  In this paper we consider interpolation in model spaces, $H^2 \ominus B H^2$
with $B$ a Blaschke product. We study unions of interpolating sequences for two
sequences that are far from each other in the pseudohyperbolic metric as well
as two sequences that are close to each other in the pseudohyperbolic metric.
The paper concludes with a discussion of the behavior of Frostman sequences
under perturbations.
