Valuation rings of the formal Laurent series field $K((x))$.

Question

Let $K$ be a field and $K((x))$ be the formal Laurent series over $K$. The ring of formal power series $K[[x]]$ is a valuation ring of $K((x))$. I would like to see another concrete example of a valuation ring of $K((x))$ that is not comparable (by inclusion) with $K[[x]]$. Thanks for any help.