  Let K be a complete field of unequal characteristics $(0,p)$. The aim of this
paper is to describe the the semi-stable models for covers $\bold
P^1_K@>>>\bold P^1_K$ of degree p, unramified outside $r\leq p$ points and
totally ramified above one of them, under the assumption that the ramified
locus has a particular reduction type (which always occurs if $r\leq4$). We are
principally concerned with the minimal semi-stable models which separate the
ramified fibers.
