The energy efficiency in metal cutting is, sometimes, very low. Recent studies show that the energy consumed for detaching chips represents only about 15% of the total energy involved in material machining. The available solutions for energy optimization in cutting processes mentioned are the improvement of manufacturing equipment, the optimization of processes, and appropriate production scheduling. Already-performed research shows that to increase energy efficiency, the cutting force must be reduced, for example, by reducing the depth of the cut and by increasing the feed rate. However, this is applicable when the cutting force is quasi-constant during the process, which is not the case for gear teeth cutting when the cutting force significantly varies. The present paper proposes a new solution for energy efficiency increase in gear teeth cutting, namely, the smoothing of the cutting force variation during the machining process, by keeping the area of the detached chip section quasi-constant during the cutting process. This can be reached by replacing the constant rolling feed, currently used in gear teeth cutting, with a rolling feed that varies after an appropriate law. An algorithm dedicated to implementing this solution has been developed. It uses graphical modeling in CATIA to find the variation in the detached chip area. Original MatLab R2018a applications were developed (i) to identify the analytical form of the law that approximates this variation and (ii) to find the variation law of the feed during the rolling motion, if imposing a constant area of the detached chip. The algorithm was successfully applied in the cases of toothing with a rack tool (by slotting) and with a pinion cutter (by slotting and turning). A technical solution for method implementation in practice is also presented.