  In a recent paper, McMullen showed an inequality between the Thurston norm
and the Alexander norm of a 3-manifold. This generalizes the well-known fact
that twice the genus of a knot is bounded from below by the degree of the
Alexander polynomial.
  We extend the Bennequin inequality for links to an inequality for all points
of the Thurston norm, if the manifold is a link complement. We compare these
two inequalities on two classes of closed braids.
  In an additional section we discuss a conjectured inequality due to Morton
for certain points of the Thurston norm. We prove Morton's conjecture for
closed 3-braids.
