Extracting non-canonical places

Let $(X,B)$ be a log canonical pair and $\mathcal{V}$ be a finite set of divisorial valuations with log discrepancy in $[0,1)$. We prove that there exists a projective birational morphism $\pi \text{\hspace{0.17em}⁣}:Y\to X$ so that the exceptional divisors are $\mathbb{Q}$-Cartier and correspond to elements of $\mathcal{V}$. We study how two such models are related. Moreover, we provide an application to the study of deformations of log canonical singularities.