While Aston Martin has never left any of its models wanting in the looks department, its cars’ performance figures—even for the range-topping models—always seem one step behind those of the competition. In an effort to keep pace with the likes of Mercedes-Benz, Porsche, and even Ferrari, Aston Martin is making some very astute changes to the Vanquish (both coupe and Volante) and Rapide S for 2015.

Many of these improvements are derived from an all-new Touchtronic III 8-speed automatic gearbox, which is desi…