  Vortex configurations in the electroweak gauge theory are investigated. Two
gauge-inequivalent solutions of the field equations, the Z and W vortices, have
previously been found. They correspond to embeddings of the abelian
Nielsen-Olesen vortex solution into a U(1) subgroup of SU(2)xU(1). It is shown
here that any electroweak vortex solution can be mapped into a solution of the
same energy with a vanishing upper component of the Higgs field. The
correspondence is a gauge equivalence for all vortex solutions except those for
which the winding numbers of the upper and lower Higgs components add to zero.
This class of solutions, which includes the W vortex, instead corresponds to a
singular solution in the one-component gauge. The results, combined with
numerical investigations, provide an argument against the existence of other
vortex solutions in the gauge-Higgs sector of the Standard Model.
