  Utilizing results on the cosmology of anomalous discrete symmetries we show
that models of spontaneous CP violation can in principle avoid the domain wall
problem first pointed out by Zel'dovich, Kobzarev and Okun. A small but nonzero
$\theta_{QCD}$ explicitly breaks CP and can lift the degeneracy of the two CP
conjugate vacua through nonperturbative effects so that the domain walls become
unstable, but survive to cosmologically interesting epochs. We explore the
viability of spontaneous CP violation in the context of two Higgs models, and
find that the invisible axion solution of the strong CP problem cannot be
implemented without further extensions of the Higgs sector.
