  A group-word w is called concise if whenever the set of w-values in a group G
is finite it always follows that the verbal subgroup w(G) is finite. More
generally, a word w is said to be concise in a class of groups X if whenever
the set of w-values is finite for a group G in X, it always follows that w(G)
is finite. P. Hall asked whether every word is concise. Due to Ivanov the
answer to this problem is known to be negative. It is still an open problem
whether every word is concise in the class of residually finite groups. A word
w is rational if the number of solutions to the equation w=g is the same as the
number of solutions to w=g^e for every finite group G and for every e
relatively prime to |G|. We observe that any rational word is concise in the
class of residually finite groups. Further we give a sufficient condition for
rationality of a word. This is used to produce a new family of words that are
concise in the class of residually finite groups.
