  This paper deals with the problem of function estimation. Using the white
noise model setting, we provide a method to construct a new wavelet procedure
based on thresholding rules which takes advantage of the dyadic structure of
the wavelet decomposition. We prove that this new procedure performs very well
since, on the one hand, it is adaptive and near-minimax over a large class of
Besov spaces and, on the other hand, the maximal functional space (maxiset)
where this procedure attains a given rate of convergence is very large. More
than this, by studying the shape of its maxiset, we prove that the new
procedure outperforms the hard thresholding procedure.
