  For sutured 3-manifolds M, there is a sutured Thurston norm due to
Scharlemann. We show how depth one foliations of M and corresponding fibrations
and the usual Thurston norm on the double of M are useful tools for computing
this norm. In many examples, the faces of the unit ball of the sutured norm are
related to cones of depth one foliations of M but examples indicate this is not
a general relationship.
