  We analyze rare kaon decays in models in which the dominant new effect is an
enhanced sbar d Z vertex Z_{ds}. We point out that in spite of large
theoretical uncertainties the CP-violating ratio epsilon'/epsilon provides at
present the strongest constraint on Im Z_{ds}. Assuming 1.5 10^{-3} <
epsilon'/epsilon < 3 10^{-3} and Standard Model values for the CKM parameters
we obtain the bounds BR(K_L -> pi^0 nu nubar) < 3.9 10^{-10} and BR(K_L -> pi^0
e^+ e^-)_{dir} < 7.9 10^{-11}. Using the bound on Re Z_{ds} from K_L -> mu^+
mu^- we find BR(K^+ -> pi^+ nu nubar) < 2.6 10^{-10}. We also discuss new
physics scenarios in which in addition to an enhanced sbar d Z vertex also
neutral meson mixing receives important new contributions. In this case our
most conservative bounds are BR(K_L -> pi^0 nu nubar) < 1.8 10^{-9}, BR(K_L ->
pi^0 e^+ e^-)_{dir} < 2.8 10^{-10} and BR(K^+ -> pi^+ nu nubar) < 6.1 10^{-10}.
The dependence of the upper bound for BR(K_L -> pi^0 nu nubar) on the CKM
parameters is also analyzed.
