  We present an ab initio study of double perovskite La$_2$VCuO$_6$, which was
one of the earliest compounds suggested as a potential compensated half-metal.
Two charge and spin configurations close in energy have been identified. (i)
The originally envisioned spin-compensated V$^{4+}$:d$^1$/Cu$^{2+}$:d$^1$
configuration is comprised of antialigned S=1/2 cations. This state is a
spin-compensated half-metal for moderate values of U (the on-site Coulomb
repulsion strength on the metal ions) and is insulating for larger values of U.
(ii) An unanticipated non-magnetic solution V$^{5+}$:d$^0$/Cu$^{+}$:d$^{10}$
consists of an empty- and a full-shell ion, both spherically symmetric, that
leads to a band insulator. This ionic band insulator is calculated to be the
ground state at small and moderate values of U. The different distortions of
the perovskite structure that occur for each state are central in determining
the energy differences. Treating the Cu$^{2+}$ Jahn-Teller distortion
self-consistently is particularly important for the magnetic solution.
