  We address the question whether so-called m-invariants of the N=2 super
Virasoro algebra can be used for the construction of reasonable
four-dimensional string models. It turns out that an infinite subset of those
are pathological in the sense that - although N=2 supersymmetric - the Ramond
sector is not isomorphic to the Neveu-Schwarz sector. Consequently, these two
properties are independent and only requiring both guarantees an N=1 space-time
supersymmetric string spectrum. However, the remaining 529 consistent spectra -
210 of them are mirrors of Gepner models and 76 real orbifolds - show exact
mirror symmetry and are contained in a recent classification of orbifolds of
Gepner models.
