  We describe a method for constructing genuinely asymmetric (2,0) heterotic
strings out of N=2 minimal models in the fermionic sector, whereas the bosonic
sector is only partly build out of N=2 minimal models. This is achieved by
replacing one minimal model plus the superfluous E_8 factor by a
non-supersymmetric CFT with identical modular properties. This CFT generically
lifts the weights in the bosonic sector, giving rise to a spectrum with fewer
massless states. We identify more than 30 such lifts, and we expect many more
to exist. This yields more than 450 different combinations. Remarkably, despite
the lifting of all Ramond states, it is still possible to get chiral spectra.
Even more surprisingly, these chiral spectra include examples with a certain
number of chiral families of SO(10), SU(5) or other subgroups, including just
SU(3) x SU(2) x U(1). The number of families and mirror families is typically
smaller than in standard Gepner models. Furthermore, in a large number of
different cases, spectra with three chiral families can be obtained. Based on a
first scan of about 10% of the lifted Gepner models we can construct, we have
collected more than 10.000 distinct spectra with three families, including
examples without mirror fermions. We present an example where the GUT group is
completely broken to the standard model, but the resulting and inevitable
fractionally charged particles are confined by an additional gauge group
factor.
