Let $f:X\dashrightarrow Y$ be the flip of a small contraction $\phi:X\rightarrow Z$, and let $\psi:Y\rightarrow Z$ be the small contraction such that $\psi\circ f = \phi$. Let $Exc(\phi), Exc(\psi)$ be the exceptional loci of $\phi$ and $\psi$ respectively.

Do we always have $\dim(Exc(\psi)) = \operatorname{codim}_X(Exc(\phi))-1$ ?