  We consider the inverse Galois problem over function fields of positive
characteristic p, for example, the inverse Galois problem over the projective
line. We describe a method to construct certain Galois covers of the projective
line and other curves, which are ordinary in the sense that their Jacobian has
maximal p-torsion. We do this by constructing Galois covers of ordinary
semi-stable curves, and then deforming them into smooth Galois covers.
