An approach adopted to consider the problem of constructing the q=1/2 maximum entropy distribution from redundant and noisy data was discussed. The advantage of this generalized approach, when dealing with very noisy data was illustrated by a numerical simulation. A strategy was proposed that evolved through different steps such as independent constraints were first preselected by recourse to a data independent technique. A backward approach was also proposed for reducing the parameters of such distributions. It was found that the sub-optimal strategies could be utilized in a broad range of situations.