In this work, a tube with internal helical fins is analyzed and optimized from an entropy generation point of view. Helical fins, in addition to providing heat transfer enhancements, have the potential to level the temperature of the tube under nonuniform circumferential heating. In this work, the geometric parameters of internal helical fins are optimized under two different entropy-based formulations. Specifically, the optimal design solution obtained through the minimization of total entropy is compared with the solutions from the multiobjective optimization of the thermal and viscous entropy contributions when considered as two separate objectives. The latter quantities being associated with heat transfer and pressure drops, it is shown that, from a design optimization point of view, it is important to separate both entropies which are conflicting objectives.