  We study asymmetric simple-current extensions of Gepner models in dimensions
$D=4,6,8$ with at least eight supercharges in the right-moving sector. The
models obtained in an extensive stochastic computer search belong to a small
number of different classes. These classes can be categorized as dimensional
reductions, asymmetric orbifolds with $(-1)^{F_L}$, extra gauge enhancement and
as coming from the super Higgs-effect. Models in the latter class are
particularly interesting, as they may correspond to non-geometric flux
compactifications.
