  SU(2) lattice gauge theory is studied after eliminating thin monopoles and
the smallest thick monopoles. Kinematically this constraint allows thick vortex
loops which produce long range Z(2) fluctuations. The thick vortex loops are
identified in a three dimensional simulation. A condensate of thick vortices
persists even after the thin vortices have all disappeared. They decouple at a
slightly lower temperature (higher $\beta$) than the thin vortices and drive a
Z(2) like phase transition.
