  In this paper we study the reduction of $p$-cyclic covers of the $p$-adic
line ramified at exactly four points. For $p=2$ these covers are elliptic
curves and Deuring has given a criterion for when such a curve has good
reduction. Here we consider the case of $p>2$ and completely determine the
stable model of the cover. In particular we obtain a finite extension $R'$ of
$R$ necessary for the stable reduction to be defined. No additional conditions
are imposed on the geometry of the branch locus and thus this work can be
viewed as a first step towards understanding the situation where branch points
coalesce.
