Supersymmetric origin of a low a_(J/psi) CP asymmetry

We show that general Minimal Supersymmetric extensions of the Standard Model (MSSM) allow for a CP asymmetry in B --> J/psi K(S) well bellow the SM expectations with dominant Supersymmetric contributions to epsilon_K and epsilon'/epsilon. Indeed, we provide an explicit example of an MSSM with non-universal soft breaking terms fully consistent with the low results of this asymmetry recently announced by Babar and Belle collaborations.