  We derive sufficient conditions that guarantee a robust solution of the
strong CP problem in theories with spontaneous CP violation, and introduce a
class of models satisfying these requirements. In the simplest scenarios the
dominant contribution to the topological angle arises at 3-loop order in the
Yukawa couplings. A variety of realizations are possible on a warped extra
dimension, which can simultaneously address the Planck-TeV hierarchy.
Experimental signatures of this approach to the strong CP problem include
flavor violation and vector-like partners of the top or bottom quarks.
