  We map the parameter space that leads to stable Z-vortices in the electroweak
model. For $sin^2 \theta_W = 0.23$, we find that the strings are unstable for a
Higgs mass larger than 24 GeV. Given the latest constraints on the Higgs mass
from LEP, this shows that, if the standard electroweak model is realized in
Nature, the Z-vortex (in the bare model) is unstable.
