  Given a subset $\Lambda$ of $\mathbb Z_+:=\{0,1,2,\dots\}$, let
$H^\infty(\Lambda)$ denote the space of bounded analytic functions $f$ on the
unit disk whose coefficients $\widehat f(k)$ vanish for $k\notin\Lambda$.
Assuming that either $\Lambda$ or $\mathbb Z_+\setminus\Lambda$ is finite, we
determine the extreme points of the unit ball in $H^\infty(\Lambda)$.
