Implications of supersymmetry phases for Higgs boson signals and limits

We study the supersymmetry parameter region excluded if no Higgs is found at LEP, and the region allowed if a Higgs boson is found at LEP. We describe the full seven parameter structure of the Higgs sector. When supersymmetry phases are included, tanβ≳2 is always allowed, and the lower limit on MH1 if no signal is found is about 20% lower than in the Standard Model and about 10% lower than in the MSSM with phases set to 0, π.