  The problem of constructing the $q=1/2$ non-extensive maximum entropy
distributions from redundant and noisy data is considered. A strategy is
proposed, which evolves through the following steps: i)independent constraints
are first pre-selected by recourse to a data-independent technique to be
discussed here. ii)the data are a posteriori used to determine the parameters
of the distribution by a previously introduced forward approach. iii) A
backward approach is proposed for reducing the parameters of such distribution.
The previously introduced forward approach is generalised here in order to make
it suitable for dealing with very noisy data.
