  One often hears that the strong $CP$ problem is the one problem which cannot
be solved by anthropic reasoning. We argue that this is not so. Due to
nonperturbative dynamics, states with a different $CP$ violating paramenter
$\theta$ acquire different vacuum energies after the QCD phase transition.
These add to the total variation of the cosmological constant in the putative
landscape of Universes. An interesting possibility arises when the cosmological
constant is mostly cancelled by the membrane nucleation mechanism. If the step
size in the resulting discretuum of cosmological constants, $\Delta \Lambda$,
is in the interval $({\rm meV})^4 < \Delta \Lambda < (100 \, {\rm MeV})^4$, the
cancellation of vacuum energy can be assisted by the scanning of $\theta$. For
$({\rm meV})^4 < \Delta \Lambda < ({\rm keV})^4$ this yields $\theta <
10^{-10}$, meeting the observational limits. This scenario opens up 24 orders
of magnitude of acceptable parameter space for $\Delta \Lambda$ compared to
membrane nucleation acting alone. In such a Universe one may not need a light
axion to solve the strong $CP$ problem.
