  In this paper, we show that the $(3k+4)$-dimensional Weisfeiler--Leman
algorithm can identify graphs of treewidth $k$ in $O(\log n)$ rounds. This
improves the result of Grohe & Verbitsky (ICALP 2006), who previously
established the analogous result for $(4k+3)$-dimensional Weisfeiler--Leman. In
light of the equivalence between Weisfeiler--Leman and the logic $\textsf{FO} +
\textsf{C}$ (Cai, F\"urer, & Immerman, Combinatorica 1992), we obtain an
improvement in the descriptive complexity for graphs of treewidth $k$.
Precisely, if $G$ is a graph of treewidth $k$, then there exists a
$(3k+5)$-variable formula $\varphi$ in $\textsf{FO} + \textsf{C}$ with
quantifier depth $O(\log n)$ that identifies $G$ up to isomorphism.
