  We briefly show how we can obtain Hamiltonians for spatially compact locally
homogeneous vacuum spacetimes. The dynamical variables are categorized into the
curvature parameters and the Teichm\"{u}ller parameters. While the
Teichm\"{u}ller parameters usually parameterise the covering group of the
spatial sections, we utilise another suitable parameterization where the
universal cover metric carries all the dynamical variables and with this we
reduce the Hamiltonians. For our models, all dynamical variables possess their
clear geometrical meaning, in contrast to the conventional open models.}
