In this paper, we compute the number of covers of curves with given branch behavior in characteristic p for one class of examples with four branch points and degree p. Our techniques involve related computations in the case of three branch points, an
d allow us to conclude in many cases that for a particular choice of degeneration, all the covers we consider degenerate to separable (admissible) covers. Starting from a good understanding of the complex case, the proof is centered on the theory of stable reduction of Galois covers.
