  The tight upper bound on the state complexity of the reverse of R-trivial and
J-trivial regular languages of the state complexity n is 2^{n-1}. The witness
is ternary for R-trivial regular languages and (n-1)-ary for J-trivial regular
languages. In this paper, we prove that the bound can be met neither by a
binary R-trivial regular language nor by a J-trivial regular language over an
(n-2)-element alphabet. We provide a characterization of tight bounds for
R-trivial regular languages depending on the state complexity of the language
and the size of its alphabet. We show the tight bound for J-trivial regular
languages over an (n-2)-element alphabet and a few tight bounds for binary
J-trivial regular languages. The case of J-trivial regular languages over an
(n-k)-element alphabet, for 2 <= k <= n-3, is open.
