  We study the implications of the absence of a direct discovery of a Higgs
boson at LEP. First we exhibit 15 physically different ways in which one or
more Higgs bosons lighter than the LEP limit could still exist. In the minimal
supersymmetric standard model (MSSM) all of these, as well as the cases where
the Higgs mass equals or exceeds 115 GeV, seem fine-tuned. We examine some
interpretations of the fine tuning in high scale theories. The least fine-tuned
MSSM outcome will have a Higgs mass at 115 GeV, while approaches that extend
the MSSM at the weak scale can naturally have larger Higgs masses.
