  We estimate the mass of the lightest neutral Higgs boson h in the minimal
supersymmetric extension of the Standard Model with universal soft
supersymmetry-breaking masses (CMSSM), subject to the available accelerator and
astrophysical constraints. For m_t = 174.3 GeV, we find that 114 GeV < m_h <
127 GeV and a peak in the tan beta distribution simeq 55. We observe two
distinct peaks in the distribution of m_h values, corresponding to two
different regions of the CMSSM parameter space. Values of m_h < 119 GeV
correspond to small values of the gaugino mass m_{1/2} and the soft trilinear
supersymmetry-breaking parameter A_0, lying along coannihilation strips, and
most of the allowed parameter sets are consistent with a supersymmetric
interpretation of the possibly discrepancy in g_mu - 2. On the other hand,
values of m_h > 119 GeV may correspond to much larger values of m_{1/2} and
A_0, lying in rapid-annihilation funnels. The favoured ranges of m_h vary with
m_t, the two peaks being more clearly separated for m_t = 178 GeV and merging
for m_t = 172.7 GeV. If the g_mu - 2 constraint is imposed, the mode of the m_h
distribution is quite stable, being sim 117 GeV for all the studied values of
m_t.
