  In the nonparametric Gaussian sequence space model an $\ell^2$-confidence
ball $C_n$ is constructed that adapts to unknown smoothness and Sobolev-norm of
the infinite-dimensional parameter to be estimated. The confidence ball has
exact and honest asymptotic coverage over appropriately defined `self-similar'
parameter spaces. It is shown by information-theoretic methods that this
`self-similarity' condition is weakest possible.
