  Two of the important unresolved issues concerning fractional superstrings
have been the appearance of new massive sectors whose spacetime statistics
properties are unclear, and the appearance of new types of ``internal
projections'' which alter or deform the worldsheet conformal field theory in a
highly non-trivial manner. In this paper we provide a systematic analysis of
these two connected issues, and explicitly map out the effective
post-projection worldsheet theories for each of the fractional-superstring
sectors. In this way we determine their central charges, highest weights,
fusion rules, and characters, and find that these theories are isomorphic to
those of free worldsheet bosons and fermions.
  We also analyze the recently-discovered parafermionic ``twist current'' which
has been shown to play an important role in reorganizing the
fractional-superstring Fock space, and find that this current can be expressed
directly in terms of the primary fields of the post-projection theory. This
thereby enables us to deduce some of the spacetime statistics properties of the
surviving states.
