  After presenting a simple procedure for testing naturalness (similar to
Bayesian inference and not more subjective than it) we show that LEP2
experiments pose a naturalness problem for `conventional' supersymmetric
models. About 95% of the parameter space of minimal supergravity MSSM is
excluded by LEP2 experiments. Moreover in this model electroweak baryogenesis,
or detectable supersymmetric corrections to mixing of K and B mesons, are
possible only in very small corners of the parameter space. The naturalness
problem is stronger in gauge mediation models, expecially with light
messengers. We recall some possible explanations (different from an improbable
numerical accident) of why supersymmetry has not (yet?) been found.
