  We prove that outer commutator words are uniformly concise, i.e. if an outer
commutator word w takes m different values in a group G, then the order of the
verbal subgroup w(G) is bounded by a function depending only on m and not on w
or G. This is obtained as a consequence of a structure theorem for the subgroup
w(G), which is valid if G is soluble, and without assuming that w takes
finitely many values in G. More precisely, there is an abelian series of w(G),
such that every section of the series can be generated by values of w all of
whose powers are also values of w in that section. For the proof of this latter
result, we introduce a new representation of outer commutator words by means of
binary trees, and we use the structure of the trees to set up an appropriate
induction.
