  A (pseudo-)metric $D$ on a finite set $X$ is said to be a `tree metric' if
there is a finite tree with leaf set $X$ and non-negative edge weights so that,
for all $x,y \in X$, $D(x,y)$ is the path distance in the tree between $x$ and
$y$. It is well known that not every metric is a tree metric. However, when
some such tree exists, one can always find one whose interior edges have
strictly positive edge weights and that has no vertices of degree 2, any such
tree is -- up to canonical isomorphism -- uniquely determined by $D$, and one
does not even need all of the distances in order to fully (re-)construct the
tree's edge weights in this case. Thus, it seems of some interest to
investigate which subsets of $\binom{X}{2}$ suffice to determine (`lasso')
these edge weights. In this paper, we use the results of a previous paper to
discuss the structure of a matroid that can be associated with an (unweighted)
$X-$tree $T$ defined by the requirement that its bases are exactly the `tight
edge-weight lassos' for $T$, i.e, the minimal subsets $\cl$ of $\ch$ that lasso
the edge weights of $T$.
