  The classical theorems of Mittag-Leffler and Weierstrass show that when
$\{\lambda_n\}$ is a sequence of distinct points in the open unit disk $\D$,
with no accumulation points in $\D$, and $\{w_n\}$ is any sequence of complex
numbers, there is an analytic function $\phi$ on $\D$ for which
$\phi(\lambda_n) = w_n$. A celebrated theorem of Carleson \cite{MR117349}
characterizes when, for a bounded sequence $\{w_n\}$, this interpolating
problem can be solved with a bounded analytic function. A theorem of Earl
\cite{MR284588} goes further and shows that when Carleson's condition is
satisfied, the interpolating function $\phi$ can be a constant multiple of a
Blaschke product. In this paper, we explore when the interpolating $\phi$ can
be an outer function. We then use our results to refine a result of McCarthy
\cite{MR1065054} and explore the common range of the co-analytic Toeplitz
operators on a model space.
