With notation as in Proposition 3.5, we suppose $D\subset D^{\prime}$ is a disc centred on the origin of radius $a\leq a^{\prime}<1$, and let $Diam(\epsilon)$ denote the diameter of the total space of the elliptic fibration over $D$, under an Ooguri–Vafa metric on $X^{\prime}$ with fibre volume $\epsilon$. There exists a constant $C_{3}$ (independent of both $\epsilon$ and $a$) such that, if $\epsilon\leq a$, then