  We present new results for classical-particle propagation subject to Lorentz
violation. Our analysis is dedicated to spin-nondegenerate operators of
arbitrary mass dimension provided by the fermion sector of the Standard-Model
Extension. In particular, classical Lagrangians are obtained for the operators
$\hat{b}_{\mu}$ and $\hat{H}_{\mu\nu}$ as perturbative expansions in Lorentz
violation. The functional dependence of the higher-order contributions in the
background fields is found to be quite peculiar, which is probably attributed
to particle spin playing an essential role for these cases. This paper closes
one of the last gaps in understanding classical-particle propagation in the
presence of Lorentz violation. Lagrangians of the kind presented will turn out
to be valuable for describing particle propagation in curved backgrounds with
diffeomorphism invariance and/or local Lorentz symmetry explicitly violated.
