There exists $\delta({\rm v})>0$ such that if $M^{4}$ satisfies $|{\rm Ric}_{M^{4}}|<2\delta$, ${\rm Vol}(B_{1}(p))>{\rm v}>0$, and $T^{\delta}_{0}(p)=0$, then there exists $B_{1}(p)\subseteq U\subseteq B_{2}(p)$ such that $U$ has at most $C({\rm v})$ diffeomorphism types. Further, $U$ can be chosen so that it’s boundary $\partial U$ is diffeomorphic to $S^{3}/\Gamma$ and satisfies the second fundamental form estimate $|A|\leq C(v)$.