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, and 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.