Let $f : X \rightarrow Y$ be a finite type morphism of Noetherian schemes. The valuative criterion for properness runs as follows. Suppose that for any DVR $R$ with fraction field $K$ that any $K$-valued point of $X$ lying above an $R$-valued point of $Y$ extends uniquely to an $R$-valued point of $X$. Then $f$ is proper.

Does it suffice to check instead that any $K$-valued point of $X$ lying above an $R$-valued point of $Y$ extends to an $R'$-valued point of $X$, where $R'$ is the integral closure of $R$ in a finite extension $K'$ of $K$?