  It is well known that many interesting realisations of string theories can be
obtained via hamiltonian reduction from WZW models. I want to point out that
string theories do in certain cases also provide the recipe to reconstruct the
ambient space of the hamiltonian reduction, including Kac--Moody currents and
the associated ghosts. The procedure of reconstructing the Kac--Moody currents
is closely related to properties of matter+gravity multiplets in noncritical
string theories. In application to KPZ gravity and its N=1 supersymmetric
extension, the `inverted hamiltonian reduction' constructions serve to
establish relation with the DDK-type formalism for matter + gravity.
