An axially hyperstatic system softener for a transmission comprising a static component and a rotatable component mounted to each other by a double ball bearing having an outer race and an inner race includes first and second biasing elements in a rigid sleeve with the outer race disposed between the first and second biasing elements. The rotatable component includes two shafts splined together with the static component mounted to one of the shafts by the bearing double ball bearing. A shim between one of the biasing elements and the sleeve enables tuning the softener.