  We calculate the masses of the low-lying states with quantum numbers
$J^{PC}=0^{++},1^{--}$ in the Higgs and confinement regions of the
three-dimensional SU(2) Higgs model, which plays an important r\^ole in the
description of the thermodynamic properties of the standard model at finite
temperatures. We extract the masses from correlation functions of
gauge-invariant operators which are calculated by means of a lattice Monte
Carlo simulation. The projection properties of our lattice operators onto the
lowest states are greatly improved by the use of smearing techniques. We also
consider cross correlations between various operators with the same quantum
numbers. From these the mass eigenstates are determined by means of a
variational calculation. In the symmetric phase, we find that some of the
ground state masses are about 30\% lighter than those reported from previous
simulations. We also obtain the masses of the first few excited states in the
symmetric phase. Remarkable among these is the occurrence of a $0^{++}$ state
composed almost entirely of gauge degrees of freedom. The mass of this state,
as well as that of its first excitations, is nearly identical to the
corresponding glueball states in three-dimensional SU(2) pure gauge theory,
indicating an approximate decoupling of the pure gauge sector from the Higgs
sector of the model. We perform a detailed study of finite size effects and
extrapolate the lattice mass spectrum to the continuum.
