  Suppose that kappa is a singular cardinal of cofinality omega and GCH holds.
Assume that for every n<omega the set of alphas with o(alpha)>= alpha^{+n} is
unbounded in kappa.Then there is a cardinal preserving extension satisfying
2^kappa=kappa^++ and GCH below kappa.
  By a result of W. Mitchell and the author the assumptions are optimal.
