  The Coulomb-Higgs phase transition of the four dimensional Z$_8$ gauge model
is studied. We find clear first order properties in contradiction with the
previously stressed second order behavior. That transition point may be
regarded as the end of a transition line of the U(1)-Higgs model with charge
$q=8$, that has been also assumed of second order. We show that this line is
first order in a wide region, with a decreasing latent heat that goes to zero
when closing to the 4--$d$ XY model limit.
