In this talk I will introduce a quantitative notion of exactness within Diophantine approximation. Given functions $\psi: (0,1) \rightarrow (0,1)$ and $\omega: (0,\infty) \rightarrow (0,1)$, we study the set of points that are $\psi$-well approximable but not $\psi(1-\omega)$-well approximable, denoted $E(\psi,\omega)$. This generalises the set of $\psi$-exact approximation order as studied by Bugeaud (Math. Ann. 2003). In joint work with Simon Baker we prove results on the cardinality and Hausdorff dimension of $E(\psi,\omega)$. In particular, for certain functions $\psi$ we find a critical threshold on $\omega$ whereby the set $E(\psi,\omega)$ drops from positive Hausdorff dimension to empty when $\omega$ is multiplied by a constant.