The design of the volute (in terms of area distribution and shape of the cross section) has a relevant impact on the efficiency and the operating range of a centrifugal compressor. This latter aspect is even more relevant in turbochargers, where the compressor has to cover a functioning range much wider than that of industrial applications. In addition, beyond conventional aerodynamic requirements, the design of the cross section shape is driven often in these applications also by space constraints imposed by the vehicle layout, leading to a variety of volute layouts. In a previous study, some of the authors highlighted the prospects of using the entropy generation rate to evaluate the losses within a volute, since this parameter allows an exact localization of irreversibilities. Starting from these results, the present study shows the suitability of this parameter as an indicator for the fine design optimization of the volute shape. A methodology is presented, which, based on the CFD computed contours of both the entropy generation rate and the total pressure, is able to drive the fine optimization of the volute cross-section at different azimuthal positions in order to maximize its efficiency. Multiple volute shapes are analysed in the paper and the effect of the operating conditions is accounted for by investigating different mass flow rates. The proposed approach indeed lead to a maximization of the volute efficiency with only a few trials and it could indeed provide room for future automatized fine optimization strategies.