The moduli dependence of $(2,2)$ superstring compactifications based on
Calabi--Yau hypersurfaces in weighted projective space has so far only been
investigated for Fermat-type polynomial constraints. These correspond to
Landau-Ginzburg orbifolds with $c=9$ whose potential is a sum of $A$-type
singularities. Here we consider the generalization to arbitrary
quasi-homogeneous singularities at $c=9$. We use mirror symmetry to derive the
dependence of the models on the complexified K\"ahler moduli and check the
expansions of some topological correlation functions against explicit genus
zero and genus one instanton calculations. As an important application we give
examples of how non-algebraic (``twisted'') deformations can be mapped to
algebraic ones, hence allowing us to study the full moduli space. We also study
how moduli spaces can be nested in each other, thus enabling a (singular)
transition from one theory to another. Following the recent work of Greene,
Morrison and Strominger we show that this corresponds to black hole
condensation in type II string theories compactified on Calabi-Yau manifolds.
