  In the infrared fixed point (IFP) scenario of the minimal supersymmetric
model (MSSM), the top-quark mass and other physical quantities of the
low-energy theory are insensitive to the values of the parameters of the theory
at some high energy scale. In this framework we evaluate the light CP-even
Higgs mass, $m_h$, taking into account some important effects that had not been
previously considered. In particular, the supersymmetric correction to the
relation between the running and the physical top-quark masses lowers the value
of $\tan\beta$, thereby implying a lower predicted value of $m_h$. Assuming a
supersymmetric threshold of $M_S\leq 1$ TeV and $M_t=175$ GeV, we find an upper
bound of $m_h\le 97\pm 2$ GeV; the most plausible value of $m_h$ lies somewhat
below the upper bound. This places the Higgs boson in the IFP scenario well
within the reach of the LEP-2 Higgs search.
