The extremization of an appropriate entropic functional may yield to the probability distribution functions maximizing the respective entropic structure. This procedure is known in Statistical Mechanics and Information Theory as Jaynes' Formalism and has been up to now a standard methodology for deriving the aforementioned distributions. However, the results of this formalism do not always coincide with the ones obtained following different approaches. In this study we analyse these inconsistencies in detail and demonstrate that Jaynes' formalism leads to correct results only for specific entropy definitions. (C) 2009 Elsevier Ltd. All rights reserved.