Let $K$ be a field complete with respect to an absolute value associated to a nontrivial discrete valuation. Let $K^{\circ}$ be the ring of integers. Let ${\mathcal{X}}$ be a proper model over $K^{\circ}$ of $\mathbb{P}^{1}_{K}$. Then there exists a finite extension $H$ of $K$ with ring of integers ${H}^{\circ}$, a semi-stable model ${\mathcal{X}}^{\prime}$ of $\mathbb{P}^{1}_{H}$, and a proper morphism of models $\mathcal{X}^{\prime}\to\mathcal{X}\times\operatorname{Spec}({H}^{\circ})$.