  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.
