For every $0<\epsilon\leq\epsilon({\rm v})$, there exists $\delta=\delta({\rm v},\epsilon)$ with the following properties. Let $M^{4}$ satisfy $|{\rm Ric}_{M^{4}}|\leq 3\delta$ and ${\rm Vol}(B_{1}(p))>{\rm v}>0$. Let $x\in B_{1}(p)$ and assume $\alpha_{1}\in\mathds{N}$ satisfies $T^{\delta}_{\alpha_{1}}(x)=0$ with $\Gamma_{\alpha_{1}}$ the corresponding group. Then if $\alpha_{2}\in\mathds{N}$ is such that $\mathcal{V}^{\delta}_{r_{\alpha_{2}}/4}(x)\geq\ln\big|\Gamma_{\alpha_{1}}\big|-\delta$, there exists a subset $A_{r_{\alpha_{2}}/2,2r_{\alpha_{1}}}(x)\subseteq U\subseteq A_{(1-\epsilon)r_{\alpha_{2}}/2,2(1+\epsilon)r_{\alpha_{1}}}(x)$ and a diffeomorphism $\Phi:A_{r_{\alpha_{2}}/2,2r_{\alpha_{1}}}(0)\to U$, where $0\in\mathds{R}^{4}/\Gamma_{\alpha_{1}}$, such that if $g_{ij}=\Phi^{*}g$ is the pullback metric, we have