  For the problem describing steady, gravity waves with vorticity on a
two-dimensional, unidirectional flow of finite depth the following results are
obtained. (i) Bounds for the free-surface profile and for Bernoulli's constant.
(ii) If only one parallel shear flow exists for a given value of Bernoulli's
constant, then there are no wave solutions provided the vorticity distribution
is subject to a certain condition.
