  We analyze the rare kaon decays $K_L \to \pi^0 \nu \bar \nu$, $K^+ \to \pi^+
\nu \bar \nu$, $K_L \to \pi^0 e^+ e^-$ and $K_L \to \mu^+ \mu^-$ in conjunction
with the CP violating ratio $\epsilon'/\epsilon$ in a general class of
supersymmetric models in which $Z$- and magnetic-penguin contributions can be
substantially larger than in the Standard Model. We point out that radiative
effects relate the double left-right mass insertion to the single left-left
one, and that the phenomenological constraints on the latter reflect into a
stringent bound on the supersymmetric contribution to the $Z$ penguin. Using
this bound, and those coming from recent data on $\epsilon'/\epsilon$ we find
${\rm BR}(K_L \to \pi^0 \nu \bar \nu)\lsim 1.2\cdot 10^{-10}$, ${\rm BR}(K^+
\to \pi^+ \nu \bar \nu)\lsim 1.7\cdot 10^{-10}$, ${\rm BR}(K_L \to \pi^0 e^+
e^-)_{\rm dir}\lsim 2.0\cdot 10^{-11}$, assuming the usual determination of the
CKM parameters and neglecting the possibility of cancellations among different
supersymmetric effects in $\epsilon'/\epsilon$. Larger values are possible, in
principle, but rather unlikely. We stress the importance of a measurement of
these three branching ratios, together with improved data and improved theory
of $\epsilon'/\epsilon$, in order to shed light on the realization of various
supersymmetric scenarios. We reemphasize that the most natural enhancement of
$\epsilon'/\epsilon$, within supersymmetric models, comes from chromomagnetic
penguins and show that in this case sizable enhancements of $BR(K_L \to \pi^0
e^+ e^-)_{\rm dir}$ can also be expected.
