Borzumati et al in which the light neutrino masses result from
higher-dimensional supersymmetry-breaking terms in the MSSM super- and
Kahler-potentials. The mechanism is closely related to the Giudice-Masiero
mechanism for the MSSM $\mu$ parameter, and leads to TeV-scale right-handed
neutrino and sneutrino states, that are in principle accessible to direct
experimental study. The dominant contribution to the light neutrino (Majorana)
mass matrix is a one-loop term induced by a lepton-number violating $B$-term
for the sneutrino states that is naturally present. We focus upon the
simplification and analysis of the flavour structure of this general class of
models, finding that simple and novel origins for the light neutrino mass
matrix are possible. We find that a subdominant tree-level `see-saw'
contribution may lead to interesting perturbations of the leading
one-loop-induced flavour structure, possibly generating the small ratio $\Delta
m_{\rm solar}^2/\Delta m_{\rm atm}^2$ dynamically.
