Let $X_{\infty}$ be a limit space then, assuming the truth of Theorem $3.2$, there is an integer $k_{X_{\infty}}$ and a $b_{X_{\infty}}>0$ such that if $X_{i}\in{\mathcal{K}}(n,C,V)$ has Gromov-Hausdorff limit $X_{\infty}$ then for sufficiently large $i$ we have $\underline{\rho}(k_{X_{\infty}},X_{i})\geq b^{2}_{X_{\infty}}$.