  We study thin interpolating sequences $\{\lambda_n\}$ and their relationship
to interpolation in the Hardy space $H^2$ and the model spaces $K_\Theta = H^2
\ominus \Theta H^2$, where $\Theta$ is an inner function. Our results, phrased
in terms of the functions that do the interpolation as well as Carleson
measures, show that under the assumption that $\Theta(\lambda_n) \to 0$ the
interpolation properties in $H^2$ are essentially the same as those in
$K_\Theta$.
