  We carry out an analytic study of odd-parity perturbations of the
self-similar Vaidya space-times that admit a naked singularity. It is found
that an initially finite perturbation remains finite at the Cauchy horizon.
This holds not only for the gauge invariant metric and matter perturbation, but
also for all the gauge invariant perturbed Weyl curvature scalars, including
the gravitational radiation scalars. In each case, `finiteness' refers to
Sobolev norms of scalar quantities on naturally occurring spacelike
hypersurfaces, as well as pointwise values of these quantities.
