  Given an inner function $B$ we classify the invariant subspaces of the
algebra $H^\infty_B:=\mathbb{C}+BH^\infty$. We derive a formula in terms of
these invariant subspaces for the distance of an element in $L^\infty$ to a
certain weak*-closed ideal in $H^\infty_B$ and use this to prove an analogue of
the Nevanlinna-Pick interpolation theorem.
