  We continue the study of $\mathcal{OL}_\infty$ structure of nuclear
$C^*$-algebras initiated by Junge, Ozawa and Ruan. In particular, we prove if
$\mathcal{OL}_\infty(A)<1.005,$ then $A$ has a separating family of
irreducible, stably finite representations. As an application we give examples
of nuclear, quasidiagonal $C^*$-algebras $A$ with $\mathcal{OL}_\infty(A)>1.$
