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We quantify the extent to which naturalness is lost as experimental lowerbounds on the Higgs boson mass increase, and we compute the natural upper boundon the lightest supersymmetric Higgs boson mass. We find that it would beunnatural for the mass of the lightest supersymmetric Higgs boson to saturateit's maximal upper bound. In the absence of significant fine-tuning, thelightest Higgs boson mass should lie below $120$ GeV, and in the most naturalcases it should be lighter than $108$ GeV. For modest $tan \beta$, these boundsare significantly lower. Our results imply that a failure to observe a lightHiggs boson in pre-LHC experiments could provide a serious challenge to theprincipal motivation for weak-scale supersymmetry.Comment: 11 pages, LaTex, 3 ps.figure

Naturalness lowers the upper bound on the lightest Higgs boson mass in supersymmetry