  The Higgs SU(2) model with fixed Higgs length is usually believed to have two
different phases at high gauge coupling (\beta), separated by a line of first
order transitions but not distinuguished by any typical symmetry associated
with a local order parameter, as first proved by Fradkin and Shenker. We show
that in regions of the parameter space where it is usually supposed to be a
first order phase transition only a smooth crossover is in fact present.
