  We reanalyze the rare decays K^+ -> pi^+ nu nu-bar and K_L -> pi^0 nu nu-bar
in a general MSSM with conserved R-parity. Working in the mass eigenstate basis
and performing adaptive scanning of a large space of supersymmetric parameters,
16 parameters in the constrained scan and 63 in the extended scan, we find that
large departures from the Standard Model expectations are possible while
satisfying all existing constraints. Both branching ratios can be as large as a
few times 10^{-10} with Br(K_L -> pi^0 nu nu-bar) often larger than Br(K^+ ->
pi^+ nu nu-bar) and close to its model independent upper bound. We give
examples of supersymmetric parameters for which large departures from the SM
expectations can be found and emphasize that the present 90% C.L. experimental
upper bound on Br(K^+ -> pi^+ nu nu-bar) gives a non trivial constraint on the
MSSM parameter space. Unlike previous analyses, we find that chargino box
diagrams can give, already for moderately light charged sleptons, a significant
contribution. As a byproduct we find that the ranges for the angles beta and
gamma in the unitarity triangle are relaxed due to the presence of new
CP-violating phases in K^0 - K^0-bar and B^0_d - B^0_d-bar mixing to 12 degrees
<= beta <= 27 degrees and 20 degrees <= gamma <= 110 degrees.
