A W--dressed Electroweak String

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.