  A "tree-partition" of a graph $G$ is a partition of $V(G)$ such that
identifying the vertices in each part gives a tree. It is known that every
graph with treewidth $k$ and maximum degree $\Delta$ has a tree-partition with
parts of size $O(k\Delta)$. We prove the same result with the extra property
that the underlying tree has maximum degree $O(\Delta)$ and $O(|V(G)|/k)$
vertices.
