  Given a group-word $w$ and a group $G$, the set of $w$-values in $G$ is
denoted by $G_w$ and the verbal subgroup $w(G)$ is the one generated by $G_w$.
The word $w$ is concise if $w(G)$ is finite for all groups $G$ in which $G_w$
is finite. We obtain several results supporting the conjecture that the word
$[u_1,\dots,u_s]$ is concise whenever the words $u_1,\dots,u_s$ are
non-commutator.
