  A $k$-block in a graph $G$ is a maximal set of at least $k$ vertices no two
of which can be separated in $G$ by removing less than $k$ vertices. It is
separable if there exists a tree-decomposition of adhesion less than $k$ of $G$
in which this $k$-block appears as a part.
  Carmesin, Diestel, Hamann, Hundertmark and Stein proved that every finite
graph has a canonical tree-decomposition of adhesion less than $k$ that
distinguishes all its $k$-blocks and tangles of order $k$. We construct such
tree-decompositions with the additional property that every separable $k$-block
is equal to the unique part in which it is contained. This proves a conjecture
of Diestel.
