Suppose ${\mathcal{X}}$ and ${\mathcal{X}}^{\prime}$ are snc models and that ${\mathcal{X}}^{\prime}$ dominates ${\mathcal{X}}$ via $\rho\colon{\mathcal{X}}^{\prime}\to{\mathcal{X}}$. Then there exists a third snc model ${\mathcal{X}}^{\prime\prime}$ dominating ${\mathcal{X}}^{\prime}$, such that the induced map ${\mathcal{X}}^{\prime\prime}\to{\mathcal{X}}$ is a composition of simple blowups.