  The non-orientable 4-genus of a knot in the 3-sphere is defined as the
smallest first Betti number of any non-orientable surface smoothly and properly
embedded in the 4-ball, with boundary the given knot. We compute the
non-orientable 4-genus for all knots with crossing number 8 or 9. As
applications we prove a conjecture of Murakami's and Yasuhara's, and give a new
lower bound for the slicing number of knot.
