This paper presents a novel method which can be helpful in assessing the optimal configuration of finned-tube heat exchangers. The method is an extension of the local irreversibilities method [17], and it is based on the determination on a local basis of the two components of the entropy generation rate: the one caused by viscous dissipations and the one due to thermal irreversibilities. Depending on the engineering purpose for which a technical device was designed, it can be argued that the optimal configuration will be that in which either one (or both) of these two entropy generation rates is minimized. For a heat exchanging device, it is important to minimize thermal irreversibilities, but more important is to minimize the mechanical power lost in achieving a prescribed heat-exchange performance: to this purpose, one can form a relative irreversibility index (named Bejan number here and in [17] because the original seed of this procedure can be found in [1]), and use it to assess the merit of a given configuration.In the procedure presented here, a circular, single-tube, finned heat exchanger configuration is considered: the velocity and temperature fields are computed (via a standard finite-element package, FIDAP) for a realistic value of the Reynolds number and for a variety of geometric configurations (various fin external diameters and fin spacing); then, the entropy generation rate is calculated from the flowfield, and is examined both at a local level, to detect possible bad design spots (ie, locations which correspond to abnormally high entropy generation rates, which could be cured by design improvements), and at an overall (integral) level, to assess the entropic performance of the heat exchanger. Optimal curves are given, and the optimal spacing of fins is determined using alternatively the entropy generation rate and the total heat transfer rate as objective functions: different optima arise, and the differences as well as the similarities are discussed in detail.