Super Gaussian (SG) distributions have proven to be very powerful prior models to induce sparsity in Bayesian Blind Deconvolution (BD) problems. Their conjugate based representations make them specially attractive when Variational Bayes (VB) inference is used since their variational parameters can be calculated in closed form with the sole knowledge of the energy function of the prior model. In this work we show how the introduction in the SG distribution of a global strength (not necessary scale) parameter can be used to improve the quality of the obtained restorations as well as to introduce additional information on the global weight of the prior. A model to estimate the new unknown parameter within the Bayesian framework is provided. Experimental results, on both synthetic and real images, demonstrate the effectiveness of the proposed approach.