  We investigate a model of a U(1)-Higgs theory on the lattice with compact
gauge fields but completely suppressed (elementary) monopoles. We study the
model at two values of the quartic Higgs self-coupling, a strong coupling,
$\lambda = 3.0$, and a weak coupling, $\lambda=0.01$. We map out the phase
diagrams and find that the monopole suppression eliminated the confined phase
of the standard lattice model at strong gauge coupling. We perform a detailed
analysis of the static potential and study the mass spectrum in the Coulomb and
Higgs phases for three values of the gauge coupling. We also probe the
existence of a scalar bosonium to the extent that our data allow and conclude
that further investigations are required in the Coulomb phase.
