  Given a group-word w and a group G, the verbal subgroup w(G) is the one
generated by all w-values in G. The word w is called concise if w(G) is finite
whenever the set of w-values in G is finite. It is an open question whether
every word is concise in residually finite groups. Let w=w(x_1,..,x_k) be a
multilinear commutator word, n a positive integer and q a prime power. In the
present article we show that the word [w^q,_n y] is concise in residually
finite groups while the word [w,_n y] is boundedly concise in residually finite
groups.
