  We use recent advances in circle packing theory to develop a constructive
method for the approximation of an analytic function $F:\Omega \to \bold C$ by
circle packing maps providing we have only been given $\Omega$,
$|F'|\big|_{\Omega}$, and the set of critical points of $F$. This extends the
earlier result of Ithiel Carter and Burt Rodin [CR] for $F$ with no critical
points.
