  We study maximal stretch laminations associated to certain best Lipschitz
circle valued maps in Dehn surgery families of hyperbolic 3-manifolds. For
these maps, we give a criterion based on the Thurston norm and Dehn filling
slope length to determine when such a stretch lamination is a union of Dehn
filling core curves. We use this to show there exist infinitely many examples
where the homotopy class of the circle valued map includes a fibration and
where the laminations have only closed leaves. This gives information about
non-maximal horospherical orbit closures in the infinite cyclic covers
associated to these fibrations.
