  We give plausibility arguments for the existence of a $W$--dressed
electroweak string for the \ws ~model with $\th_W = 0$. This string is a
$Z$--string which in the core has a finite energy contribution from
$W$--condensation induced by the anomalous magnetic moment in the \ym field.
The solution which has minimum energy at $r=0$ interpolates between the
unbroken $(r=0)$ and the broken $(r \ra \infty) \ SU(2) \times U_y(1)$ phase.
