  We consider the quantization of a general spatially homogeneous space-time
belonging to an arbitrary but fixed Class A Bianchi type. Exploiting the
information furnished by the quantum version of the momentum constraints, we
use as variables the two simplest contractions of $C^{\alpha}_{\beta \gamma}$
and $\gamma_{\alpha \beta}$ as well as the determinant of $\gamma_{\alpha
\beta}$ ; We thus arrive at an equation for the wave function in terms of these
quantities. This fact enables us to treat in a uniform manner all Class A
cosmologies. For these spacetimes the Langrangian used correctly reproduces
Einstein's equations. We also discuss the imposition of simplifying
ans\"{a}tzen at the quantum level in a way that respects the scalings of the
quadratic Hamiltonian constraint.
