  It was noted recently that the ADM-diffeomorphism-constraint does not
generate all observed symmetries for several Bianchi-models. We will suggest
not to use the ADM-constraint restricted to homogeneous variables, but some
equivalent which is derived from a restricted action principle. This will
generate all homogeneity preserving diffeomorphisms, which will be shown to be
automorphism generating vector fields, in class A and class B models. Following
Dirac's constraint formalism one will naturally be restricted to the unimodular
part of the automorphism group.
