  If $V$ is an analytic set in a pseudoconvex domain $\Omega$, we show there is
always a pseudoconvex domain $G \subseteq \Omega$ that contains $V$ and has the
property that every bounded holomorphic function on $V$ extends to a bounded
holomorphic function on $G$ with the same norm. We find such a $G$ for some
particular analytic sets.
  When $\Omega$ is an operhedron we show there is a norm on holomorphic
functions on $V$ that can always be preserved by extensions to $\Omega$.
