  The recent classification of Landau--Ginzburg potentials and their abelian
symmetries focuses attention on a number of models with large positive Euler
number for which no mirror partner is known. All of these models are related to
Calabi--Yau manifolds in weighted $\IP_4$, with a characteristic structure of
the defining polynomials. A closer look at these potentials suggests a series
of non-linear transformations, which relate the models to configurations for
which a construction of the mirror is known, though only at certain points in
moduli space. A special case of these transformations generalizes the $\ZZ_2$
orbifold representation of the $D$ invariant, implying a hidden symmetry in
tensor products of minimal models.
