  In dirty superconducting wires, quasiparticle states at the Fermi level need
not be exponentially localized if spin-rotation symmetry is broken [Brouwer
{\em et al.}, Phys. Rev. Lett. {\bf 85}, 1064 (2000)]. Here we present evidence
that not-localized states are generic in the thick-wire limit, while for wires
of finite thickness delocalization requires fine tuning of the disorder,
consistent with earlier results of Motrunich {\em et al.} [Phys. Rev. B {\bf
63}, 224204 (2001)]. The thick-wire limit is defined as the simultaneous limit
where the length $L$ of the wire and the number $N$ of propagating channels at
the Fermi energy are both taken to infinity with their ratio held fixed.
