  The non-minimal flavour violating interactions of mirror quarks and new heavy
gauge bosons in the Littlest Higgs model with T-parity (LHT) give rise to
naturally large CP-violating effects in the B_s system. In view of a large new
CP phase in B_s - anti-B_s mixing hinted by the CDF and D0 data and the recent
UTfit analysis, we update our 2006 analysis of particle-antiparticle mixing and
rare K and B decays in the LHT model, using the most recent values of a number
of input parameters and performing a more careful error analysis. We find that
the CP-asymmetry S_{psi phi} can easily reach values ~ 0.15-0.20, compared to
the SM value ~ 0.04, while higher values are rather unlikely though not
excluded. Large enhancements are also possible in the branching ratios for K_L
-> pi0 nu anti-nu, K+ -> pi+ nu anti-nu and K_L -> pi0 l+ l- with much more
modest effects in B_{s,d} -> mu+ mu-. We perform a detailed study of
correlations between the latter decays and S_{psi phi} as well as of the
correlation between S_{psi phi} and S_{psi K_S}. We also point out that the
possible tension between epsilon_K and the tree level CKM determination
recently hinted by various analyses can easily be resolved in the LHT model.
