  We point out that the observed CP violation in Bd - bar{Bd} mixing, taking
into account the measured ratio Delta Md / Delta Ms, the recently improved
lattice value of the non-perturbative parameter BK and an additional effective
suppression factor kappa_epsilon ~= 0.92 in epsilon_K neglected sofar in most
analyses, may be insufficient to describe the measured value of epsilon_K
within the Standard Model (SM), thus hinting at new CP violating contributions
to the K - bar{K} and/or Bd - bar{Bd} systems. Furthermore, assuming that Delta
Md / Delta Ms is SM-like, the signs and the magnitudes of new physics effects
in epsilon_K and in the CP asymmetries S_{psi Ks} and S_{psi phi} may turn out
to be correlated. For example, in a scenario with new CP-phases in Bd and Bs
mixings being approximately equal and negative, a common new phase ~= - 5
degrees could remove the tension between epsilon_K and S_{psi Ks} present in
the SM and simultaneously accommodate, at least partly, the recent claim of
S_{psi phi} being much larger than the SM expectation. We emphasize the
importance of precise determinations of Vcb, BK, FK and xi_s, to which the
parameter epsilon_K and its correlation with the CP violation in the Bd -
bar{Bd} system are very sensitive.
