  The phase structure of the 3D SU(2)--Higgs model, the dimensionally reduced
effective theory for the electroweak model at finite temperature, is analysed
on the lattice using a variant of the linear $\de$--expansion. We develop a
systematic variational cumulant expansion for general application to the study
of gauge invariant operators in 3D gauge-Higgs models, with emphasis on the
symmetric phase. In particular, the technique is not restricted to finite
lattice volumes, and application to the fundamental 3D SU(2)--Higgs model
allows the discontinuity of certain observables across the first--order
transition to be observed directly for small 4D Higgs masses. The resulting
phase structure agrees well with Monte Carlo simulations for small Higgs
masses, but, at least to the order calculated, the technique is less sensitive
to the expected evolution of the transition to a crossover for Higgs masses
above 80 GeV.
