  Let $B$ be a separable $C^*$-algebra, let $\Gamma$ be a discrete countable
group, let $\alpha: \Gamma \to \text{Aut}(B)$ be an action, and let $A$ be an
invariant subalgebra. We find certain freeness conditions which guarantee that
any intermediate $C^*$-algebra $A \rtimes_{\alpha,r} \Gamma \subseteq C
\subseteq B \rtimes_{\alpha,r} \Gamma$ is a crossed product of an intermediate
invariant subalgebra $A \subseteq C_0 \subseteq B$ by $\Gamma$. Those are used
to generalize related results by Suzuki.
