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The optimal control of hybrid powertrains represents one of the most challenging tasks for the compliance with the legislation concerning CO2 and pollutant emission of vehicles. Most common off-line optimization strategies (Pontryagin minimum principle - PMP - or dynamic programming) allow to identify the optimal control along a predefined driving mission at the expense of a quite relevant computational effort. On-line strategies, suitable for on-vehicle implementation, involve a certain performance degradation depending on their degree of simplification and computational effort. In this work, a simplified control strategy is presented, where the conventional power-split logics, typical of the above-mentioned strategies, is here replaced with an alternative utilization of the thermal and electric units for the vehicle driving (Efficient Thermal Electric Skipping Strategy - ETESS).