What $e^+e^-$ collider could make a ``no-lose'' search for MSSM Higgs bosons?

The lightest CP-even Higgs boson $h$ in the minimum supersymmetric standard model (MSSM) has a mass upper bound depending on the top quark and squark masses. An $e^+e^-$ collider with enough energy and luminosity to produce $h+Z$ at measurable rates up to the maximum $h$ mass would cover the entire MSSM parameter space, if $h+A$ production was also searched for. We explore the energy and/or luminosity needed for various top quark and squark masses. For $m_t=150$\,GeV and 1\,TeV SUSY mass scale, a 230\,GeV collider with 10\,fb$^{-1}$ luminosity would suffice.