  We complete the classification of (2,2) vacua that can be constructed from
Landau--Ginzburg models by abelian twists with arbitrary discrete torsions.
Compared to the case without torsion the number of new spectra is surprisingly
small. In contrast to a popular expectation mirror symmetry does not seem to be
related to discrete torsion (at least not in the present compactification
framework): The Berglund-H"ubsch construction naturally extends to orbifolds
with torsion; for more general potentials, on the other hand, the new spectra
neither have nor provide mirror partners in our class of models.
