  The classical Benjamin and Lighthill conjecture about steady water waves
states that the non-dimensional flow force constant of a solution is bounded by
the corresponding constants of the supercritical and subcritical uniform
streams respectively. These inequalities determine a parameter region that
covers all steady motions. In fact not all points of the region determine a
steady wave. In this note we prove a new and explicit lower bound for the flow
force constant, which is asymptotically sharp in a certain sense. In
particular, this recovers the well known inequality F<2 for the Froude number,
while significantly reducing the parameter region supporting steady waves.
