  We apply dimensional reduction to the finite temperature U(1)+Higgs theory
and study the properties of the reduced 3-dimensional theory in the broken
phase using lattice Monte Carlo simulations. We compute analytically the scalar
condensate in optimized 2-loop perturbation theory and the correlators in
1-loop perturbation theory. These quantities are also calculated numerically.
The two results for the condensate agree well but a 25\% difference is observed
for the scalar correlator, indicating the need for optimized 2-loop
perturbative results.
