  For analytic functions in the unit disk, general bounds on the Schwarzian
derivative in terms of Nehari functions are shown to imply uniform local
univalence and in some cases finite and bounded valence. Similar results are
obtained for the Weierstrass--Enneper lifts of planar harmonic mappings to
their associated minimal surfaces. Finally certain classes of harmonic mappings
are shown to have finite Schwarzian norm.
