  We reconsider a class of heterotic string theories studied in 1989, based on
tensor products of N=2 minimal models with asymmetric simple current
invariants. We extend this analysis from (2,2) and (1,2) spectra to (0,2)
spectra with SO(10) broken to the Standard Model. In the latter case the
spectrum must contain fractionally charged particles. We find that in nearly
all cases at least some of them are massless. However, we identify a large
subclass where the fractional charges are at worst half-integer, and often
vector-like. The number of families is very often reduced in comparison to the
1989 results, but there are no new tensor combinations yielding three families.
All tensor combinations turn out to fall into two classes: those where the
number of families is always divisible by three, and those where it is never
divisible by three. We find an empirical rule to determine the class, which
appears to extend beyond minimal N=2 tensor products. We observe that
distributions of physical quantities such as the number of families, singlets
and mirrors have an interesting tendency towards smaller values as the gauge
groups approaches the Standard Model. We compare our results with an analogous
class of free fermionic models. This displays similar features, but with less
resolution.Finally we present a complete scan of the three family models based
on the triply-exceptional combination (1,16*,16*,16*) identified originally by
Gepner. We find 1220 distinct three family spectra in this case, forming 610
mirror pairs. About half of them have the gauge group SU(3) x SU(2)_L x SU(2)_R
x U(1)^5, the theoretical minimum, and many others are trinification models.
