  We prove two Liouville type theorems for the stationary Navier-Stokes
equations in $\mathbb{R}^3$ under some assumptions on 1) the growth of the
$L^s$ mean oscillation of a potential function of the velocity field, or 2) the
relative decay of the head pressure and the square of the velocity field at
infinity. The main idea is to use Saint-Venant type estimates to characterize
the growth of Dirichlet energy of nontrivial solutions. These assumptions are
weaker than those previously known of a similar nature.
