  We show pathwise uniqueness for a class of degenerate It\^{o}-SDE among all
of its weak solutions that spend zero time at the points of degeneracy of the
dispersion matrix. Consequently, by the Yamada-Watanabe Theorem and a weak
existence result, the pathwise unique solutions can be shown to be strong and
to exist. The main tools to show pathwise uniqueness are inequalities
associated with maximal functions and a Krylov type estimate derived from
elliptic regularity and uniqueness in law.
