  The question of smoothness at the ergosurface of the space-time metric
constructed out of solutions (E,phi) of the Ernst electro-vacuum equations is
considered. We prove smoothness of those ergosurfaces at which Re(E) provides
the dominant contribution to f=-(Re(E)+|phi|^2) at the zero-level-set of f.
Some partial results are obtained in the remaining cases: in particular we give
examples of leading-order solutions with singular isolated "ergocircles".
