  In this paper we complete a chain of explicit Quillen equivalences between
the model category for $\Theta_{n+1}$-spaces and the model category of small
categories enriched in $\Theta_n$-spaces. The Quillen equivalences given here
connect Segal category objects in $\Theta_n$-spaces, complete Segal objects in
$\Theta_n$-spaces, and $\Theta_{n+1}$-spaces.
