  We discuss a class of models in which CP is violated softly in a heavy sector
adjoined to the standard model. Heavy-sector loops produce the observed CP
violation in kaon physics, yielding a tiny and probably undetectable value for
$\epsilon^\prime$. All other CP-violating parameters in the effective
low-energy standard model, including the area of the unitarity triangle and
$\bar\theta$, are finite, calculable and can be made very small. The leading
contribution to $\bar\theta$ comes from a four-loop graph. These models offer a
natural realization of superweak CP violation and can resolve the strong CP
puzzle. In one realization of this idea, CP is violated in the mass matrix of
heavy majorana neutrinos.
