  A tangle of order $k$ in a matroid or graph may be thought of as a
"$k$-connected component". For a tangle of order $k$ in a matroid or graph that
satisfies a certain robustness condition, we describe a tree decomposition of
the matroid or graph that displays, up to a certain natural equivalence, all of
the $k$-separations of the matroid or graph that are non-trivial with respect
to the tangle.
