We analyze the CP violating ratio ε ′ /ε and rare K and B decays in the MSSM with minimal flavour and CP violation, including NLO QCD corrections and imposing constraints on the supersymmetric parameters coming from ε, B 0 d,s −B 0 d,s mixings, B → X s γ, ∆̺ in the electroweak precision studies and from the lower bound on the neutral Higgs mass. We provide a compendium of phenomenologically relevant formulae in the MSSM. Denoting by T (Q) the MSSM prediction for a given quantity normalized to the Standard Model result we find the ranges: 0.53We point out that these ranges will be considerably reduced when the lower bounds on the neutral Higgs mass and tan β improve. Some contour plots illustrate the dependences of the quantities above on the relevant supersymmetric parameters. As a byproduct of this work we update our previous analysis of ε ′ /ε in the SM and find in NDR ε ′ /ε = (9.2 +6.8 −4.0 ), a value 15% higher than in our 1999 analysis.