  Let $f$ be an entire transcendental function of finite order and $\Delta$ be
a forward invariant bounded Siegel disk for $f$ with rotation number in
Herman's class $\mathcal{H}$. We show that if $f$ has two singular values with
bounded orbit, then the boundary of $\Delta$ contains a critical point. We also
give a criterion under which the critical point in question is recurrent. We
actually prove a more general theorem with less restrictive hypotheses, from
which these results follow.
