  We establish an estimate of the BMO-norm of a divergence-free vector field in
${\mathbb R}^3$ in terms of the operator norm of an associated paracommutator.
The latter is essentially a $\Psi$DO, whose symbol depends linearly on the
vector field. Together with the result of P.~Auscher and M.~Taylor concerning
the converse estimate, this provides an equivalent norm in the space of
divergence-free fields from BMO.
