  We prove: If $f(z)$ is a critically finite rational map which has exactly two
critical points and which is not conjugate to a polynomial, then the boundary
of every Fatou component of $f$ is a Jordan curve. If $f(z)$ is a hyperbolic
critically finite rational map all of whose postcritical points are periodic,
then there exists a cycle of Fatou components whose boundaries are Jordan
curves. We give examples of critically finite hyperbolic rational maps $f$ with
the property that on the closure of a Fatou component $\Omega$ satisfying
$f(\Omega)=\Omega$, $f|_{\bdry \Omega}$ is not topologically conjugate to the
dynamics of any polynomial on its Julia set.
